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2014-01-13 | On List-decodability of Random Rank Metric Codes | In the present paper, we consider list decoding for both random rank metric
codes and random linear rank metric codes. Firstly, we show that, for arbitrary
$0<R<1$ and $\epsilon>0$ ($\epsilon$ and $R$ are independent), if
$0<\frac{n}{m}\leq \epsilon$, then with high probability a random rank metric
code in $F_{q}^{m\times n}$ of rate $R$ can be list-decoded up to a fraction
$(1-R-\epsilon)$ of rank errors with constant list size $L$ satisfying $L\leq
O(1/\epsilon)$. Moreover, if $\frac{n}{m}\geq\Theta_R(\epsilon)$, any rank
metric code in $F_{q}^{m\times n}$ with rate $R$ and decoding radius
$\rho=1-R-\epsilon$ can not be list decoded in ${\rm poly}(n)$ time. Secondly,
we show that if $\frac{n}{m}$ tends to a constant $b\leq 1$, then every
$F_q$-linear rank metric code in $F_{q}^{m\times n}$ with rate $R$ and list
decoding radius $\rho$ satisfies the Gilbert-Varsharmov bound, i.e., $R\leq
(1-\rho)(1-b\rho)$. Furthermore, for arbitrary $\epsilon>0$ and any $0<\rho<1$,
with high probability a random $F_q$-linear rank metric codes with rate
$R=(1-\rho)(1-b\rho)-\epsilon$ can be list decoded up to a fraction $\rho$ of
rank errors with constant list size $L$ satisfying $L\leq O(\exp(1/\epsilon))$. | 1401.2693v2 |
2003-03-13 | Vibrational sidebands and dissipative tunneling in molecular transistors | Transport through molecular devices with strong coupling to a single
vibrational mode is considered in the case where the vibration is damped by
coupling to the environment. We focus on the weak tunneling limit, for which a
rate equation approach is valid. The role of the environment can be
characterized by a frictional damping term $\mysig(\omega)$ and corresponding
frequency shift. We consider a molecule that is attached to a substrate,
leading to frequency-dependent frictional damping of the single oscillator mode
of the molecule, and compare it to a reference model with frequency-independent
damping featuring a constant quality factor $Q$. For large values of $Q$, the
transport is governed by tunneling between displaced oscillator states giving
rise to the well-known series of the Frank-Condon steps, while at small $Q$,
there is a crossover to the classical regime with an energy gap given by the
classical displacement energy. Using realistic values for the elastic
properties of the substrate and the size of the molecule, we calculate $I$-$V$
curves and find qualitative agreement between our theory and recent experiments
on $C_{60}$ single-molecule devices. | 0303236v3 |
2001-01-16 | Nonlinear Landau damping of a plasmino in the quark-gluon plasma | On the basis of the Blaizot-Iancu equations, which are a local formulation of
the hard thermal loop (HTL) equations of motion for soft fluctuating quark and
gluon fields and their induced sources, the coupled kinetic equations for
plasminos and plasmons are obtained. The equality of matrix elements for
nonlinear scattering of a plasmino by hard particles in covariant and temporal
gauges is established by using effective Ward identities. The model problem of
the interaction of two infinitely narrow packets with fermion and boson quantum
numbers is considered. The kinematical relations between wave vectors of the
plasmino and plasmon are derived, when the effective pumping over of the plasma
excitation energy from the fermion branch of plasma excitations to the boson
branch and vice versa occur. The expression for the nonlinear Landau damping
rate of a plasmino at rest is found, and a comparison with a plasmino damping
constant obtained within the framework of the hard thermal loop approximation
is made. The nonlinear Landau damping rate for normal quark excitations is
shown to diverge like $1/\sqrt{q^2}$ near the light cone where $q$ is a
four-momentum of excitations, and the improved Blaizot-Iancu equations removing
this divergence are proposed. | 0101167v2 |
2005-10-21 | Non-contact atomic force microscopy: Stability criterion and dynamical responses of the shift of frequency and damping signal | The aim of this article is to provide a complete analysis of the behavior of
a noncontact atomic force microscope (NC-AFM). We start with a review of the
equations of motion of a tip interacting with a surface in which the stability
conditions are first revisited for tapping mode. Adding the equations of
automatic gain control (AGC), which insures constant amplitude of the
oscillations in the NC-AFM, to the equations of motion of the tip, a new
analytical stability criterion that involves proportional and integral gains of
AGC is deduced. Stationary solutions for the shift of frequency and for the
damping signal are obtained. Special attention is paid to the damping signal in
order to clarify its physical origin. The theoretical results are then compared
to those given by a virtual machine. The virtual machine is a set of equations
solved numerically without any approximation. The virtual machine is of great
help in understanding the dynamical behavior of the NC-AFM as images are
recorded. Transient responses of the shift in frequency and of the damping
signal are discussed in relation to the values of proportional and integral
gains of AGC. | 0510192v1 |
2008-06-09 | Relaxation Time and Relaxation Function of Quark-Gluon Plasma with Lattice QCD | We propose a method which enables a QCD-based calculation of a relaxation
time for a dissipative current in the causal and dissipative hydrodynamic
equation derived by Israel and Stewart. We point out that the Israel-Stewart
equation is not unique as a causal and dissipative hydrodynamic equation, and
the form of the causal and dissipative hydrodynamic equation is determined by
the shape of a spectral function reflecting the properties of elementary
excitations in the system we consider. Our method utilizes a relaxation
function, which can be calculated from QCD using the linear response theory. We
show that the relaxation function can be derived from a spectral function for a
microscopic representation of the dissipative current. We also show that the
Israel-Stewart equation is acceptable only as long as the calculated relaxation
function is approximated well by a exponentially damping function, and the
relaxation time can be obtained as its damping time constant. Taking a
baryon-number dissipative current of a plasma consisting of charm quarks and
gluons as a simple example, we present the first calculation of the relaxation
function with use of the spectral function derived employing the quenched
lattice QCD together with the maximum entropy method. The calculated relaxation
function shows a strongly-oscillation damping behaviour due to the charmed
vector hadron $J/\Psi$ surviving above the deconfinement phase transition
temperature in QCD. This result suggests that the applicability of the
Israel-Stewart equation to the baryon-number dissipative current of the charm
quark-gluon plasma is quite doubtful. We present an idea for the improvement of
the Israel-Stewart equation by deriving the hydrodynamic equation consistent
with the strongly-oscillation damping relaxation function. | 0806.1481v1 |
2018-02-18 | On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation | We develop a provably energy stable discontinuous Galerkin spectral element
method (DGSEM) approximation of the perfectly matched layer (PML) for the three
and two space dimensional (3D and 2D) linear acoustic wave equations, in first
order form, subject to well-posed linear boundary conditions. First, using the
well-known complex coordinate stretching, we derive an efficient un-split modal
PML for the 3D acoustic wave equation. Second, we prove asymptotic stability of
the continuous PML by deriving energy estimates in the Laplace space, for the
3D PML in a heterogeneous acoustic medium, assuming piece-wise constant PML
damping. Third, we develop a DGSEM for the wave equation using physically
motivated numerical flux, with penalty weights, which are compatible with all
well-posed, internal and external, boundary conditions. When the PML damping
vanishes, by construction, our choice of penalty parameters yield an upwind
scheme and a discrete energy estimate analogous to the continuous energy
estimate. Fourth, to ensure numerical stability when PML damping is present, it
is necessary to systematically extend the numerical numerical fluxes, and the
inter-element and boundary procedures, to the PML auxiliary differential
equations. This is critical for deriving discrete energy estimates analogous to
the continuous energy estimates. Finally, we propose a procedure to compute PML
damping coefficients such that the PML error converges to zero, at the optimal
convergence rate of the underlying numerical method. Numerical experiments are
presented in 2D and 3D corroborating the theoretical results. | 1802.06388v1 |
2018-11-15 | Damping rate of a fermion in ultradegenerate chiral matter | We compute the damping rate of a fermion propagating in a chiral plasma when
there is an imbalance between the densities of left- and right-handed fermions,
after generalizing the hard thermal loop resummation techniques for these
systems. In the ultradegenerate limit, for very high energies the damping rate
of this external fermion approaches a constant value. Closer to the two Fermi
surfaces, however, we find that the rate depends on both the energy and the
chirality of the fermion, being higher for the predominant chirality. This
comes out as a result of its scattering with the particles of the plasma,
mediated by the exchange of Landau damped photons. In particular, we find that
the chiral imbalance is responsible for a different propagation of the left and
right circular polarised transverse modes of the photon, and that a chiral
fermion interacts differently with these two transverse modes. We argue that
spontaneous radiation of energetic fermions is kinematically forbidden, and
discuss the time regime where our computation is valid. | 1811.06394v3 |
2020-07-19 | Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping | In this paper, the smooth solution of the physical vacuum problem for the one
dimensional compressible Euler equations with time-dependent damping is
considered. Near the vacuum boundary, the sound speed is $C^{1/2}$-H\"{o}lder
continuous. The coefficient of the damping depends on time, given by this form
$\frac{\mu}{(1+t)^\lambda}$, $\lambda$, $\mu>0$, which decays by order
$-\lambda$ in time. Under the assumption that $0<\lambda<1$, $0<\mu$ or
$\lambda=1$, $2<\mu$, we will prove the global existence of smooth solutions
and convergence to the modified Barenblatt solution of the related porous media
equation with time-dependent dissipation and the same total mass when the
initial data of the Euler equations is a small perturbation of that of the
Barenblatt solution. The pointwise convergence rates of the density, velocity
and the expanding rate of the physical vacuum boundary are also given. The
proof is based on space-time weighted energy estimates, elliptic estimates and
Hardy inequality in the Lagrangian coordinates. Our result is an extension of
that in Luo-Zeng [Comm. Pure Appl. Math. 69 (2016), no. 7, 1354-1396], where
the authors considered the physical vacuum free boundary problem of the
compressible Euler equations with constant-coefficient damping. | 2007.14802v2 |
2020-11-16 | Thresholds for loss of Landau damping in longitudinal plane | Landau damping mechanism plays a crucial role in providing single-bunch
stability in LHC, High-Luminosity LHC, other existing as well as previous and
future (like FCC) circular hadron accelerators. In this paper, the thresholds
for the loss of Landau damping (LLD) in the longitudinal plane are derived
analytically using the Lebedev matrix equation (1968) and the concept of the
emerged van Kampen modes (1983). We have found that for the commonly-used
particle distribution functions from a binomial family, the LLD threshold
vanishes in the presence of the constant inductive impedance Im$Z/k$ above
transition energy. Thus, the effect of the cutoff frequency or the resonant
frequency of a broad-band impedance on beam dynamics is studied in detail. The
findings are confirmed by direct numerical solutions of the Lebedev equation as
well as using the Oide-Yokoya method (1990). Moreover, the characteristics,
which are important for beam operation, as the amplitude of residual
oscillations and the damping time after a kick (or injection errors) are
considered both above and below the threshold. Dependence of the threshold on
particle distribution in the longitudinal phase space is also analyzed,
including some special cases with a non-zero threshold for Im$Z/k = const$. All
main results are confirmed by macro-particle simulations and consistent with
available beam measurements in the LHC. | 2011.07985v1 |
2021-11-15 | Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters | A second order accurate, linear numerical method is analyzed for the
Landau-Lifshitz equation with large damping parameters. This equation describes
the dynamics of magnetization, with a non-convexity constraint of unit length
of the magnetization. The numerical method is based on the second-order
backward differentiation formula in time, combined with an implicit treatment
of the linear diffusion term and explicit extrapolation for the nonlinear
terms. Afterward, a projection step is applied to normalize the numerical
solution at a point-wise level. This numerical scheme has shown extensive
advantages in the practical computations for the physical model with large
damping parameters, which comes from the fact that only a linear system with
constant coefficients (independent of both time and the updated magnetization)
needs to be solved at each time step, and has greatly improved the numerical
efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme
has not been available. In this paper, we provide a rigorous error estimate of
the numerical scheme, in the discrete $\ell^{\infty}(0,T; \ell^2) \cap
\ell^2(0,T; H_h^1)$ norm, under suitable regularity assumptions and reasonable
ratio between the time step-size and the spatial mesh-size. In particular, the
projection operation is nonlinear, and a stability estimate for the projection
step turns out to be highly challenging. Such a stability estimate is derived
in details, which will play an essential role in the convergence analysis for
the numerical scheme, if the damping parameter is greater than 3. | 2111.07537v1 |
1991-08-22 | On the Perturbations of String-Theoretic Black Holes | The perturbations of string-theoretic black holes are analyzed by
generalizing the method of Chandrasekhar. Attention is focussed on the case of
the recently considered charged string-theoretic black hole solutions as a
representative example. It is shown that string-intrinsic effects greatly alter
the perturbed motions of the string-theoretic black holes as compared to the
perturbed motions of black hole solutions of the field equations of general
relativity, the consequences of which bear on the questions of the scattering
behavior and the stability of string-theoretic black holes. The explicit forms
of the axial potential barriers surrounding the string-theoretic black hole are
derived. It is demonstrated that one of these, for sufficiently negative values
of the asymptotic value of the dilaton field, will inevitably become negative
in turn, in marked contrast to the potentials surrounding the static black
holes of general relativity. Such potentials may in principle be used in some
cases to obtain approximate constraints on the value of the string coupling
constant. The application of the perturbation analysis to the case of
two-dimensional string-theoretic black holes is discussed. | 9108012v1 |
1992-10-31 | All Or Nothing: On the Small Fluctuations of Two-Dimensional String-Theoretic Black Holes | A comprehensive analysis of small fluctuations about two-dimensional
string-theoretic and string-inspired black holes is presented. It is shown with
specific examples that two-dimensional black holes behave in a radically
different way from all known black holes in four dimensions. For both the
$SL(2,R)/U(1)$ black hole and the two-dimensional black hole coupled to a
massive dilaton with constant field strength, it is shown that there are a {\it
continuous infinity} of solutions to the linearized equations of motion, which
are such that it is impossible to ascertain the classical linear response. It
is further shown that the two-dimensional black hole coupled to a massive,
linear dilaton admits {\it no small fluctuations at all}. We discuss possible
implications of our results for the Callan-Giddings-Harvey-Strominger black
hole. | 9210165v3 |
2005-12-19 | More on the Asymmetric Infinite Square Well: Energy Eigenstates with Zero Curvature | We extend the standard treatment of the asymmetric infinite square well to
include solutions that have zero curvature over part of the well. This type of
solution, both within the specific context of the asymmetric infinite square
well and within the broader context of bound states of arbitrary
piecewise-constant potential energy functions, is not often discussed as part
of quantum mechanics texts at any level. We begin by outlining the general
mathematical condition in one-dimensional time-independent quantum mechanics
for a bound-state wave function to have zero curvature over an extended region
of space and still be a valid wave function. We then briefly review the
standard asymmetric infinite square well solutions, focusing on zero-curvature
solutions as represented by energy eigenstates in position and momentum space. | 0512156v1 |
2007-12-01 | On Precision - Redundancy Relation in the Design of Source Coding Algorithms | We study the effects of finite-precision representation of source's
probabilities on the efficiency of classic source coding algorithms, such as
Shannon, Gilbert-Moore, or arithmetic codes. In particular, we establish the
following simple connection between the redundancy $R$ and the number of bits
$W$ necessary for representation of source's probabilities in computer's memory
($R$ is assumed to be small): \begin{equation*} W \lesssim \eta \log_2
\frac{m}{R}, \end{equation*} where $m$ is the cardinality of the source's
alphabet, and $\eta \leqslant 1$ is an implementation-specific constant. In
case of binary alphabets ($m=2$) we show that there exist codes for which $\eta
= 1/2$, and in $m$-ary case ($m > 2$) we show that there exist codes for which
$\eta = m/(m+1)$. In general case, however (which includes designs relying on
progressive updates of frequency counters), we show that $\eta = 1$. Usefulness
of these results for practical designs of source coding algorithms is also
discussed. | 0712.0057v1 |
2008-04-07 | Energy equilibriation processes of electrons, magnons and phonons on the femtosecond timescale | By means of time-resolved Kerr spectroscopy experiments we relate the energy
dissipation processes on the femtosecond (electron-spin relaxation time
$\tau_{el-sp}$) and nanosecond timescale (Gilbert relaxation $\tau_{\alpha}$)
and compare the results to the first microscopic model, which was proposed by
Koopmans. For both energy dissipation processes, Elliot-Yafet scattering is
proposed as the dominant contributor. We controllably manipulate the energy
dissipation processes by transition metal doping (Pd) and rare earth doping
(Dy) of a Permalloy film and find that while a change of $\tau_{\alpha}$ of
more than a factor two is observed, \tau_{el-sp}$ remains constant, contrary to
the predictions of the model. We explain the discrepancies by relaxation
channels not considered in the original microscopic model and identify thereby
the applicability of the model and possible necessary extensions to the model. | 0804.0985v1 |
2008-07-10 | Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using Ultrafast Coherent Acoustic Phonons | Ultrafast two-color pump-probe measurements, involving coherent acoustic
phonon (CAP) waves, have provided information simultaneously on the mechanical
properties and on the electronic structure of ferromagnetic GaMnAs. The elastic
constant C11 of Ga1-xMnxAs (0.03<x<0.07) are observed to be systematically
smaller than those of GaAs. Both C11 and Vs of GaMnAs are found to increase
with temperature (78 K<T<295 K), again in contrast to the opposite behavior in
GaAs. In addition, the fundamental bandgap (at E0 critical point) of Ga1-xMnxAs
is found to shift slightly to higher energies with Mn concentration. | 0807.1740v2 |
2008-08-26 | Codes on hypergraphs | Codes on hypergraphs are an extension of the well-studied family of codes on
bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes
on regular t-partite hypergraphs whose minimum distance improves earlier
estimates of the distance of bipartite-graph codes. They also suggested a
decoding algorithm for such codes and estimated its error-correcting
capability.
In this paper we study two aspects of hypergraph codes. First, we compute the
weight enumerators of several ensembles of such codes, establishing conditions
under which they attain the Gilbert-Varshamov bound and deriving estimates of
their distance. In particular, we show that this bound is attained by codes
constructed on a fixed bipartite graph with a large spectral gap.
We also suggest a new decoding algorithm of hypergraph codes that corrects a
constant fraction of errors, improving upon the algorithm of Bilu and Hoory. | 0808.3453v2 |
2011-03-02 | Switching dynamics of a magnetostrictive single-domain nanomagnet subjected to stress | The temporal evolution of the magnetization vector of a single-domain
magnetostrictive nanomagnet, subjected to in-plane stress, is studied by
solving the Landau-Lifshitz-Gilbert equation. The stress is ramped up linearly
in time and the switching delay, which is the time it takes for the
magnetization to flip, is computed as a function of the ramp rate. For high
levels of stress, the delay exhibits a non-monotonic dependence on the ramp
rate, indicating that there is an {\it optimum} ramp rate to achieve the
shortest delay. For constant ramp rate, the delay initially decreases with
increasing stress but then saturates showing that the trade-off between the
delay and the stress (or the energy dissipated in switching) becomes less and
less favorable with increasing stress. All of these features are due to a
complex interplay between the in-plane and out-of-plane dynamics of the
magnetization vector induced by stress. | 1103.0352v1 |
2011-05-12 | Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance | We present two on-line algorithms for maintaining a topological order of a
directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when
one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$
time. For sparse graphs ($m/n = O(1)$), this bound improves the best previous
bound by a logarithmic factor, and is tight to within a constant factor among
algorithms satisfying a natural {\em locality} property. Our second algorithm
handles an arbitrary sequence of arc additions in $O(n^{5/2})$ time. For
sufficiently dense graphs, this bound improves the best previous bound by a
polynomial factor. Our bound may be far from tight: we show that the algorithm
can take $\Omega(n^2 2^{\sqrt{2\lg n}})$ time by relating its performance to a
generalization of the $k$-levels problem of combinatorial geometry. A
completely different algorithm running in $\Theta(n^2 \log n)$ time was given
recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to
the maintenance of strong components, without affecting the asymptotic time
bounds. | 1105.2397v1 |
2011-11-10 | Magnetic friction: From Stokes to Coulomb behavior | We demonstrate that in a ferromagnetic substrate, which is continuously
driven out of equilibrium by a field moving with constant velocity $v$, at
least two types of friction may occur when $v$ goes to zero: The substrate may
feel a friction force proportional to $v$ (Stokes friction), if the field
changes on a time scale which is longer than the intrinsic relaxation time. On
the other hand, the friction force may become independent of $v$ in the
opposite case (Coulomb friction). These observations are analogous to e.g.
solid friction. The effect is demonstrated in both, the Ising (one spin
dimension) and the Heisenberg model (three spin dimensions), irrespective which
kind of dynamics (Metropolis spin-flip dynamics or Landau-Lifshitz-Gilbert
precessional dynamics) is used. For both models the limiting case of Coulomb
friction can be treated analytically. Furthermore we present an empiric
expression reflecting the correct Stokes behavior and therefore yielding the
correct cross-over velocity and dissipation. | 1111.2494v1 |
2011-11-15 | Revisiting No-Scale Supergravity Inspired Scenarios | We consider no-scale supergravity inspired scenarios, emphasizing the
possible dynamical determination of the soft supersymmetry-breaking parameters
as triggered by the radiative corrections that lift an essentially flat
tree-level potential in the hidden sector. We (re)emphasize the important role
played by the scale-dependent vacuum energy contribution to the effective
potential for the occurrence of consistent no-scale minima. The most relevant
input parameters are introduced as $B_0$ (the soft breaking mixing Higgs
parameter) and $\eta_0$ (the cosmological constant value at high energy)
instead of $\mhalf$ and $\tan \beta$, the latter being determined through a
(generalized) potential minimization at electroweak scales. We examine the
theoretical and phenomenological viability of such a mechanism when confronted
with up-to-date calculations of the low energy sparticle spectrum and with
present constraints from the LHC and other observables. The tight dark matter
relic density constraint for a neutralino LSP scenario can be considerably
relaxed for a gravitino LSP scenario possible in this framework. | 1111.3455v1 |
2011-12-05 | Vortex core magnetization dynamics induced by thermal excitation | We investigate the effect of temperature on the dynamic properties of
magnetic vortices in small disks. Our calculations use a stochastic version of
the Landau-Lifshitz-Gilbert (LLG) equation, valid for finite temperatures well
below the Curie critical temperature. We show that a finite temperature induces
a vortex precession around the center of the disk, even in the absence of other
excitation sources. We discuss the origin and implications of the appearance of
this new dynamics. We also show that a temperature gradient plays a role
similar to that of a small constant magnetic field. | 1112.0911v2 |
2015-07-07 | Dynamic Reallocation Problems in Scheduling | In this paper we look at the problem of scheduling tasks on a
single-processor system, where each task requires unit time and must be
scheduled within a certain time window, and each task can be added to or
removed from the system at any time. On each operation, the system is allowed
to reschedule any tasks, but the goal is to minimize the number of rescheduled
tasks. Our main result is an allocator that maintains a valid schedule for all
tasks in the system if their time windows have constant size and reschedules
O(1/{\epsilon}*log(1/{\epsilon})) tasks on each insertion as {\epsilon}->0,
where {\epsilon} is a certain measure of the schedule flexibility of the
system. We also show that it is optimal for any allocator that works on
arbitrary instances. We also briefly mention a few variants of the problem,
such as if the tasks have time windows of difference sizes, for which we have
an allocator that we conjecture reschedules only 1 task on each insertion if
the schedule flexibility remains above a certain threshold. | 1507.01981v2 |
2015-09-02 | Topological dynamics and current-induced motion in a skyrmion lattice | We study the Thiele equation for current-induced motion in a skyrmion lattice
through two soluble models of the pinning potential. Comprised by a Magnus
term, a dissipative term and a pinning force, Thiele's equation resembles
Newton's law but in virtue of the topological character of the first two, it
differs significantly from Newtonian mechanics and because the Magnus force is
dominant, unlike its mechanical counterpart, the Coriolis force, skyrmion
trajectories do not necessarily have mechanical counterparts. This is important
if we are to understand skykrmion dynamics and tap into its potential for
data-storage technology. We identify a pinning threshold velocity for the
one-dimensional potential and for a two-dimensional potential we find a pinning
point and the skyrmion trajectories toward the point are spirals whose
frequency (compare Kepler's second law) and amplitude decay depends only on the
Gilbert constant and potential at the pinning point. | 1509.00591v1 |
2018-04-16 | Anisotropy of exchange stiffness based on atomic-scale magnetic properties in rare-earth permanent magnet Nd$_2$Fe$_{14}$B | We examine the anisotropic properties of the exchange stiffness constant,
$\mathcal{A}$, for rare-earth permanent magnet, Nd$_2$Fe$_{14}$B, by connecting
analyses with two different scales of length, i.e., Monte Carlo (MC) method
with an atomistic spin model and Landau-Lifshitz-Gilbert (LLG) equation with a
continuous magnetic model. The atomistic MC simulations are performed on the
spin model of Nd$_2$Fe$_{14}$B constructed from ab-initio calculations, and the
LLG micromagnetics simulations are performed with the parameters obtained by
the MC simulations. We clarify that the amplitude and the thermal property of
$\mathcal{A}$ depend on the orientation in the crystal, which are attributed to
the layered structure of Nd atoms and weak exchange couplings between Nd and Fe
atoms. We also confirm that the anisotropy of $\mathcal{A}$ significantly
affects the threshold field for the magnetization reversal (coercivity) given
by the depinning process. | 1804.05824v2 |
2018-03-14 | Subnanosecond magnetization reversal of magnetic nanoparticle driven by chirp microwave field pulse | We investigate the magnetization reversal of single-domain magnetic
nanoparticle driven by linear down-chirp microwave magnetic field pulse.
Numerical simulations based on the Landau-Lifshitz-Gilbert equation reveal that
solely down-chirp pulse is capable of inducing subnanosecond magnetization
reversal. With a certain range of initial frequency and chirp rate, the
required field amplitude is much smaller than that of constant-frequency
microwave field. The fast reversal is because the down-chirp microwave field
acts as an energy source and sink for the magnetic particle before and after
crossing over the energy barrier, respectively. Applying a spin-polarized
current additively to the system further reduces the microwave field amplitude.
Our findings provide a new way to realize low-cost and fast magnetization
reversal. | 1803.05261v1 |
2018-03-19 | Dynamics and Stability of Meshed Multiterminal HVDC Networks | This paper investigates the existence of an equilibrium point in
multiterminal HVDC (MT-HVDC) grids, assesses its uniqueness and defines
conditions to ensure its stability. An offshore MT-HVDC system including two
wind farms is selected as application test case. At first, a generalized
dynamic model of the network is proposed, using hypergraph theory. Such model
captures the frequency dependence of transmission lines and cables, it is
non-linear due to the constant power behavior of the converter terminals using
droop regulation, and presents a suitable degree of simplifications of the MMC
converters, under given conditions, to allow system level studies over
potentially large networks. Based on this model, the existence and uniqueness
of the equilibrium point is demonstrated by returning the analysis to a
load-flow problem and using the Banach fixed point theorem. Additionally, the
stability of the equilibrium is analyzed by obtaining a Lyapunov function by
the Krasovskii's theorem. Computational results obtained for the selected 4
terminals MT-HVDC grid corroborate the requirement for the existence and
stability of the equilibrium point. | 1803.06892v2 |
2015-12-24 | Eroding dipoles and vorticity growth for Euler flows in $ \scriptstyle{\mathbb{R}}^3$ I. Axisymmetric flow without swirl | A review of analyses based upon anti-parallel vortex structures suggests that
structurally stable vortex structures with eroding circulation may offer a path
to the study of rapid vorticity growth in solutions of Euler's equations in $
\scriptstyle{\mathbb{R}}^3$. We examine here the possible formation of such a
structure in axisymmetric flow without swirl, leading to maximal growth of
vorticity as $t^{4/3}$. Our study suggests that the optimizing flow giving the
$t^{4/3}$ growth mimics an exact solution of Euler's equations representing an
eroding toroidal vortex dipole which locally conserves kinetic energy. The
dipole cross-section is a perturbation of the classical Sadovskii dipole having
piecewise constant vorticity, which breaks the symmetry of closed streamlines.
The structure of this perturbed Sadovskii dipole is analyzed asymptotically at
large times, and its predicted properties are verified numerically. | 1512.07898v1 |
2014-01-03 | Spin-Transfer-Torque Driven Magneto-Logic Gates Using Nano Spin-Valve Pillars | We propose model magneto-logic NOR and NAND gates using a spin valve pillar,
wherein the logical operation is induced by spin-polarized currents which also
form the logical inputs. The operation is facilitated by the simultaneous
presence of a constant controlling magnetic field. The same spin-valve assembly
can also be used as a magnetic memory unit. We identify regions in the
parameter space of the system where the logical operations can be effectively
performed. The proposed gates retain the non-volatility of a magnetic random
access memory,(MRAM). We verify the functioning of the gate by numerically
simulating its dynamics, governed by the appropriate Landau-Lifshitz-Gilbert
equation with the spin-transfer torque term. The flipping time for the logical
states is estimated to be within nano seconds. | 1401.0723v1 |
2018-11-12 | New Theoretical Bounds and Constructions of Permutation Codes under Block Permutation Metric | Permutation codes under different metrics have been extensively studied due
to their potentials in various applications. Generalized Cayley metric is
introduced to correct generalized transposition errors, including previously
studied metrics such as Kendall's $\tau$-metric, Ulam metric and Cayley metric
as special cases. Since the generalized Cayley distance between two
permutations is not easily computable, Yang et al. introduced a related metric
of the same order, named the block permutation metric. Given positive integers
$n$ and $d$, let $\mathcal{C}_{B}(n,d)$ denote the maximum size of a
permutation code in $S_n$ with minimum block permutation distance $d$. In this
paper, we focus on the theoretical bounds of $\mathcal{C}_{B}(n,d)$ and the
constructions of permutation codes under block permutation metric. Using a
graph theoretic approach, we improve the Gilbert-Varshamov type bound by a
factor of $\Omega(\log{n})$, when $d$ is fixed and $n$ goes into infinity. We
also propose a new encoding scheme based on binary constant weight codes.
Moreover, an upper bound beating the sphere-packing type bound is given when
$d$ is relatively close to $n$. | 1811.04600v1 |
2019-07-11 | Astro2020 Activity, Project of State of the Profession Consideration (APC) White Paper: All-Sky Near Infrared Space Astrometry. State of the Profession Considerations: Development of Scanning NIR Detectors for Astronomy | Gaia is a revolutionary space mission developed by ESA and is delivering 5
parameter astrometry, photometry and radial velocities over the whole sky with
astrometric accuracies down to a few tens of micro-arcseconds. A weakness of
Gaia is that it only operates at optical wavelengths. However, much of the
Galactic centre and the spiral arm regions, important for certain studies, are
obscured by interstellar extinction and this makes it difficult for Gaia to
deeply probe. This problem can be overcome by switching to the Near Infra-Red
(NIR) but this is not possible with silicon CCDs. Additionally, to scan the
entire sky and make global absolute parallax measurements the spacecraft must
have a constant rotation and this requires the detectors operate in Time
Delayed Integration (TDI) mode or similar. | 1907.05191v1 |
2019-11-05 | Numerical methods for antiferromagnetics | Compared with ferromagnetic counterparts, antiferromagnetic materials are
considered as the future of spintronic applications since these materials are
robust against the magnetic perturbation, produce no stray field, and display
ultrafast dynamics. There are (at least) two sets of magnetic moments in
antiferromagnets (with magnetization of the same magnitude but antiparallel
directions) and ferrimagnets (with magnetization of the different magnitude).
The coupled dynamics for the bipartite collinear antiferromagnets is modeled by
a coupled system of Landau-Lifshitz-Gilbert equations with an additional term
originated from the antiferromagnetic exchange, which leads to femtosecond
magnetization dynamics. In this paper, we develop three Gauss-Seidel projection
methods for micromagnetics simulation in antiferromagnets and ferrimagnets.
They are first-order accurate in time and second-order in space, and only solve
linear systems of equations with constant coefficients at each step.
Femtosecond dynamics, N\'{e}el wall structure, and phase transition in presence
of an external magnetic field for antiferromagnets are provided with the
femtosecond stepsize. | 1911.01717v1 |
2019-12-17 | SINR percolation for Cox point processes with random powers | Signal-to-interference plus noise ratio (SINR) percolation is an
infinite-range dependent variant of continuum percolation modeling connections
in a telecommunication network. Unlike in earlier works, in the present paper
the transmitted signal powers of the devices of the network are assumed random,
i.i.d. and possibly unbounded. Additionally, we assume that the devices form a
stationary Cox point process, i.e., a Poisson point process with stationary
random intensity measure, in two or higher dimensions. We present the following
main results. First, under suitable moment conditions on the signal powers and
the intensity measure, there is percolation in the SINR graph given that the
device density is high and interferences are sufficiently reduced, but not
vanishing. Second, if the interference cancellation factor $\gamma$ and the
SINR threshold $\tau$ satisfy $\gamma \geq 1/(2\tau)$, then there is no
percolation for any intensity parameter. Third, in the case of a Poisson point
process with constant powers, for any intensity parameter that is supercritical
for the underlying Gilbert graph, the SINR graph also percolates with some
small but positive interference cancellation factor. | 1912.07895v2 |
2020-02-17 | How fast can you update your MST? (Dynamic algorithms for cluster computing) | Imagine a large graph that is being processed by a cluster of computers,
e.g., described by the $k$-machine model or the Massively Parallel Computation
Model. The graph, however, is not static; instead it is receiving a constant
stream of updates. How fast can the cluster process the stream of updates? The
fundamental question we want to ask in this paper is whether we can update the
graph fast enough to keep up with the stream. We focus specifically on the
problem of maintaining a minimum spanning tree (MST), and we give an algorithm
for the $k$-machine model that can process $O(k)$ graph updates per $O(1)$
rounds with high probability. (And these results carry over to the Massively
Parallel Computation (MPC) model.) We also show a lower bound, i.e., it is
impossible to process $k^{1+\epsilon}$ updates in $O(1)$ rounds. Thus we
provide a nearly tight answer to the question of how fast a cluster can respond
to a stream of graph modifications while maintaining an MST. | 2002.06762v1 |
2023-04-04 | Direct in situ determination of the surface area and structure of deposited metallic lithium within lithium metal batteries using ultra small and small angle neutron scattering | Despite being the major cause of battery safety issues and detrimental
performance, a comprehensive growth mechanism for metallic lithium deposited at
electrode surfaces in lithium metal batteries remains elusive. While lithium
surface morphology is often derived indirectly, here, detailed information is
directly obtained using in situ small and ultra-small angle neutron scattering,
in bulk and non-destructively. Features of 1-10 um and 100-300 nm are
identified; the latter contribute to most of the surface area and their size
inversely correlates to applied current density. Surface area per unit volume
increases continuously during charging from 1-4 h at 2 mA/cm2 but more slowly
during discharge. Comparatively higher values are reached after just 1 h at 20
mA/cm2 which remain constant in subsequent cycles. Such quantitative insight
into the processes of metallic lithium growth within batteries may enable the
development of safer high performance lithium metal batteries. | 2304.01557v1 |
2023-08-07 | Strong Byzantine Agreement with Adaptive Word Complexity | The strong Byzantine agreement (SBA) problem is defined among n processes,
out of which t < n can be faulty and behave arbitrarily. SBA allows correct
(non-faulty) processes to agree on a common value. Moreover, if all correct
processes have proposed the same value, only that value can be agreed upon. It
has been known for a long time that any solution to the SBA problem incurs
quadratic worst-case word complexity; additionally, the bound was known to be
tight. However, no existing protocol achieves adaptive word complexity, where
the number of exchanged words depends on the actual number of faults, and not
on the upper bound. Therefore, it is still unknown whether SBA with adaptive
word complexity exists. This paper answers the question in the affirmative.
Namely, we introduce STRONG, a synchronous protocol that solves SBA among n =
(2 + Omega(1))t + 1 processes and achieves adaptive word complexity. We show
that the fundamental challenge of adaptive SBA lies in efficiently solving
certification, the problem of obtaining a constant-sized, locally-verifiable
proof that a value can safely be decided. | 2308.03524v1 |
2019-08-21 | Generalized Metric Repair on Graphs | Many modern data analysis algorithms either assume or are considerably more
efficient if the distances between the data points satisfy a metric. These
algorithms include metric learning, clustering, and dimension reduction. As
real data sets are noisy, distances often fail to satisfy a metric. For this
reason, Gilbert and Jain and Fan et al. introduced the closely related sparse
metric repair and metric violation distance problems. The goal of these
problems is to repair as few distances as possible to ensure they satisfy a
metric. Three variants were considered, one admitting a polynomial time
algorithm. The other variants were shown to be APX-hard, and an
$O(OPT^{1/3})$-approximation was given, where $OPT$ is the optimal solution
size.
In this paper, we generalize these problems to no longer consider all
distances between the data points. That is, we consider a weighted graph $G$
with corrupted weights $w$, and our goal is to find the smallest number of
weight modifications so that the resulting weighted graph distances satisfy a
metric. This is a natural generalization and is more flexible as it takes into
account different relationships among the data points. As in previous work, we
distinguish among the types of repairs permitted and focus on the increase only
and general versions. We demonstrate the inherent combinatorial structure of
the problem, and give an approximation-preserving reduction from MULTICUT.
Conversely, we show that for any fixed constant $\varsigma$, for the large
class of $\varsigma$-chordal graphs, the problems are fixed parameter
tractable. Call a cycle broken if it contains an edge whose weight is larger
than the sum of all its other edges, and call the amount of this difference its
deficit. We present approximation algorithms, one which depends on the maximum
number of edges in a broken cycle, and one which depends on the number of
distinct deficit values. | 1908.08411v1 |
2018-08-08 | Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients | We consider the forward problem of uncertainty quantification for the
generalised Dirichlet eigenvalue problem for a coercive second order partial
differential operator with random coefficients, motivated by problems in
structural mechanics, photonic crystals and neutron diffusion. The PDE
coefficients are assumed to be uniformly bounded random fields, represented as
infinite series parametrised by uniformly distributed i.i.d. random variables.
The expectation of the fundamental eigenvalue of this problem is computed by
(a) truncating the infinite series which define the coefficients; (b)
approximating the resulting truncated problem using lowest order conforming
finite elements and a sparse matrix eigenvalue solver; and (c) approximating
the resulting finite (but high dimensional) integral by a randomly shifted
quasi-Monte Carlo lattice rule, with specially chosen generating vector. We
prove error estimates for the combined error, which depend on the truncation
dimension $s$, the finite element mesh diameter $h$, and the number of
quasi-Monte Carlo samples $N$. Under suitable regularity assumptions, our
bounds are of the particular form $\mathcal{O}(h^2+N^{-1+\delta})$, where
$\delta>0$ is arbitrary and the hidden constant is independent of the
truncation dimension, which needs to grow as $h\to 0$ and $N\to\infty$.
Although the eigenvalue problem is nonlinear, which means it is generally
considered harder than the analogous source problem, in almost all cases we
obtain error bounds that converge at the same rate as the corresponding rate
for the source problem. The proof involves a detailed study of the regularity
of the fundamental eigenvalue as a function of the random parameters. As a key
intermediate result in the analysis, we prove that the spectral gap (between
the fundamental and the second eigenvalues) is uniformly positive over all
realisations of the random problem. | 1808.02639v3 |
2019-09-19 | Parameterized Complexity of Manipulating Sequential Allocation | The sequential allocation protocol is a simple and popular mechanism to
allocate indivisible goods, in which the agents take turns to pick the items
according to a predefined sequence. While this protocol is not strategy-proof,
it has been shown recently that finding a successful manipulation for an agent
is an NP-hard problem (Aziz et al., 2017). Conversely, it is also known that
finding an optimal manipulation can be solved in polynomial time in a few
cases: if there are only two agents or if the manipulator has a binary or a
lexicographic utility function. In this work, we take a parameterized approach
to provide several new complexity results on this manipulation problem. More
precisely, we give a complete picture of its parameterized complexity w.r.t.
the following three parameters: the number $n$ of agents, the number $\mu(a_1)$
of times the manipulator $a_1$ picks in the picking sequence, and the maximum
range $\mathtt{rg}^{\max}$ of an item. This third parameter is a correlation
measure on the preference rankings of the agents. In particular, we show that
the problem of finding an optimal manipulation can be solved in polynomial time
if $n$ or $\mu(a_1)$ is a constant, and that it is fixed-parameter tractable
w.r.t. $\mathtt{rg}^{\max}$ and $n+\mu(a_1)$. Interestingly enough, we show
that w.r.t. the single parameters $n$ and $\mu(a_1)$ it is W[1]-hard. Moreover,
we provide an integer program and a dynamic programming scheme to solve the
manipulation problem and we show that a single manipulator can increase the
utility of her bundle by a multiplicative factor which is at most 2. | 1909.08920v4 |
2020-11-11 | Unique Decoding of Explicit $ε$-balanced Codes Near the Gilbert-Varshamov Bound | The Gilbert-Varshamov bound (non-constructively) establishes the existence of
binary codes of distance $1/2 -\epsilon$ and rate $\Omega(\epsilon^2)$ (where
an upper bound of $O(\epsilon^2\log(1/\epsilon))$ is known). Ta-Shma [STOC
2017] gave an explicit construction of $\epsilon$-balanced binary codes, where
any two distinct codewords are at a distance between $1/2 -\epsilon/2$ and
$1/2+\epsilon/2$, achieving a near optimal rate of
$\Omega(\epsilon^{2+\beta})$, where $\beta \to 0$ as $\epsilon \to 0$.
We develop unique and list decoding algorithms for (essentially) the family
of codes constructed by Ta-Shma. We prove the following results for
$\epsilon$-balanced codes with block length $N$ and rate
$\Omega(\epsilon^{2+\beta})$ in this family:
- For all $\epsilon, \beta > 0$ there are explicit codes which can be
uniquely decoded up to an error of half the minimum distance in time
$N^{O_{\epsilon, \beta}(1)}$.
- For any fixed constant $\beta$ independent of $\epsilon$, there is an
explicit construction of codes which can be uniquely decoded up to an error of
half the minimum distance in time $(\log(1/\epsilon))^{O(1)} \cdot
N^{O_\beta(1)}$.
- For any $\epsilon > 0$, there are explicit $\epsilon$-balanced codes with
rate $\Omega(\epsilon^{2+\beta})$ which can be list decoded up to error $1/2 -
\epsilon'$ in time $N^{O_{\epsilon,\epsilon',\beta}(1)}$, where $\epsilon',
\beta \to 0$ as $\epsilon \to 0$.
The starting point of our algorithms is the list decoding framework from Alev
et al. [SODA 2020], which uses the Sum-of-Squares SDP hierarchy. The rates
obtained there were quasipolynomial in $\epsilon$. Here, we show how to
overcome the far from optimal rates of this framework obtaining unique decoding
algorithms for explicit binary codes of near optimal rate. These codes are
based on simple modifications of Ta-Shma's construction. | 2011.05500v1 |
2005-05-11 | Social Behaviour of Agents: Capital Markets and Their Small Perturbations | We study social behaviour of agents on capital markets when these are
perturbed by small perturbations. We use the mean field method. Social
behaviour of agents on capital markets is described: volatility of the market,
aversion constant and equilibrium states are discussed. Relaxation behaviour of
agents on the capital market is studied. Equation of motion for the agent
average number is of the relaxation type. Development of the group of agents in
the states corresponding to minimum of the aim function is either linear either
exponentially damped. There exist characteristic volatility constants $ V_{c3}
$ and $ V_{c3} $. The constant b of verification of information contribution to
the aversion constant A and the $ A_{0} $ constant of aversion are
distinguishing three types of dependencies of the minimum of the aim function
on the expected volatility EV and on the expected returns E. Arbitrage trades
and group forces lead the group into the equilibrium state. Verification of
information intensity influences return back to the equilibrium state. The
linear in time damping to the equilibrium state is characterized with the
characteristic time $ T_{3}$ and $ T_{6} $, the exponential with a
characteristic time $ \tau $. Their dependence on the expected volatility, on
the expected profit and characteristics of agents is discussed. | 0505086v2 |
2017-06-18 | Diffusion constant of slowly rotating black three-brane | In this paper, we take the slowly rotating black three-brane background and
perturb it by introducing a vector gauge field. We find the components of the
gauge field through Maxwell equations and Bianchi identities. Using currents
and some ansatz we find Fick's first law at long wavelength regime. An
interesting result for this non-trivial supergravity background is that the
diffusion constant on the stretched horizon which emerges from Fick's first law
is a complex constant. The pure imaginary part of the diffusion constant
appears because the black three-brane has angular momentum. By taking the
static limit of the corresponding black brane the well known diffusion constant
will be recovered. On the other hand, from the point of view of the Fick's
second law, we have the dispersion relation $\omega=-iDq^{2}$ and we found a
damping of hydrodynamical flow in the holographically dual theory. Existence of
imaginary term in the diffusion constant introduces an oscillating propagation
of the gauge field in the dual field theory. | 1706.05669v2 |
2023-04-24 | On elastic constants of zero-temperature amorphous solids | Elastic constants of zero-temperature amorphous solids are given as the
difference between the Born term, which results from a hypothetical affine
deformation of an amorphous solid, and a correction term which originates from
the fact that the deformation of an amorphous solid due to an applied stress
is, at the microscopic level, non-affine. Both terms are non-negative and thus
it is a priori not obvious that the resulting elastic constants are
non-negative. In particular, theories that approximate the correction term may
spuriously predict negative elastic constants and thus an instability of an
amorphous solid. Here we derive alternative expressions for elastic constants
of zero-temperature amorphous solids that are explicitly non-negative. These
expressions provide a useful blueprint for approximate theories for elastic
constants and sound damping in zero temperature amorphous solids. | 2304.12374v1 |
2005-10-17 | Comment on "Operator Quantum Error Correction" | The attempt to equate operator quantum error correction (quant-ph/0504189v1)
with the quantum computer condition (quant-ph/0507141) in version two of
quant-ph/0504189 is shown to be invalid. | 0510116v1 |
2007-09-17 | H-Decompositions | We show that for all graphs H of size n, the complete graph $K_{2n+1}$ has an
$H$-decomposition. | 0709.2525v5 |
2008-10-06 | Unsolvability of the isomorphism problem for [free abelian]-by-free groups | The isomorphism problem for [free abelian]-by-free groups is unsolvable. | 0810.0935v2 |
2011-11-27 | Comment on "Capturing correlations in chaotic diffusion by approximation methods" | This is a comment on [G. Knight and R. Klages, Phys. Rev. E 84, 041135
(2011); also available at arXiv:1107.5293v2 [math-ph]]. | 1111.6271v1 |
2017-01-04 | Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound | We prove that there exist non-linear binary cyclic codes that attain the
Gilbert-Varshamov bound. | 1701.01043v1 |
2007-02-23 | Organization of the Modulopt collection of optimization problems in the Libopt environment -- Version 1.0 | This note describes how the optimization problems of the Modulopt collection
are organized within the Libopt environment. It is aimed at being a guide for
using and enriching this collection in this environment. | 0702695v1 |
2014-01-11 | Hashimoto transform for stochastic Landau-Lifshitz-Gilbert equation | We show that Hashimoto transformation is applicable to the one dimensional
stochastic Landau-Lifshitz-Gilbert (LLG) equation and transforms it to the
stochastic generalized heat equation with nonlocal (in space) interaction. | 1401.2520v1 |
2019-01-28 | Conformal deformations preserving the Finslerian $R$-Einstein criterion | Given a Finslerian metric $F$ on a $C^4$-manifold, conformal deformations of
$F$ preserving the $R$-Einstein criterion are presented. In particular, locally
conformal invariance between two Finslerian $R$-Einstein metrics is
characterized. | 1902.00069v1 |
2022-04-07 | How to design a network architecture using availability | The best way to design a network is to take into account Availability values
and Capacity Planning. You already saw Availability expressed with numbers such
as 99.99%. The purpose of this document is to introduce the way to compute
Availability values using Reliability Block Diagrams. | 2204.03311v1 |
2003-08-24 | Numerical analysis of quasinormal modes in nearly extremal Schwarzschild-de Sitter spacetimes | We calculate high-order quasinormal modes with large imaginary frequencies
for electromagnetic and gravitational perturbations in nearly extremal
Schwarzschild-de Sitter spacetimes. Our results show that for low-order
quasinormal modes, the analytical approximation formula in the extremal limit
derived by Cardoso and Lemos is a quite good approximation for the quasinormal
frequencies as long as the model parameter $r_1\kappa_1$ is small enough, where
$r_1$ and $\kappa_1$ are the black hole horizon radius and the surface gravity,
respectively. For high-order quasinormal modes, to which corresponds
quasinormal frequencies with large imaginary parts, on the other hand, this
formula becomes inaccurate even for small values of $r_1\kappa_1$. We also find
that the real parts of the quasinormal frequencies have oscillating behaviors
in the limit of highly damped modes, which are similar to those observed in the
case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating
${\rm Re(\omega)}$ as a function of ${\rm Im}(\omega)$ approaches a non-zero
constant value for gravitational perturbations and zero for electromagnetic
perturbations in the limit of highly damped modes, where $\omega$ denotes the
quasinormal frequency. This means that for gravitational perturbations, the
real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter
spacetime appears not to approach any constant value in the limit of highly
damped modes. On the other hand, for electromagnetic perturbations, the real
part of frequency seems to go to zero in the limit. | 0308077v4 |
2010-12-08 | Nonequilibrium dynamics of the Holstein polaron driven by external electric field | This work represents a fundamental study of a Holstein polaron in one
dimension driven away from the ground state by a constant electric field.
Taking fully into account quantum effects we follow the time-evolution of the
system from its ground state as the constant electric field is switched on at t
= 0, until it reaches a steady state. At weak electron phonon coupling (EP) the
system experiences damped Bloch oscillations (BO) characteristic for
noninteracting electron band. An analytic expression of the steady state
current is proposed in terms of weak EP coupling and large electric field. For
moderate values of EP coupling the oscillations are almost critically damped
and the system reaches the steady state after a short time. In the strong
coupling limit weakly damped BO, consistent with nearly adiabatic evolution
within the polaron band, persist up to extremely large electric fields. A
traveling polaron under the influence of the electric field leaves behind a
trail of phonon excitations absorbing the excess energy gained from the
electric field. The shape of the traveling polaron is investigated in details. | 1012.1716v3 |
2015-06-23 | Resonant absorption of kink magnetohydrodynamic waves by a magnetic twist in coronal loops | There is ample evidence of twisted magnetic structures in the solar corona.
This motivates us to consider the magnetic twist as the cause of Alfven
frequency continuum in the coronal loops, which can support the resonant
absorption as a rapid damping mechanism for the observed coronal kink
magnetohydrodynamic (MHD) oscillations. We model a coronal loop with a straight
cylindrical magnetic flux tube which has constant but different densities in
the interior and exterior regions. The magnetic field is assumed to be constant
and aligned with the cylinder axis everywhere except a thin layer near the
boundary of the flux tube which has an additional small magnetic field twist.
Then, we investigate a number of possible instabilities that may arise in our
model. In the thin tube thin boundary approximation, we derive the dispersion
relation and solve it analytically to obtain the frequencies and damping rates
of the fundamental (l=1) and first/second overtone (l=2,3) kink (m=1) MHD
modes. We conclude that the resonant absorption by the magnetic twist can
justify the rapid damping of kink MHD waves observed in coronal loops.
Furthermore, the magnetic twist in the inhomogeneous layer can cause deviations
from P1/P2=2 and P1/P3=3 which are comparable with the observations. | 1507.02653v4 |
2003-05-21 | Magnetoresistive response of a high mobility 2DES under electromagnetic wave excitation | Oscillations of the resistance observed under electromagnetic wave excitation
in the high mobility GaAs/AlGaAs 2DES are examined as a function of the
radiation frequency and the power, utilizing an empirical lineshape based on
exponentially damped sinusoids. The fit-analysis indicates the resistance
oscillation frequency, F, increases with the radiation frequency, n, at the
rate dF/dn = 2.37 mTesla/GHz; the damping parameter, a, is approximately
independent of n at constant power; and the amplitude, A, of the oscillations
grows slowly with the incident power, at a constant temperature and frequency.
The lineshape appears to provide a good description of the data. | 0305507v2 |
2005-10-26 | Multiple electron-hole scattering effect on quasiparticle properties in a homogeneous electron gas | We present a detailed study of a contribution of the T matrix accounting for
multiple scattering between an electron and a hole to the quasiparticle
self-energy. This contribution is considered as an additional term to the GW
self-energy. The study is based on a variational solution of the T-matrix
integral equation within a local approximation. A key quantity of such a
solution, the local electron-hole interaction, is obtained at the small
four-momentum transfer limit. Performed by making use of this limit form,
extensive calculations of quasiparticle properties in the homogeneous electron
gas over a broad range of electron densities are reported. We carry out an
analysis of how the T-matrix contribution affects the quasiparticle damping
rate, the quasiparticle energy, the renormalization constant, and the effective
mass enhancement. We find that in comparison with the GW approximation the
inclusion of the T matrix leads to an essential increase of the damping rate, a
slight reduction of the GW band narrowing, a decrease of the renormalization
constant at the Fermi wave vector, and some "weighting" of quasiparticles at
the Fermi surface. | 0510684v2 |
1995-01-03 | High temperature QCD and QED with unstable excitations | We consider the partition functions of QCD and QED at high temperature
assuming small coupling constants, and present arguments in favor of an
improved perturbative expansion in terms of unstable excitations. Our effective
propagators are derived from spectral functions with a constant width. These
spectral functions describe screening and damping of gluons (photons) as well
as ``Brownian'' motion of quarks (electrons). BRST-invariance allows us to
reduce the number of independent width parameters to three. These are
determined in a self-consistent way from the one-loop self energy and
polarization tensor in the infrared limit thus rendering this limit finite. All
spectral width parameters are found to be proportional to $g T$. We reproduce
the well known expression for the electric ``Debye''-screening mass. The
transverse (magnetic) gluons (photons) are found to interact only at nonzero
momentum or energy, at least to leading order. As a consequence their spectral
function acquires a width only away from the infrared limit. Finally, plasmon
modes are determined and found to be strongly damped. | 9501203v1 |
2002-06-22 | Yank and Hooke's constant group theoretically | We study the second central extension of the (1+1) Aristotle Lie.We find that
the first central extension admit four orbits on the dual of second central
extension of the (1+1) Aristotle Lie group.The generic orbit is characterised
by a Hooke's constant k and a yank y.If the physics of the orbit is studied
with respect the evolution in time,it represents an elementary system with
internal energy U in a posotion-momentum under the conjugation of a Hooke's
force and a damping one proportional to the velocity as in particle
mechanics.If the physics of the orbit is studied with respect the evolution in
space, it represents an elementary system with an internal momentum P under the
conjugation of a kind of Hooke's force and a damping one proportional to a
slowness, slowness usually used in time travel waves. | 0206038v1 |
2010-11-21 | Regular and chaotic transport of discrete solitons in asymmetric potentials | Ratchet dynamics of topological solitons of the forced and damped discrete
double sine-Gordon system are studied. Directed transport occurring both in
regular and in chaotic regions of the phase space and its dependence on
damping, amplitude and frequency of the driving, asymmetry parameter, coupling
constant, has been extensively investigated. We show that the passage from
ratchet phase-locked regime to chaotic ratchets occurs via a period doubling
route to chaos and that, quite surprisingly, pinned states can exist inside
phase-locking and chaotic transport regions for intermediate values of the
coupling constant. The possibility to control chaotic discrete soliton ratchets
by means of both small subharmonic signals and more general periodic drivings,
has also been investigated. | 1011.4707v1 |
2011-07-13 | q-damped Oscillator and degenerate roots of constant coefficients q-difference ODE | The classical model of q-damped oscillator is introduced and solved in terms
of Jackson q-exponential function for three different cases, under-damped,
over-damped and the critical one. It is shown that in all three cases solution
is oscillating in time but is unbounded and non-periodic. By q-periodic
function modulation, the self-similar micro-structure of the solution for small
time intervals is derived. In the critical case with degenerate roots, the
second linearly independent solution is obtained as a limiting case of two
infinitesimally close roots. It appears as standard derivative of q-exponential
and is rewritten in terms of the q-logarithmic function. We extend our result
by constructing n linearly independent set of solutions to a generic constant
coefficient q-difference equation degree N with n degenerate roots. | 1107.2518v1 |
2013-04-24 | Finite amplitude inhomogeneous waves in Mooney-Rivlin viscoelastic solids | New exact solutions are exhibited within the framework of finite
viscoelasticity. More precisely, the solutions correspond to finite-amplitude,
transverse, linearly-polarized, inhomogeneous motions superposed upon a finite
homogeneous static deformation. The viscoelastic body is composed of a
Mooney-Rivlin viscoelastic solid, whose constitutive equation consists in the
sum of an elastic part (Mooney-Rivlin hyperelastic model) and a viscous part
(Newtonian viscous fluid model). The analysis shows that the results are
similar to those obtained for the purely elastic case; inter alia, the normals
to the planes of constant phase and to the planes of constant amplitude must be
orthogonal and conjugate with respect to the B-ellipsoid, where B is the left
Cauchy-Green strain tensor associated with the initial large static
deformation. However, when the constitutive equation is specialized either to
the case of a neo-Hookean viscoelastic solid or to the case of a Newtonian
viscous fluid, a greater variety of solutions arises, with no counterpart in
the purely elastic case. These solutions include travelling inhomogeneous
finite-amplitude damped waves and standing damped waves. | 1304.6748v1 |
2017-02-14 | Electron-nuclear coherent spin oscillations probed by spin dependent recombination | We demonstrate the detection of coherent electron-nuclear spin oscillations
related to the hyperfine interaction and revealed by the band-to-band
photoluminescence (PL) in zero external magnetic field. On the base of a
pump-probe PL experiment we measure, directly in the temporal domain, the
hyperfine constant of an electron coupled to a gallium defect in GaAsN by
tracing the dynamical behavior of the conduction electron spin-dependent
recombination to the defect site. The hyperfine constants and the relative
abundance of the nuclei isotopes involved can be determined without the need of
electron spin resonance technique and in the absence of any magnetic field.
Information on the nuclear and electron spin relaxation damping parameters can
also be estimated from the oscillations damping and the long delay behavior. | 1702.04129v1 |
2017-05-02 | The response of a Unruh-deWitt particle detector in a thin-shell wormhole spacetime | We investigate the transition probability of a Unruh-deWitt particle detector
evolving in flat space and in a wormhole spacetime, in various scenarios. In
Minkowski space, we look at the response of the detector on trajectories having
discontinuities and rapid variations, as well as the effect of finite-time
coupling. It is found that these features induce spurious oscillations in the
probability and rate of transition. At large times the oscillations are damped
and the probability tends to a constant value. Next, we look at the response of
an inertial detector on a radial trajectory that passes through a thin-shell
wormhole. After finding the appropriate modes, we look at the renormalized
detector response, defined by subtracting the flat space analogues from the
partial probabilities. The resulting curve has a peak around the wormhole
throat followed by a period of damped oscillations, before stabilizing to a
constant value. This is very similar to the flat space results, which is
surprising given that in this case the trajectory is continuous. The features
of the transition probability are due entirely to the nontrivial topology
induced by the wormhole. | 1705.00890v1 |
2017-08-11 | On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion | We study the small mass limit (or: the Smoluchowski-Kramers limit) of a class
of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic
bath spectral density with a Lorentz-Drude cutoff, we derive the
Heisenberg-Langevin equations for the particle's observables using a quantum
stochastic calculus approach. We set the mass of the particle to equal $m =
m_{0} \epsilon$, the reduced Planck constant to equal $\hbar = \epsilon$ and
the cutoff frequency to equal $\Lambda = E_{\Lambda}/\epsilon$, where $m_0$ and
$E_{\Lambda}$ are positive constants, so that the particle's de Broglie
wavelength and the largest energy scale of the bath are fixed as $\epsilon \to
0$. We study the limit as $\epsilon \to 0$ of the rescaled model and derive a
limiting equation for the (slow) particle's position variable. We find that the
limiting equation contains several drift correction terms, the quantum
noise-induced drifts, including terms of purely quantum nature, with no
classical counterparts. | 1708.03685v1 |
2015-12-02 | Flow of colloidal solids and fluids through constrictions: dynamical density functional theory versus simulation | Using both dynamical density functional theory and particle-resolved Brownian
dynamics simulations, we explore the flow of two-dimensional colloidal solids
and fluids driven through a linear channel with a geometric constriction. The
flow is generated by a constant external force acting on all colloids. The
initial configuration is equilibrated in the absence of flow and then the
external force is switched on instantaneously. Upon starting the flow, we
observe four different scenarios: a complete blockade, a monotonic decay to a
constant particle flux (typical for a fluid), a damped oscillatory behaviour in
the particle flux, and a long-lived stop-and-go behaviour in the flow (typical
for a solid). The dynamical density functional theory describes all four
situations but predicts infinitely long undamped oscillations in the flow which
are always damped in the simulations. We attribute the mechanisms of the
underlying stop-and-go flow to symmetry conditions on the flowing solid. Our
predictions are verifiable in real-space experiments on magnetic colloidal
monolayers which are driven through structured microchannels and can be
exploited to steer the flow throughput in microfluidics. | 1512.00751v1 |
2017-03-08 | System-Theoretic Performance Metrics for Low-Inertia Stability of Power Networks | As bulk synchronous generators in the power grid are replaced by distributed
generation interfaced through power electronics, inertia is removed from the
system, prompting concerns over grid stability. Different metrics are available
for quantifying grid stability and performance; however, no theoretical results
are available comparing and contrasting these metrics. This paper presents a
rigorous system-theoretic study of performance metrics for low-inertia
stability. For networks with uniform parameters, we derive explicit expressions
for the eigenvalue damping ratios, and for the $\mathcal{H}_{2}$ and
$\mathcal{H}_{\infty}$ norms of the linearized swing dynamics, from external
power disturbances to different phase/frequency performance outputs.These
expressions show the dependence of system performance on inertia constants,
damping constants, and on the grid topology. Surprisingly, we find that the
$\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ norms can display contradictory
behavior as functions of the system inertia, indicating that low-inertia
performance depends strongly on the chosen performance metric. | 1703.02646v1 |
2017-03-30 | Study of spin pumping in Co thin film vis-a-vis seed and capping layer using ferromagnetic resonance spectroscopy | We investigated the dependence of the seed [Ta/Pt, Ta/Au] and capping [Pt/Ta,
Au/Ta] layers on spin pumping effect in the ferromagnetic 3 nm thick Co thin
film using ferromagnetic resonance spectroscopy. The data is fitted with Kittel
equation to evaluate damping constant and g-factor. A strong dependence of seed
and capping layers on spin pumping has been discussed. The value of damping
constant {alpha} is found to be relatively large i.e. 0.0326 for the
Ta{3}/Pt{3}/Co{3}/Pt{3}/Ta{3} {nm} multi-layer structure, while it is 0.0104
for Ta{3}/Co{3}/Ta{3} {nm}. Increase in {alpha} is observed due to Pt layer
that works as a good sink for spins due to high spin orbit coupling. In
addition, we measured the effective spin conductance = 2.0e18 m-2 for the
trilayer structure Pt{3}/Co{3}/Pt{3} {nm} as a result of the enhancement in
{alpha} relative to its bulk value. We observed that the evaluated g-factor
decreases as effective demagnetizing magnetic field increases in all the
studied samples. The azimuthal dependence of magnetic resonance field and line
width showed relatively high anisotropy in the trilayer Ta{3}/Co{3}/Ta{3} {nm}
structure. | 1703.10630v1 |
2012-02-07 | The Fine Structure Constant and the CMB Damping Scale | The recent measurements of the Cosmic Microwave Background anisotropies at
arcminute angular scales performed by the ACT and SPT experiments are probing
the damping regime of CMB fluctuations. The analysis of these datasets
unexpectedly suggests that the effective number of relativistic degrees of
freedom is larger than the standard value of Neff = 3.04, and inconsistent with
it at more than two standard deviations. In this paper we study the role of a
mechanism that could affect the shape of the CMB angular fluctuations at those
scales, namely a change in the recombination process through variations in the
fine structure constant. We show that the new CMB data significantly improve
the previous constraints on variations of {\alpha}, with {\alpha}/{\alpha}0 =
0.984 \pm 0.005, i.e. hinting also to a more than two standard deviation from
the current, local, value {\alpha}0. A significant degeneracy is present
between {\alpha} and Neff, and when variations in the latter are allowed the
constraints on {\alpha} are relaxed and again consistent with the standard
value. Deviations of either parameter from their standard values would imply
the presence of new, currently unknown physics. | 1202.1476v1 |
2023-09-27 | Exploring antisymmetric tensor effects on black hole shadows and quasinormal frequencies | This study explores the impact of antisymmetric tensor effects on spherically
symmetric black holes, investigating photon spheres, shadows, emission rate and
quasinormal frequencies in relation to a parameter which triggers the Lorentz
symmetry breaking. We examine these configurations without and with the
presence of a cosmological constant. In the first scenario, the Lorentz
violation parameter, denoted as $\lambda$, plays a pivotal role in reducing
both the photon sphere and the shadow radius, while also leading to a damping
effect on quasinormal frequencies. Conversely, in the second scenario, as the
values of the cosmological constant ($\Lambda$) increase, we observe an
expansion in the shadow radius. Also, we provide the constraints of the shadows
based on the analysis observational data obtained from the Event Horizon
Telescope (EHT) focusing on Sagittarius $A^{*}$ shadow images. Additionally,
with the increasing $\Lambda$, the associated gravitational wave frequencies
exhibit reduced damping modes. | 2309.15778v3 |
2006-01-11 | Ab initio calculations of inelastic losses and optical constants | Ab initio approaches are introduced for calculations of inelastic losses and
vibrational damping in core level x-ray and electron spectroscopies. From the
dielectric response function we obtain system-dependent self-energies,
inelastic mean free paths, and losses due to multiple-electron excitations,
while from the dynamical matrix we obtain phonon spectra and Debye-Waller
factors. These developments yield various spectra and optical constants from
the UV to x-ray energies in aperiodic materials, and significantly improve both
the near edge and extended fine structure. | 0601241v1 |
2006-04-06 | Measurement of the complex dielectric constant of a single gold nanoparticle | A differential interference contrast microscopy technique, which employs a
photonic crystal fiber as a white-light source, is used to measure both the
real and imaginary parts of the complex dielectric constant of single 10 and 15
nm gold nanoparticles over a wavelength range of 480 to 610 nm. Noticeable
deviations from bulk gold measurements are observed at short wavelengths and
for individual particles even after taking into account finite-size surface
damping effects. | 0604174v2 |
1998-03-08 | Wormholes in spacetimes with cosmological horizons | A generalisation of the asymptotic wormhole boundary condition for the case
of spacetimes with a cosmological horizon is proposed. In particular, we
consider de Sitter spacetime with small cosmological constant. The wave
functions selected by this proposal are exponentially damped in WKB
approximation when the scale factor is large but still much smaller than the
horizon size. In addition, they only include outgoing gravitational modes in
the region beyond the horizon. We argue that these wave functions represent
quantum wormholes and compute the local effective interactions induced by them
in low-energy field theory. These effective interactions differ from those for
flat spacetime in terms that explicitly depend on the cosmological constant. | 9803029v1 |
2003-08-01 | The pushing force of a propagating electromagnetic wave | The effect of the electrodynamic forces on a charged particle in a
propagating plane electromagnetic wave is investigated. First it is pointed out
that for constant fields fulfilling the radiation condition there will be an
acceleration in the direction of the Poynting vector. When oscillating fields
are considered the Lorentz force on the particle only causes a drift, with
constant average velocity, in the direction of propagation of the wave, i.e.\
the direction of the Poynting vector. Finally, when the radiative reaction
(radiation damping) force is added the result is again an acceleration in the
direction of wave propagation. PACS classification numbers: 03.50.De, 41.60.-m,
41.75.Jv | 0308007v1 |
2002-05-20 | Selection of Squeezed States via Decoherence | In the framework of Lindblad theory for open quantum systems, we calculate
the entropy of a damped quantum harmonic oscillator which is initially in a
quasi-free state. The maximally predictable states are identified as those
states producing the minimum entropy increase after a long enough time. In
general, the states with a squeezing parameter depending on the environment's
diffusion coefficients and friction constant are singled out, but if the
friction constant is much smaller than the oscillator's frequency, coherent
states
(or thermalized coherent states) are obtained as the preferred classical
states. | 0205127v1 |
2007-12-17 | A single-time two-point closure based on fluid particle displacements | A new single-time two-point closure is proposed, in which the equation for
the two-point correlation between the displacement of a fluid particle and the
velocity allows one to estimate a Lagrangian timescale. This timescale is used
to specify the nonlinear damping of triple correlations in the closure. A
closed set of equations is obtained without ad hoc constants. Taking advantage
of the analogy between particle displacements and scalar fluctuations in
isotropic turbulence subjected to a mean scalar gradient, the model is
numerically integrated. Results for the energy spectrum are in agreement with
classical scaling predictions. An estimate for the Kolmogorov constant is
obtained. | 0712.2496v1 |
2011-02-14 | Non-gaussianity in the strong regime of warm inflation | The bispectrum of scalar mode density perturbations is analysed for the
strong regime of warm inflationary models. This analysis generalises previous
results by allowing damping terms in the inflaton equation of motion that are
dependent on temperature. A significant amount of non-gaussianity emerges with
constant (or local) non-linearity parameter $f_{NL}\sim 20$, in addition to the
terms with non-constant $f_{NL}$ which are characteristic of warm inflation. | 1102.2833v2 |
2012-11-15 | Bondi accretion onto cosmological black holes | In this paper we investigate a steady accretion within the Einstein-Straus
vacuole, in the presence of the cosmological constant. The dark energy damps
the mass accretion rate and --- above certain limit --- completely stops the
steady accretion onto black holes, which in particular is prohibited in the
inflation era and after (roughly) $10^{12}$ years from Big Bang (assuming the
presently known value of the cosmological constant). Steady accretion would not
exist in the late phases of the Penrose's scenario - known as the Weyl
curvature hypothesis - of the evolution of the Universe. | 1211.3618v2 |
2015-02-10 | Tunable subwavelength strong absorption by graphene wrapped dielectric particles | The optical absorption properties of graphene wrapped dielectric particles
have been investigated by using Mie scattering theory and exact
multi-scattering method. It is shown that subwavelength strong absorption in
infrared spectra can take place in such systems due to the excitation of
plasmon resonance in graphene. The absorption characteristics and efficiency
are tunable by varying Fermi level and damping constant of graphene, or by
changing size and dielectric constant of small particles. For a cluster of
these particles, the absorption characteristics are also affected by the
separation distance between them. These extreme light resonances and
absorptions in graphene wrapped nanostructures have great potential for
opto-electronic devices. | 1502.02913v1 |
2015-02-25 | Barotropic FRW cosmologies with Chiellini damping in comoving time | For non-zero cosmological constant Lambda, we show that the barotropic FRW
cosmologies as worked out in the comoving time lead in the radiation-dominated
case to scale factors of identical form as for the Chiellini dissipative scale
factors in conformal time obtained recently by us in Phys. Lett. A 379 (2015)
882-887. This is due to the Ermakov equation which is obtained in this case.
For zero cosmological constant, several textbook solutions are provided as
particular cases of Lambda different from zero. | 1502.07033v2 |
2022-01-27 | Thermodynamics of the classical spin triangle | The classical spin system consisting of three spins with Heisenberg
interaction is an example of a completely integrable mechanical system. In this
paper we explicitly calculate thermodynamic quantities as density of states,
specific heat, susceptibility and spin autocorrelation functions. These
calculations are performed (semi-)analytically and shown to agree with
corresponding Monte Carlo simulations. For the long-time autocorrelation
function, we find, for certain values of the coupling constants, a decay to
constant values in the form of an $1/t$ damped harmonic oscillation and propose
a theoretical explanation. | 2201.11401v1 |
2008-05-05 | On Expanded Cyclic Codes | The paper has a threefold purpose. The first purpose is to present an
explicit description of expanded cyclic codes defined in $\GF(q^m)$. The
proposed explicit construction of expanded generator matrix and expanded parity
check matrix maintains the symbol-wise algebraic structure and thus keeps many
important original characteristics. The second purpose of this paper is to
identify a class of constant-weight cyclic codes. Specifically, we show that a
well-known class of $q$-ary BCH codes excluding the all-zero codeword are
constant-weight cyclic codes. Moreover, we show this class of codes achieve the
Plotkin bound. The last purpose of the paper is to characterize expanded cyclic
codes utilizing the proposed expanded generator matrix and parity check matrix.
We characterize the properties of component codewords of a codeword and
particularly identify the precise conditions under which a codeword can be
represented by a subbasis. Our developments reveal an alternative while more
general view on the subspace subcodes of Reed-Solomon codes. With the new
insights, we present an improved lower bound on the minimum distance of an
expanded cyclic code by exploiting the generalized concatenated structure. We
also show that the fixed-rate binary expanded Reed-Solomon codes are
asymptotically "bad", in the sense that the ratio of minimum distance over code
length diminishes with code length going to infinity. It overturns the
prevalent conjecture that they are "good" codes and deviates from the ensemble
of generalized Reed-Solomon codes which asymptotically achieves the
Gilbert-Varshamov bound. | 0805.0615v2 |
2010-03-12 | Anosov branches of dynamo spectra in one dimensional plasmas | Recently Guenther et al the globally diagonalized ${\alpha}^{2}$ dynamo
operator spectrum [J Phys A 2007) in mean field media, and its Krein space
related perturbation theory [J Phys A 2006). Earlier, an example of fast
dynamos in stretch shear and fold Anosov maps have been given by Gilbert [PRSA
[1993)). In this paper, analytical solutions representing general turbulent
dynamo filaments are obtained in resistive plasmas. When turbulent diffusivity
is present and kinetic helicity vanishes, a fast dynamo mode is obtained, and
the Anosov eigenvalue obtained. The magnetic field lays down on a Frenet 2
plane along the filaments embedded in a 3D flow. Curvature effects on fast
dynamo are also investigate. In case of weak curvature filaments the one
dimensional manifolds in plasmas present a fast dynamo action. A parallel
result has been obtained by Chicone et al [Comm Math Phys), in the case fast
dynamo spectrum in two dimensional compact Riemannian manifolds of negative
constant curvature, called Anosov spaces. While problems of embedding may
appear in their case here no embedding problems appear since the one
dimensional curved plasmas are embedded in three dimensional Euclidean spaces.
In the examples considered here, equipartion between normal and binormal
components of the magnetic field components is considered. In the opposite
case, non Anosov oscillatory, purely imaginary, branches of the spectrum are
found in dynamo manifold. Negative constant curvature non-compact
$\textbf{H}^{2}$ manifold, has also been used in one-component electron 2D
plasma by Fantoni and Tellez (Stat. Phys, (2008)) | 1003.2482v1 |
2014-02-07 | For-all Sparse Recovery in Near-Optimal Time | An approximate sparse recovery system in $\ell_1$ norm consists of parameters
$k$, $\epsilon$, $N$, an $m$-by-$N$ measurement $\Phi$, and a recovery
algorithm, $\mathcal{R}$. Given a vector, $\mathbf{x}$, the system approximates
$x$ by $\widehat{\mathbf{x}} = \mathcal{R}(\Phi\mathbf{x})$, which must satisfy
$\|\widehat{\mathbf{x}}-\mathbf{x}\|_1 \leq
(1+\epsilon)\|\mathbf{x}-\mathbf{x}_k\|_1$. We consider the 'for all' model, in
which a single matrix $\Phi$, possibly 'constructed' non-explicitly using the
probabilistic method, is used for all signals $\mathbf{x}$. The best existing
sublinear algorithm by Porat and Strauss (SODA'12) uses $O(\epsilon^{-3}
k\log(N/k))$ measurements and runs in time $O(k^{1-\alpha}N^\alpha)$ for any
constant $\alpha > 0$.
In this paper, we improve the number of measurements to $O(\epsilon^{-2} k
\log(N/k))$, matching the best existing upper bound (attained by super-linear
algorithms), and the runtime to $O(k^{1+\beta}\textrm{poly}(\log
N,1/\epsilon))$, with a modest restriction that $\epsilon \leq (\log k/\log
N)^{\gamma}$, for any constants $\beta,\gamma > 0$. When $k\leq \log^c N$ for
some $c>0$, the runtime is reduced to $O(k\textrm{poly}(N,1/\epsilon))$. With
no restrictions on $\epsilon$, we have an approximation recovery system with $m
= O(k/\epsilon \log(N/k)((\log N/\log k)^\gamma + 1/\epsilon))$ measurements. | 1402.1726v2 |
2016-07-15 | Influence of grain size and exchange interaction on the LLB modeling procedure | Reliably predicting bit-error rates in realistic heat-assisted magnetic
recording simulations is a challenging task. Integrating the
Landau-Lifshitz-Bloch (LLB) equation can reduce the computational effort to
determine the magnetization dynamics in the vicinity of the Curie temperature.
If one aims that these dynamics coincide with trajectories calculated from the
atomistic Landau-Lifshitz-Gilbert equation, one has to carefully model required
temperature dependent material functions such as the zero-field equilibrium
magnetization as well as the parallel and normal susceptibilities. We present
an extensive study on how these functions depend on grain size and exchange
interactions. We show that, if the size or the exchange constant of a reference
grain is modified, the material functions can be scaled, according to the
changed Curie temperature, yielding negligible errors. This is shown to be
valid for volume changes of up to $\pm 40$ % and variations of the exchange
constant of up to $\pm10$ %. Besides the temperature dependent material curves,
computed switching probabilities also agree well with probabilities separately
determined for each system. Our study suggest that there is no need to
recalculate the required LLB input functions for each particle. Within the
presented limits it is sufficient to scale them to the Curie temperature of the
altered system. | 1607.04480v1 |
2023-05-30 | Hardness of Approximation in PSPACE and Separation Results for Pebble Games | We consider the pebble game on DAGs with bounded fan-in introduced in
[Paterson and Hewitt '70] and the reversible version of this game in [Bennett
'89], and study the question of how hard it is to decide exactly or
approximately the number of pebbles needed for a given DAG in these games. We
prove that the problem of eciding whether $s$~pebbles suffice to reversibly
pebble a DAG $G$ is PSPACE-complete, as was previously shown for the standard
pebble game in [Gilbert, Lengauer and Tarjan '80]. Via two different graph
product constructions we then strengthen these results to establish that both
standard and reversible pebbling space are PSPACE-hard to approximate to within
any additive constant. To the best of our knowledge, these are the first
hardness of approximation results for pebble games in an unrestricted setting
(even for polynomial time). Also, since [Chan '13] proved that reversible
pebbling is equivalent to the games in [Dymond and Tompa '85] and [Raz and
McKenzie '99], our results apply to the Dymond--Tompa and Raz--McKenzie games
as well, and from the same paper it follows that resolution depth is
PSPACE-hard to determine up to any additive constant. We also obtain a
multiplicative logarithmic separation between reversible and standard pebbling
space. This improves on the additive logarithmic separation previously known
and could plausibly be tight, although we are not able to prove this. We leave
as an interesting open problem whether our additive hardness of approximation
result could be strengthened to a multiplicative bound if the computational
resources are decreased from polynomial space to the more common setting of
polynomial time. | 2305.19104v1 |
2010-02-22 | Transport and magnetization dynamics in a superconductor/single-molecule magnet/superconductor junction | We study dc-transport and magnetization dynamics in a junction of arbitrary
transparency consisting of two spin-singlet superconducting leads connected via
a single classical spin precessing at the frequency $\Omega$. The presence of
the spin in the junction provides different transmission amplitudes for spin-up
and spin-down quasiparticles as well as a time-dependent spin-flip transmission
term. For a phase biased junction, we show that a steady-state superconducting
charge current flows through the junction and that an out-of-equilibrium
circularly polarized spin current, of frequency $\Omega$, is emitted in the
leads. Detailed understanding of the charge and spin currents is obtained in
the entire parameter range. In the adiabatic regime, $\hbar \Omega \ll 2\Delta$
where $\Delta$ is the superconducting gap, and for high transparencies of the
junction, a strong suppression of the current takes place around $\vp \approx
0$ due to an abrupt change in the occupation of the Andreev bound-states. At
higher values of the phase and/or precession frequency, extended
(quasi-particle like) states compete with the bound-states in order to carry
the current. Well below the superconducting transition, these results are shown
to be weakly affected by the back-action of the spin current on the dynamics of
the precessing spin. Indeed, we show that the Gilbert damping due to the
quasi-particle spin current is strongly suppressed at low-temperatures, which
goes along with a shift of the precession frequency due to the condensate. The
results obtained may be of interest for on-going experiments in the field of
molecular spintronics. | 1002.3929v4 |
2013-06-18 | Baryons do trace dark matter 380,000 years after the big bang: Search for compensated isocurvature perturbations with WMAP 9-year data | Primordial isocurvature fluctuations between photons and either neutrinos or
non-relativistic species such as baryons or dark matter are known to be
sub-dominant to adiabatic fluctuations. Perturbations in the relative densities
of baryons and dark matter (known as compensated isocurvature perturbations, or
CIPs), however, are surprisingly poorly constrained. CIPs leave no imprint in
the cosmic microwave background (CMB) on observable scales, at least at linear
order in their amplitude and zeroth order in the amplitude of adiabatic
perturbations. It is thus not yet empirically known if baryons trace dark
matter at the surface of last scattering. If CIPs exist, they would spatially
modulate the Silk damping scale and acoustic horizon, causing distinct
fluctuations in the CMB temperature/polarization power spectra across the sky:
this effect is first order in both the CIP and adiabatic mode amplitudes. Here,
temperature data from the Wilkinson Microwave Anisotropy Probe (WMAP) are used
to conduct the first CMB-based observational search for CIPs, using
off-diagonal correlations and the CMB trispectrum. Reconstruction noise from
weak lensing and point sources is shown to be negligible for this data set. No
evidence for CIPs is observed, and a 95%-confidence upper limit of $1.1\times
10^{-2}$ is imposed to the amplitude of a scale-invariant CIP power spectrum.
This limit agrees with CIP sensitivity forecasts for WMAP, and is competitive
with smaller scale constraints from measurements of the baryon fraction in
galaxy clusters. It is shown that the root-mean-squared CIP amplitude on 5-100
degree scales is smaller than 0.07-0.17 (depending on the scale) at the
95%-confidence level. Temperature data from the Planck satellite will provide
an even more sensitive probe for the existence of CIPs, as will the upcoming
ACTPol and SPTPol experiments on smaller angular scales. | 1306.4319v1 |
2016-04-28 | Dynamics of skyrmionic states in confined helimagnetic nanostructures | In confined helimagnetic nanostructures, skyrmionic states in the form of
incomplete and isolated skyrmion states can emerge as the ground state in
absence of both external magnetic field and magnetocrystalline anisotropy. In
this work, we study the dynamic properties (resonance frequencies and
corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples.
We employ two different methods in finite-element based micromagnetic
simulation: eigenvalue and ringdown method. The eigenvalue method allows us to
identify all resonance frequencies and corresponding eigenmodes that can exist
in the simulated system. However, using a particular experimentally feasible
excitation can excite only a limited set of eigenmodes. Because of that, we
perform ringdown simulations that resemble the experimental setup using both
in-plane and out-of-plane excitations. In addition, we report the nonlinear
dependence of resonance frequencies on the external magnetic bias field and
disk sample diameter and discuss the possible reversal mode of skyrmionic
states. We compare the power spectral densities of incomplete skyrmion and
isolated skyrmion states and observe several key differences that can
contribute to the experimental identification of the state present in the
sample. We measure the FeGe Gilbert damping, and using its value we determine
what eigenmodes can be expected to be observed in experiments. Finally, we show
that neglecting the demagnetisation energy contribution or ignoring the
magnetisation variation in the out-of-film direction - although not changing
the eigenmode's magnetisation dynamics significantly - changes their resonance
frequencies substantially. Apart from contributing to the understanding of
skyrmionic states physics, this systematic work can be used as a guide for the
experimental identification of skyrmionic states in confined helimagnetic
nanostructures. | 1604.08347v2 |
2017-08-25 | Role of dimensional crossover on spin-orbit torque efficiency in magnetic insulator thin films | Magnetic insulators (MIs) attract tremendous interest for spintronic
applications due to low Gilbert damping and absence of Ohmic loss. Magnetic
order of MIs can be manipulated and even switched by spin-orbit torques (SOTs)
generated through spin Hall effect and Rashba-Edelstein effect in heavy
metal/MI bilayers. SOTs on MIs are more intriguing than magnetic metals since
SOTs cannot be transferred to MIs through direct injection of electron spins.
Understanding of SOTs on MIs remains elusive, especially how SOTs scale with
the film thickness. Here, we observe the critical role of dimensionality on the
SOT efficiency by systematically studying the MI layer thickness dependent SOT
efficiency in tungsten/thulium iron garnet (W/TmIG) bilayers. We first show
that the TmIG thin film evolves from two-dimensional to three-dimensional
magnetic phase transitions as the thickness increases, due to the suppression
of long-wavelength thermal fluctuation. Then, we report the significant
enhancement of the measured SOT efficiency as the thickness increases. We
attribute this effect to the increase of the magnetic moment density in concert
with the suppression of thermal fluctuations. At last, we demonstrate the
current-induced SOT switching in the W/TmIG bilayers with a TmIG thickness up
to 15 nm. The switching current density is comparable with those of heavy
metal/ferromagnetic metal cases. Our findings shed light on the understanding
of SOTs in MIs, which is important for the future development of ultrathin
MI-based low-power spintronics. | 1708.07584v2 |
2018-07-04 | Phase Boundary Exchange Coupling in the Mixed Magnetic Phase Regime of a Pd-doped FeRh Epilayer | Spin-wave resonance measurements were performed in the mixed magnetic phase
regime of a Pd-doped FeRh epilayer that appears as the first-order
ferromagnetic-antiferromagnetic phase transition takes place. It is seen that
the measured value of the exchange stiffness is suppressed throughout the
measurement range when compared to the expected value of the fully
ferromagnetic regime, extracted via the independent means of a measurement of
the Curie point, for only slight changes in the ferromagnetic volume fraction.
This behavior is attributed to the influence of the antiferromagnetic phase:
inspired by previous experiments that show ferromagnetism to be most persistent
at the surfaces and interfaces of FeRh thin films, we modelled the
antiferromagnetic phase as forming a thin layer in the middle of the epilayer
through which the two ferromagnetic layers are coupled up to a certain critical
thickness. The development of this exchange stiffness is then consistent with
that expected from the development of an exchange coupling across the magnetic
phase boundary, as a consequence of a thickness dependent phase transition
taking place in the antiferromagnetic regions and is supported by complimentary
computer simulations of atomistic spin-dynamics. The development of the Gilbert
damping parameter extracted from the ferromagnetic resonance investigations is
consistent with this picture. | 1807.01615v6 |
2018-07-26 | EPIC 246851721 b: A Tropical Jupiter Transiting a Rapidly Rotating Star in a Well-Aligned Orbit | We report the discovery of EPIC 246851721 b, a "tropical" Jupiter in a
6.18-day orbit around the bright ($V=11.439$) star EPIC 246851721 (TYC
1283-739-1). We present a detailed analysis of the system using $K2$ and
ground-based photometry, radial velocities, Doppler tomography and adaptive
optics imaging. From our global models, we infer that the host star is a
rapidly rotating ($v \sin i = 74.92 $ km s$^{-1}$) F dwarf with
$T_\mathrm{eff}$ = 6202 K, $R_\star = 1.586 \ R_\odot$ and $M_\star= 1.317 \
M_\odot$. EPIC 246851721 b has a radius of $1.051 \pm 0.044 R_J$, and a mass of
3.0$^{+1.1}_{-1.2} M_J$ . Doppler tomography reveals an aligned spin-orbit
geometry, with a projected obliquity of $-1.47^{\circ\ +0.87}_{\ -0.86}$,
making EPIC 246851721 the fourth hottest star to host a Jovian planet with $P >
5$ days and a known obliquity. Using quasi-periodic signatures in its light
curve that appear to be spot modulations, we estimate the star's rotation
period, and thereby infer the true obliquity of the system to be $3.7^{\circ\
+3.7}_{\ -1.8}$. We argue that this near-zero obliquity is likely to be
primordial rather than a result of tidal damping. The host star also has a
bound stellar companion, a $0.4 \ M_\odot$ M dwarf at a projected separation of
2100 AU, but the companion is likely incapable of emplacing EPIC 246851721 b in
its current orbit via high eccentricity Kozai-Lidov migration. | 1807.10298v2 |
2017-04-13 | Low energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu$_2$OSeO$_3$ | In this work, we present a comprehensive study of the low energy optical
magnetic response of the skyrmionic Mott insulator Cu$_2$OSeO$_3$ via high
resolution time-domain THz spectroscopy. In zero field, a new magnetic
excitation not predicted by spin-wave theory with frequency $f$ = 2.03 THz is
observed and shown, with accompanying time-of-flight neutron scattering
experiments, to be a zone folded magnon from the $\mathrm{R}$ to
$\mathrm{\Gamma}$ points of the Brillouin zone. Highly sensitive polarimetry
experiments performed in weak magnetic fields, $\mu_0$H $<$ 200 mT, observe
Faraday and Kerr rotations which are proportional to the sample magnetization,
allowing for optical detection of the skyrmion phase and construction of a
magnetic phase diagram. From these measurements, we extract a critical exponent
of $\beta$ = 0.35 $\pm$ 0.04, in good agreement with the expected value for the
3D Heisenberg universality class of $\beta$ = 0.367. In large magnetic fields,
$\mu_0$H $>$ 5 T, we observe the magnetically active uniform mode of the
ferrimagnetic field polarized phase whose dynamics as a function of field and
temperature are studied. In addition to extracting a $g_\text{eff}$ = 2.08
$\pm$ 0.03, we observe the uniform mode to decay through a non-Gilbert damping
mechanism and to possesses a finite spontaneous decay rate, $\Gamma_0$
$\approx$ 25 GHz, in the zero temperature limit. Our observations are
attributed to Dzyaloshinkii-Moriya interactions, which have been proposed to be
exceptionally strong in Cu$_2$OSeO$_3$ and are expected to impact the low
energy magnetic response of such chiral magnets. | 1704.04228v1 |
2018-09-10 | Magnetic properties and field-driven dynamics of chiral domain walls in epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers | Chiral domain walls in ultrathin perpendicularly magnetised layers have a
N\'{e}el structure stabilised by a Dzyaloshinskii-Moriya interaction (DMI) that
is generated at the interface between the ferromagnet and a heavy metal.
Different heavy metals are required above and below a ferromagnetic film in
order to generate the structural inversion asymmetry needed to ensure that the
DMI arising at the two interfaces does not cancel. Here we report on the
magnetic properties of epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers grown by
sputtering onto sapphire substrates with 0.6 nm thick Co. As $x$ rises from 0
to 1 a structural inversion asymmetry is generated. We characterise the
epilayer structure with x-ray diffraction and cross-sectional transmission
electron microscopy, revealing (111) stacking. The saturation magnetization
falls as the proximity magnetisation in Pt is reduced, whilst the perpendicular
magnetic anisotropy $K_\mathrm{u}$ rises. The micromagnetic DMI strength $D$
was determined using the bubble expansion technique and also rises from a
negligible value when $x=0$ to $\sim 1$ mJ/m$^2$ for $x = 1$. The depinning
field at which field-driven domain wall motion crosses from the creep to the
depinning regime rises from $\sim 40$ to $\sim 70$ mT, attributed to greater
spatial fluctuations of the domain wall energy with increasing Au
concentration. Meanwhile, the increase in DMI causes the Walker field to rise
from $\sim 10$ to $\sim 280$ mT, meaning that only in the $x = 1$ sample is the
steady flow regime accessible. The full dependence of domain wall velocity on
driving field bears little resemblance to the prediction of a simple
one-dimensional model, but can be described very well using micromagnetic
simulations with a realistic model of disorder. These reveal a rise in Gilbert
damping as $x$ increases. | 1809.03217v2 |
2019-09-06 | Macrospin analysis of RF excitations within fully perpendicular magnetic tunnel junctions with second order easy-axis magnetic anisotropy contribution | The conditions of field and voltage for inducing steady state excitations in
fully perpendicular magnetic tunnel junctions (pMTJs), adapted for memory
applications, were numerically investigated by the resolution of the
Landau-Lifshitz-Gilbert equation in the macrospin approach. Both damping-like
and the field-like spin transfer torque terms were taken into account in the
simulations, as well as the contribution of the second order uniaxial
anisotropy term (K2), which has been recently revealed in MgO-based pMTJs. An
in-plane applied magnetic field balances the out of plane symmetry of the pMTJ
and allows the signal detection. Using this model, we assessed the states of
the free layer magnetization as a function of strength of K2 and polar theta_H
angle of the applied field (varied from 90 to 60 deg.). There are two stable
states, with the magnetization in-plane or out of plane of the layer, and two
dynamic states with self-sustained oscillations, called in-plane precession
state (IPP) or out of plane precession state (OPP). The IPP mode, with
oscillation frequencies up to 7 GHz, appears only for positive voltages if
theta_H = 90 deg. However, it shows a more complex distribution when the field
is slightly tilted out of plane. The OPP mode is excited only if K2 is
considered and reaches a maximum oscillation frequency of 15 GHz. Large areas
of dynamic states with high frequencies are obtained for strong values of the
field-like torque and K2, when applying a slightly tilted external field toward
the out of plane direction. The non-zero temperature does not modify the phase
diagrams, but reduces drastically the power spectral density peak amplitudes. | 1909.02926v1 |
2021-04-21 | Atomic Layer Deposition of Yttrium Iron Garnet Thin Films for 3D Magnetic Structures | A wide variety of new phenomena such as novel magnetization configurations
have been predicted to occur in three dimensional magnetic nanostructures.
However, the fabrication of such structures is often challenging due to the
specific shapes required, such as magnetic tubes and spirals. Furthermore, the
materials currently used to assemble these structures are predominantly
magnetic metals that do not allow to study the magnetic response of the system
separately from the electronic one. In the field of spintronics, the
prototypical material used for such experiments is the ferrimagnetic insulator
yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$, YIG). YIG is one of the best
materials especially for magnonic studies due to its low Gilbert damping. Here,
we report the first successful fabrication of YIG thin films via atomic layer
deposition. To that end we utilize a supercycle approach based on the
combination of sub-nanometer thin layers of the binary systems Fe$_2$O$_3$ and
Y$_2$O$_3$ in the correct atomic ratio on Y$_3$Al$_5$O$_{12}$ substrates with a
subsequent annealing step. Our process is robust against typical growth-related
deviations, ensuring a good reproducibility. The ALD-YIG thin films exhibit a
good crystalline quality as well as magnetic properties comparable to other
deposition techniques. One of the outstanding characteristics of atomic layer
deposition is its ability to conformally coat arbitrarily-shaped substrates.
ALD hence is the ideal deposition technique to grant an extensive freedom in
choosing the shape of the magnetic system. The atomic layer deposition of YIG
enables the fabrication of novel three dimensional magnetic nanostructures,
which in turn can be utilized for experimentally investigating the phenomena
predicted in those structures. | 2104.10293v2 |
2023-08-07 | $\textit{In situ}$ electric-field control of ferromagnetic resonance in the low-loss organic-based ferrimagnet V[TCNE]$_{x\sim 2}$ | We demonstrate indirect electric-field control of ferromagnetic resonance
(FMR) in devices that integrate the low-loss, molecule-based, room-temperature
ferrimagnet vanadium tetracyanoethylene (V[TCNE]$_{x \sim 2}$) mechanically
coupled to PMN-PT piezoelectric transducers. Upon straining the V[TCNE]$_x$
films, the FMR frequency is tuned by more than 6 times the resonant linewidth
with no change in Gilbert damping for samples with $\alpha = 6.5 \times
10^{-5}$. We show this tuning effect is due to a strain-dependent magnetic
anisotropy in the films and find the magnetoelastic coefficient $|\lambda_S|
\sim (1 - 4.4)$ ppm, backed by theoretical predictions from DFT calculations
and magnetoelastic theory. Noting the rapidly expanding application space for
strain-tuned FMR, we define a new metric for magnetostrictive materials,
$\textit{magnetostrictive agility}$, given by the ratio of the magnetoelastic
coefficient to the FMR linewidth. This agility allows for a direct comparison
between magnetostrictive materials in terms of their comparative efficacy for
magnetoelectric applications requiring ultra-low loss magnetic resonance
modulated by strain. With this metric, we show V[TCNE]$_x$ is competitive with
other magnetostrictive materials including YIG and Terfenol-D. This combination
of ultra-narrow linewidth and magnetostriction in a system that can be directly
integrated into functional devices without requiring heterogeneous integration
in a thin-film geometry promises unprecedented functionality for electric-field
tuned microwave devices ranging from low-power, compact filters and circulators
to emerging applications in quantum information science and technology. | 2308.03353v1 |
2023-08-18 | Large thermo-spin effects in Heusler alloy based spin-gapless semiconductor thin films | Recently, Heusler alloys-based spin gapless semiconductors (SGSs) with high
Curie temperature (TC) and sizeable spin polarization have emerged as potential
candidates for tunable spintronic applications. We report comprehensive
investigation of the temperature dependent ANE and intrinsic longitudinal spin
Seebeck effect (LSSE) in CoFeCrGa thin films grown on MgO substrates. Our
findings show the anomalous Nernst coefficient for the MgO/CoFeCrGa (95 nm)
film is $\cong 1.86$ micro V/K at room temperature which is nearly two orders
of magnitude higher than that of the bulk polycrystalline sample of CoFeCrGa (=
0.018 micro V/K) but comparable to that of the magnetic Weyl semimetal Co2MnGa
thin film (2-3 micro V/K). Furthermore, the LSSE coefficient for our
MgO/CoFeCrGa(95nm)/Pt(5nm) heterostructure is $\cong 20.5$ $\mu$V/K/$\Omega$ at
room temperature which is twice larger than that of the half-metallic
ferromagnetic La$_{0.7}$Sr$_{0.3}$MnO$_3$ thin films ($\cong$ 20.5
$\mu$V/K/$\Omega$). We show that both ANE and LSSE coefficients follow
identical temperature dependences and exhibit a maximum at $\cong$ 225 K which
is understood as the combined effects of inelastic magnon scatterings and
reduced magnon population at low temperatures. Our analyses not only indicate
that the extrinsic skew scattering is the dominating mechanism for ANE in these
films but also provide critical insights into the functional form of the
observed temperature dependent LSSE at low temperatures. Furthermore, by
employing radio frequency transverse susceptibility and broadband ferromagnetic
resonance in combination with the LSSE measurements, we establish a correlation
among the observed LSSE signal, magnetic anisotropy and Gilbert damping of the
CoFeCrGa thin films, which will be beneficial for fabricating tunable and
highly efficient Heusler alloys based spincaloritronic nanodevices. | 2308.09843v1 |
2009-10-28 | Nonlinear envelope equation and nonlinear Landau damping rate for a driven electron plasma wave | In this paper, we provide a theoretical description, and calculate, the
nonlinear frequency shift, group velocity and collionless damping rate, $\nu$,
of a driven electron plasma wave (EPW). All these quantities, whose physical
content will be discussed, are identified as terms of an envelope equation
allowing one to predict how efficiently an EPW may be externally driven. This
envelope equation is derived directly from Gauss law and from the investigation
of the nonlinear electron motion, provided that the time and space rates of
variation of the EPW amplitude, $E_p$, are small compared to the plasma
frequency or the inverse of the Debye length. $\nu$ arises within the EPW
envelope equation as more complicated an operator than a plain damping rate,
and may only be viewed as such because $(\nu E_p)/E_p$ remains nearly constant
before abruptly dropping to zero. We provide a practical analytic formula for
$\nu$ and show, without resorting to complex contour deformation, that in the
limit $E_p \to 0$, $\nu$ is nothing but the Landau damping rate. We then term
$\nu$ the "nonlinear Landau damping rate" of the driven plasma wave. As for the
nonlinear frequency shift of the EPW, it is also derived theoretically and
found to assume values significantly different from previously published ones,
assuming that the wave is freely propagating. Moreover, we find no limitation
in $k \lambda_D$, $k$ being the plasma wavenumber and $\lambda_D$ the Debye
length, for a solution to the dispertion relation to exist, and want to stress
here the importance of specifying how an EPW is generated to discuss its
properties. Our theoretical predictions are in excellent agreement with results
inferred from Vlasov simulations of stimulated Raman scattering (SRS), and an
application of our theory to the study of SRS is presented. | 0910.5289v1 |
2014-10-17 | Hunting down systematics in baryon acoustic oscillations after cosmic high noon | Future dark energy experiments will require better and more accurate
theoretical predictions for the baryonic acoustic oscillations (BAO) signature
in the spectrum of cosmological perturbations. Here, we use large N-body
simulations of the \LambdaCDM Planck cosmology to study any possible systematic
shifts and damping in BAO due to the impact of nonlinear gravitational growth
of structure, scale dependent and non-local bias, and redshift-space
distortions. The effect of cosmic variance is largely reduced by dividing the
tracer power spectrum by that from a BAO-free simulation starting with the same
phases. This permits us to study with unprecedented accuracy (better than 0.02%
for dark matter and 0.07% for low-bias halos) small shifts of the pristine BAO
wavenumbers towards larger k, and non-linear damping of BAO wiggles in the
power spectrum of dark matter and halo populations in the redshift range z=0-1.
For dark matter, we provide an accurate parametrization of the evolution of
\alpha as a function of the linear growth factor D(z). For halo samples, with
bias ranging from 1.2 to 2.8, we measure a typical BAO shift of ~0.25%,
observed in real-space, which does not show an appreciable evolution with
redshift within the uncertainties. Moreover, we report a constant shift as a
function of halo bias. We find a different evolution of the damping of the
acoustic feature in all halo samples as compared to dark matter with haloes
suffering less damping, and also find some weak dependence on bias. A larger
BAO shift and damping is measured in redshift-space which can be well explained
by linear theory due to redshift-space distortions. A clear modulation in phase
with the acoustic scale is observed in the scale-dependent halo bias due to the
presence of the baryonic acoustic oscillations. | 1410.4684v2 |
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