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2022-09-21
|
Asymptotic profile of L^2-norm of solutions for wave equations with critical log-damping
|
We consider wave equations with a special type of log-fractional damping. We
study the Cauchy problem for this model in the whole space, and we obtain an
asymptotic profile and optimal estimates of solutions as time goes to infinity
in L^2-sense. A maximal discovery of this note is that under the effective
damping, in case of n = 1 L^2-norm of the solution blows up in infinite time,
and in case of n = 2 L^2-norm of the solution never decays and never blows up
in infinite time. The latter phenomenon seems to be a rare case.
|
2209.10154v2
|
2022-09-25
|
Origin of Immediate Damping of Coherent Oscillations in Photoinduced Charge Density Wave Transition
|
In stark contrast to the conventional charge density wave (CDW) materials,
the one-dimensional CDW on the In/Si(111) surface exhibits immediate damping of
the CDW oscillation during the photoinduced phase transition. Here, by
successfully reproducing the experimentally observed photoinduced CDW
transition on the In/Si(111) surface by performing real-time time-dependent
density functional theory (rt-TDDFT) simulations, we demonstrate that
photoexcitation promotes valence electrons from Si substrate to empty surface
bands composed primarily of the covalent p-p bonding states of the long In-In
bonds, generating interatomic forces to shorten the long bonds and in turn
drives coherently the structural transition. We illustrate that after the
structural transition, the component of these surface bands occurs a switch
among different covalent In bonds, causing a rotation of the interatomic forces
by about {\pi}/6 and thus quickly damping the oscillations in feature CDW
modes. These findings provide a deeper understanding of photoinduced phase
transitions.
|
2209.12135v1
|
2022-10-11
|
QKD in the NISQ era: enhancing secure key rates via quantum error correction
|
Error mitigation is one of the key challenges in realising the full potential
of quantum cryptographic protocols. Consequently, there is a lot of interest in
adapting techniques from quantum error correction (QEC) to improve the
robustness of quantum cryptographic protocols. In this work, we benchmark the
performance of different QKD protocols on noisy quantum devices, with and
without error correction. We obtain the secure key rates of BB84, B92 and BBM92
QKD protocols over a quantum channel that is subject to amplitude-damping
noise. We demonstrate, theoretically and via implementations on the IBM quantum
processors, that B92 is the optimal protocol under amplitude-damping and
generalized amplitude-damping noise. We then show that the security of the
noisy BBM92 protocol crucially depends on the type and the mode of distribution
of an entangled pair. Finally, we implement an error-corrected BB84 protocol
using dual-rail encoding on a noisy quantum processor, and show that the
dual-rail BB84 implementation outperforms the conventional BB84 in the presence
of noise. Our secure key rate calculation also takes into account the effects
of CNOT imperfections on the error rates of the protocols.
|
2210.05297v1
|
2022-10-17
|
Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{PT}$ symmetry, K symmetry and localized damping
|
We study an imaginary stark ladder model and propose a realization of the
model in a dissipative chain with linearly increasing site-dependent
dissipation strength. Due to the existence of a $K$-symmetry and passive
$\mathcal{PT}$ symmetry, the model exhibits quite different feature from its
Hermitian counterpart. With the increase of dissipation strength, the system
first undergoes a passive $\mathcal{PT}$-symmetry breaking transition, with the
shifted eigenvalues changing from real to complex, and then a $K$-symmetry
restoring transition, characterized by the emergence of pure imaginary spectrum
with equal spacing. Accordingly, the eigenstates change from
$\mathcal{PT}$-unbroken extended states to the $\mathcal{PT}$-broken states,
and finally to stark localized states. In the framework of the quantum open
system governed by Lindblad equation with linearly increasing site-dependent
dissipation, we unveil that the dynamical evolution of single particle
correlation function is governed by the Hamiltonian of the imaginary stark
ladder model. By studying the dynamical evolution of the density distribution
under various initial states, we demonstrate that the damping dynamics displays
distinct behaviors in different regions. A localized damping is observed in the
strong dissipation limit.
|
2210.08725v3
|
2022-10-18
|
A quasi-local inhomogeneous dielectric tensor for arbitrary distribution functions
|
Treatments of plasma waves usually assume homogeneity, but the parallel
gradients ubiquitous in plasmas can modify wave propagation and absorption. We
derive a quasilocal inhomogeneous correction to the plasma dielectric for
arbitrary distributions by expanding the phase correlation integral and develop
a novel integration technique that allows our correction to be applied in many
situations and has greater accuracy than other inhomogeneous dielectric
formulas found in the literature. We apply this dielectric tensor to the
lower-hybrid current drive problem and demonstrate that inhomogeneous wave
damping does not affect the lower-hybrid wave's linear damping condition, and
in the non-Maxwellian problem damping and propagation should remain unchanged
except in the case of waves with very large phase velocities.
|
2210.10214v1
|
2022-11-04
|
On the collisional damping of plasma velocity space instabilities
|
For plasma velocity space instabilities driven by particle distributions
significantly deviated from a Maxwellian, weak collisions can damp the
instabilities by an amount that is significantly beyond the collisional rate
itself. This is attributed to the dual role of collisions that tend to relax
the plasma distribution toward a Maxwellian and to suppress the linearly
perturbed distribution function. The former effect can dominate in cases where
the unstable non-Maxwellian distribution is driven by collisionless transport
on a time scale much shorter than that of collisions, and the growth rate of
the ideal instability has a sensitive dependence on the distribution function.
The whistler instability driven by electrostatically trapped electrons is used
as an example to elucidate such a strong collisional damping effect of plasma
velocity space instabilities, which is confirmed by first-principles kinetic
simulations.
|
2211.02723v3
|
2022-11-12
|
Exponential Stability and exact controllability of a system of coupled wave equations by second order terms (via Laplacian) with only one non-smooth local damping
|
The purpose of this work is to investigate the exponential stability of a
second order coupled wave equations by laplacian with one locally internal
viscous damping. Firstly, using a unique continuation theorem combined with a
Carleman estimate, we prove that our system is strongly stable without any
geometric condition. Secondly, using a combination of the multiplier techniques
and the frequency domain approach, we show that our system is exponentially
stable under \textbf{(PMGC)} condition on the damping region without any
restriction on wave propagation speed (i.e whether the two wave equations
propagate at the same speed or not)
|
2211.06706v2
|
2022-11-10
|
Generalized Bagley-Torvik Equation and Fractional Oscillators
|
In this paper the Bagley-Torvik Equation is considered with the order of the
damping term allowed to range between one and two. The solution is found to be
representable as a convolution of trigonometric and exponential functions with
the driving force. The properties of the effective decay rate and the
oscillation frequency with respect to the order of the fractional damping are
also studied. It is found that the effective decay rate and oscillation
frequency have a complex dependency on the order of the derivative of the
damping term and exhibit properties one might expect of a thermodynamic
Equation of state: critical point, phase change, and lambda transition.
|
2211.07575v1
|
2022-11-21
|
Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
|
In this paper we are interested in the upper bound of the lifespan estimate
for the compressible Euler system with time dependent damping and small initial
perturbations. We employ some techniques from the blow-up study of nonlinear
wave equations. The novelty consists in the introduction of tools from the
Orlicz spaces theory to handle the nonlinear term emerging from the pressure $p
\equiv p(\rho)$, which admits different asymptotic behavior for large and small
values of $\rho-1$, being $\rho$ the density. Hence we can establish, in high
dimensions $n\in\{2,3\}$, unified upper bounds of the lifespan estimate
depending only on the dimension $n$ and on the damping strength, and
independent of the adiabatic index $\gamma>1$. We conjecture our results to be
optimal. The method employed here not only improves the known upper bounds of
the lifespan for $n\in\{2,3\}$, but has potential application in the study of
related problems.
|
2211.11377v1
|
2022-11-24
|
A brief introduction to the mathematics of Landau damping
|
In these short, rather informal, expository notes I review the current state
of the field regarding the mathematics of Landau damping, based on lectures
given at the CIRM Research School on Kinetic Theory, November 14--18, 2022.
These notes are mainly on Vlasov-Poisson in $(x,v) \in \mathbb T^d \times
\mathbb R^d$ however a brief discussion of the important case of $(x,v) \in
\mathbb R^d \times \mathbb R^d$ is included at the end. The focus will be
nonlinear and these notes include a proof of Landau damping on $(x,v) \in
\mathbb T^d \times \mathbb R^d$ in the Vlasov--Poisson equations meant for
graduate students, post-docs, and others to learn the basic ideas of the
methods involved. The focus is also on the mathematical side, and so most
references are from the mathematical literature with only a small number of the
many important physics references included. A few open problems are included at
the end.
These notes are not currently meant for publication so they may not be
perfectly proof-read and the reference list might not be complete. If there is
an error or you have some references which you think should be included, feel
free to send me an email and I will correct it when I get a chance.
|
2211.13707v1
|
2022-12-04
|
Vibration suppression of a state-of-the-art wafer gripper
|
In this paper the implementation of piezoelectrics to a state-of-the-art
wafer gripper is investigated. The objective is to propose and validate a
solution method, which includes a mechanical design and control system, to
achieve at least 5% damping for two eigenmodes of a wafer gripper. This
objective serves as a 'proof of concept' to show the possibilities of
implementing a state-of-the-art damping method to an industrial application,
which in turn can be used to dampen different thin structures. The coupling
relation between the piezoelectrics and their host structure were used to
design the placement of the piezoelectric patches, together with modal analysis
data of the a state-of-the-art wafer gripper. This data had been measured
through an experimental setup. Active damping has been succesfully implemented
onto the wafer gripper where positive position feedback (PPF) is used as a
control algorithm to dampen two eigenmodes.
|
2212.01854v1
|
2022-12-20
|
Algebra of L-banded Matrices
|
Convergence is a crucial issue in iterative algorithms. Damping is commonly
employed to ensure the convergence of iterative algorithms. The conventional
ways of damping are scalar-wise, and either heuristic or empirical. Recently,
an analytically optimized vector damping was proposed for memory
message-passing (iterative) algorithms. As a result, it yields a special class
of covariance matrices called L-banded matrices. In this paper, we show these
matrices have broad algebraic properties arising from their L-banded structure.
In particular, compact analytic expressions for the LDL decomposition, the
Cholesky decomposition, the determinant after a column substitution, minors,
and cofactors are derived. Furthermore, necessary and sufficient conditions for
an L-banded matrix to be definite, a recurrence to obtain the characteristic
polynomial, and some other properties are given. In addition, we give new
derivations of the determinant and the inverse. (It's crucial to emphasize that
some works have independently studied matrices with this special structure,
named as L-matrices. Specifically, L-banded matrices are regarded as L-matrices
with real and finite entries.)
|
2212.12431v3
|
2023-01-23
|
Non-Markovianity in the time evolution of open quantum systems assessed by means of quantum state distance
|
We provide a quantitative evaluation of non-Markovianity (NM) for an XX chain
of interacting qubits with one end coupled to a reservoir. The NM of several
non-Markovian spectral densities is assessed in terms of various quantum state
distance (QSD) measures. Our approach is based on the construction of the
density matrix of the open chain, without the necessity of a master equation.
For the quantification of NM we calculate the dynamics of the QSD measures
between the Markovian-damped and various types of non-Markovian-damped cases.
Since in the literature several QSD measures, appear in forms that imply trace
preserving density matrices, we introduced appropriate modifications so as to
render them applicable to the case of decaying traces. The results produce
remarkable consistency between the various QSD measures. They also reveal a
subtle and potentially useful interplay between qubit-qubit interaction and
non-Markovian damping. Our calculations have also uncovered a surprisingly
dramatic slowing-down of dissipation by the squared Lorentzian reservoir.
|
2301.09323v2
|
2023-01-26
|
Optimisation of Power Grid Stability Under Uncertainty
|
The increased integration of intermittent and decentralised forms of power
production has eroded the stability margins of power grids and made it more
challenging to ensure reliable and secure power transmission. Reliable grid
operation requires system-scale stability in response to perturbations in
supply or load; previous studies have shown that this can be achieved by tuning
the effective damping parameters of the generators in the grid. In this paper,
we present and analyse the problem of tuning damping parameters when there is
some uncertainty in the underlying system. We show that sophisticated methods
that assume no uncertainty can yield results that are less robust than those
produced by simpler methods. We define a quantile-based metric of stability
that ensures that power grids remain stable even as worst-case scenarios are
approached, and we develop optimisation methods for tuning damping parameters
to achieve this stability. By comparing optimisation methods that rely on
different assumptions, we suggest efficient heuristics for finding parameters
that achieve highly stable and robust grids.
|
2301.11215v1
|
2023-02-11
|
Uniform stabilization for the semi-linear wave equation with nonlinear Kelvin-Voigt damping
|
This paper is concerned with the decay estimate of solutions to the
semilinear wave equation subject to two localized dampings in a bounded domain.
The first one is of the nonlinear Kelvin-Voigt type and is distributed around a
neighborhood of the boundary according to the Geometric Control Condition.
While the second one is a frictional damping and we consider it hurting the
geometric condition of control. We show uniform decay rate results of the
corresponding energy for all initial data taken in bounded sets of finite
energy phase-space. The proof is based on obtaining an observability inequality
which combines unique continuation properties and the tools of the Microlocal
Analysis Theory.
|
2302.05667v1
|
2023-02-20
|
Exponentially stable breather solutions in nonautonomous dissipative nonlinear Schrödinger lattices
|
We consider damped and forced discrete nonlinear Schr\"odinger equations on
the lattice $\mathbb{Z}$. First we establish the existence of periodic and
quasiperiodic breather solutions for periodic and quasiperiodic driving,
respectively. Notably, quasiperiodic breathers cannot exist in the system
without damping and driving. Afterwards the existence of a global uniform
attractor for the dissipative dynamics of the system is shown. For strong
dissipation we prove that the global uniform attractor has finite fractal
dimension and consists of a single trajectory that is confined to a finite
dimensional subspace of the infinite dimensional phase space, attracting any
bounded set in phase space exponentially fast. Conclusively, for strong damping
and periodic (quasiperiodic) forcing the single periodic (quasiperiodic)
breather solution possesses a finite number of modes and is exponentially
stable.
|
2302.09869v2
|
2023-02-11
|
Quasinormal modes, Hawking radiation and absorption of the massless scalar field for Bardeen black hole surrounded by perfect fluid dark matter
|
Bardeen black hole surrounded by perfect fluid dark matter for a massless
scalar field. Our result shows that the oscillation frequency of quasinormal
modes is enhanced as magnetic charge $g$ or the dark matter parameter $\alpha$
increases. For damping rate of quasinormal modes, the influence of them is
different. Specifically, the increase of dark matter parameter $\alpha$ makes
the damping rate increasing at first and then decreasing. While the damping
rate is continuously decreasing with the increase of the magnetic charge $g$.
Moreover, we find that the increase of the dark matter parameter $\alpha$
enhances the power emission spectrum whereas magnetic charge $g$ suppresses it.
This means that the lifespan of black holes increases for smaller value of
$\alpha$ and larger value of $g$ when other parameters are fixed. Finally, the
absorption cross section of the considered black hole is calculated with the
help of the partial wave approach. Our result suggests that the absorption
cross section decreases with the dark matter $\alpha$ or the magnetic charge
$g$ increasing.
|
2302.10758v1
|
2023-02-24
|
A Numerical Approach for Modeling the Shunt Damping of Thin Panels with Arrays of Separately Piezoelectric Patches
|
Two-dimensional thin plates are widely used in many aerospace and automotive
applications. Among many methods for the attenuation of vibration of these
mechanical structures, piezoelectric shunt damping is a promising way. It
enables a compact vibration damping method without adding significant mass and
volumetric occupancy. Analyzing the dynamics of these electromechanical systems
requires precise modeling tools that properly consider the coupling between the
piezoelectric elements and the host structure. This paper presents a
methodology for separately shunted piezoelectric patches for achieving higher
performance on vibration attenuation. The Rayleigh-Ritz method is used for
performing the modal analysis and obtaining the frequency response functions of
the electro-mechanical system. The effectiveness of the method is investigated
for a broader range of frequencies, and it was shown that separately shunted
piezoelectric patches are more effective.
|
2302.12525v1
|
2023-02-27
|
Enhancing quantum synchronization through homodyne measurement, noise and squeezing
|
Quantum synchronization has been a central topic in quantum nonlinear
dynamics. Despite rapid development in this field, very few have studied how to
efficiently boost synchronization. Homodyne measurement emerges as one of the
successful candidates for this task, but preferably in the semi-classical
regime. In our work, we focus on the phase synchronization of a harmonic-driven
quantum Stuart-Landau oscillator, and show that the enhancement induced by
homodyne measurement persists into the quantum regime. Interestingly, optimal
two-photon damping rates exist when the oscillator and driving are at resonance
and with a small single-photon damping rate. We also report noise-induced
enhancement in quantum synchronization when the single-photon damping rate is
sufficiently large. Apart from these results, we discover that adding a
squeezing Hamiltonian can further boost synchronization, especially in the
semi-classical regime. Furthermore, the addition of squeezing causes the
optimal two-photon pumping rates to shift and converge.
|
2302.13465v2
|
2023-03-06
|
Larmor precession in strongly correlated itinerant electron systems
|
Many-electron systems undergo a collective Larmor precession in the presence
of a magnetic field. In a paramagnetic metal, the resulting spin wave provides
insight into the correlation effects generated by the electron-electron
interaction. Here, we use dynamical mean-field theory to investigate the
collective Larmor precession in the strongly correlated regime, where dynamical
correlation effects such as quasiparticle lifetimes and non-quasiparticle
states are essential. We study the spin excitation spectrum, which includes a
dispersive Larmor mode as well as electron-hole excitations that lead to Stoner
damping. We also extract the momentum-resolved damping of slow spin waves. The
accurate theoretical description of these phenomena relies on the Ward
identity, which guarantees a precise cancellation of self-energy and vertex
corrections at long wavelengths. Our findings pave the way towards a better
understanding of spin wave damping in correlated materials.
|
2303.03468v2
|
2023-03-19
|
Asymptotic-preserving finite element analysis of Westervelt-type wave equations
|
Motivated by numerical modeling of ultrasound waves, we investigate robust
conforming finite element discretizations of quasilinear and possibly nonlocal
equations of Westervelt type. These wave equations involve either a strong
dissipation or damping of fractional-derivative type and we unify them into one
class by introducing a memory kernel that satisfies non-restrictive regularity
and positivity assumptions. As the involved damping parameter is relatively
small and can become negligible in certain (inviscid) media, it is important to
develop methods that remain stable as the said parameter vanishes. To this end,
the contributions of this work are twofold. First, we determine sufficient
conditions under which conforming finite element discretizations of (non)local
Westervelt equations can be made robust with respect to the dissipation
parameter. Secondly, we establish the rate of convergence of the semi-discrete
solutions in the singular vanishing dissipation limit. The analysis hinges upon
devising appropriate energy functionals for the semi-discrete solutions that
remain uniformly bounded with respect to the damping parameter.
|
2303.10743v1
|
2023-03-31
|
Measurement of the cosmic p+He energy spectrum from 46 GeV to 316 TeV with the DAMPE space mission
|
Recent observations of the light component of the cosmic-ray spectrum have
revealed unexpected features that motivate further and more precise
measurements up to the highest energies. The Dark Matter Particle Explorer
(DAMPE) is a satellite-based cosmic-ray experiment that is operational since
December 2015, continuously collecting data on high-energy cosmic particles
with very good statistics, energy resolution, and particle identification
capabilities. In this work, the latest measurements of the energy spectrum of
proton+helium in the energy range from 46 GeV to 316 TeV are presented. Among
the most distinctive features of the spectrum, a spectral hardening at
$\sim$600 GeV has been observed, along with a softening at $\sim$29 TeV
measured with a 6.6$\sigma$ significance. Moreover, by measuring the energy
spectrum up to 316 TeV, a strong link is established between space- and
ground-based experiments, also suggesting the presence of a second hardening at
$\sim$150 TeV.
|
2304.00137v4
|
2023-04-18
|
Edge-selective extremal damping from topological heritage of dissipative Chern insulators
|
One of the most important practical hallmarks of topological matter is the
presence of topologically protected, exponentially localised edge states at
interfaces of regions characterised by unequal topological invariants. Here, we
show that even when driven far from their equilibrium ground state, Chern
insulators can inherit topological edge features from their parent Hamiltonian.
In particular, we show that the asymptotic long-time approach of the
non-equilibrium steady state, governed by a Lindblad Master equation, can
exhibit edge-selective extremal damping. This phenomenon derives from edge
states of non-Hermitian extensions of the parent Chern insulator Hamiltonian.
The combination of (non-Hermitian) topology and dissipation hence allows to
design topologically robust, spatially localised damping patterns.
|
2304.09040v3
|
2023-04-25
|
Weakly damped bosons and precursor gap in the vicinity of an antiferromagnetic metallic transition
|
We study the electronic spectral function of a metal in the vicinity of an
antiferromagnetic (AFM) quantum critical point, focusing on a situation where
the bare bandwidth of the spin fluctuations is significantly smaller than the
Fermi energy. In this limit, we identify a range of energies where the
fermionic quasiparticles near the "hot spots'' on the Fermi surface are
strongly scattered by the quantum critical fluctuations, whereas the damping of
the AFM fluctuations by the electrons is negligible. Within a one-loop
approximation, there is a parameter range where the $T=0$ spectral function at
the hot spots has a "precursor gap'' feature, with a local maximum at a finite
frequency. However, the ratio of the bare spin wave velocity to the Fermi
velocity required to obtain a precursor gap is probably too small to explain
experiments in the electron-doped cuprate superconductors (He et al., Proc.
Natl. Acad. Sci 116, 3449 (2019)). At lower frequencies, the Landau damping of
the AFM fluctuations becomes important, and the electronic spectral function
has the familiar ${\omega}^{-1/2}$ singularity. Our one-loop perturbative
results are supported by a numerical Monte Carlo simulation of electrons
coupled to an undamped, nearly-critical AFM mode.
|
2304.12697v1
|
2023-05-04
|
Vibrational resonance in a damped and two-frequency driven system of particle on a rotating parabola
|
In the present work, we examine the role of nonlinearity in vibrational
resonance (VR) of a forced and damped form of a velocity-dependent potential
system. Many studies have focused on studying the vibrational resonance in
different potentials, like bistable potential, asymmetrically deformed
potential, and rough potential. In this connection, velocity-dependent
potential systems are very important from a physical point of view (Ex:
pion-pion interaction, cyclotrons and other electromagnetic devices influenced
by the Lorentz force, magnetrons, mass spectrometers). They also appear in
several mechanical contexts. In this paper, we consider a nonlinear dynamical
system with velocity-dependent potential along with additional damping and
driven forces, namely a particle moving on a rotating-parabola system, and
study the effect of two-frequency forcing with a wide difference in the
frequencies. We report that the system exhibits vibrational resonance in a
certain range of nonlinear strength. Using the method of separation of motions
(MSM), an analytical equation for the slow oscillations of the system is
obtained in terms of the parameters of the fast signal. The analytical
computations and the numerical studies concur well.
|
2305.02674v1
|
2023-05-06
|
Stochastic wave equation with Hölder noise coefficient: well-posedness and small mass limit
|
We construct unique martingale solutions to the damped stochastic wave
equation $$ \mu \frac{\partial^2u}{\partial t^2}(t,x)=\Delta
u(t,x)-\frac{\partial u}{\partial
t}(t,x)+b(t,x,u(t,x))+\sigma(t,x,u(t,x))\frac{dW_t}{dt},$$
where $\Delta$ is the Laplacian on $[0,1]$ with Dirichlet boundary condition,
$W$ is space-time white noise, $\sigma$ is $\frac{3}{4}+\epsilon$ -H\"older
continuous in $u$ and uniformly non-degenerate, and $b$ has linear growth. The
same construction holds for the stochastic wave equation without damping term.
More generally, the construction holds for SPDEs defined on separable Hilbert
spaces with a densely defined operator $A$, and the assumed H\"older regularity
on the noise coefficient depends on the eigenvalues of $A$ in a quantitative
way. We further show the validity of the Smoluchowski-Kramers approximation:
assume $b$ is H\"older continuous in $u$, then as $\mu$ tends to $0$ the
solution to the damped stochastic wave equation converges in distribution, on
the space of continuous paths, to the solution of the corresponding stochastic
heat equation. The latter result is new even in the case of additive noise.
|
2305.04068v2
|
2023-05-08
|
Information capacity analysis of fully correlated multi-level amplitude damping channels
|
The primary objective of quantum Shannon theory is to evaluate the capacity
of quantum channels. In spite of the existence of rigorous coding theorems that
quantify the transmission of information through quantum channels,
superadditivity effects limit our understanding of the channel capacities. In
this paper, we mainly focus on a family of channels known as multi-level
amplitude damping channels. We investigate some of the information capacities
of the simplest member of multi-level Amplitude Damping Channel, a qutrit
channel, in the presence of correlations between successive applications of the
channel. We find the upper bounds of the single-shot classical capacities and
calculate the quantum capacities associated with a specific class of maps after
investigating the degradability property of the channels. Additionally, the
quantum and classical capacities of the channels have been computed in
entanglement-assisted scenarios.
|
2305.04481v2
|
2023-05-09
|
Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain
|
Lifespan estimates for semilinear damped wave equations of the form
$\partial_t^2u-\Delta u+\partial_tu=|u|^p$ in a two dimensional exterior domain
endowed with the Dirichlet boundary condition are dealt with. For the critical
case of the semilinear heat equation $\partial_tv-\Delta v=v^2$ with the
Dirichlet boundary condition and the initial condition $v(0)=\varepsilon f$,
the corresponding lifespan can be estimated from below and above by
$\exp(\exp(C\varepsilon^{-1}))$ with different constants $C$. This paper
clarifies that the same estimates hold even for the critical semilinear damped
wave equation in the exterior of the unit ball under the restriction of radial
symmetry. To achieve this result, a new technique to control $L^1$-type norm
and a new Gagliardo--Nirenberg type estimate with logarithmic weight are
introduced.
|
2305.05124v1
|
2023-05-19
|
Cold damping of levitated optically coupled nanoparticles
|
Methods for controlling the motion of single particles, optically levitated
in vacuum, have developed rapidly in recent years. The technique of cold
damping makes use of feedback-controlled, electrostatic forces to increase
dissipation without introducing additional thermal fluctuations. This process
has been instrumental in the ground-state cooling of individual electrically
charged nanoparticles. Here we show that the same method can be applied to a
pair of nanoparticles, coupled by optical binding forces. These optical binding
forces are about three orders of magnitude stronger than typical Coulombic
inter-particle force and result in a coupled motion of both nanoparticles
characterized by a pair of normal modes. We demonstrate cold damping of these
normal modes, either independently or simultaneously, to sub-Kelvin
temperatures at pressures of 5x10^{-3} mbar. Experimental observations are
captured by a theoretical model which we use to survey the parameter space more
widely and to quantify the limits imposed by measurement noise and time delays.
Our work paves the way for the study of quantum interactions between meso-scale
particles and the exploration of multiparticle entanglement in levitated
optomechanical systems.
|
2305.11809v1
|
2023-05-25
|
Damping of three-dimensional waves on coating films dragged by moving substrates
|
Paints and coatings often feature interfacial defects due to disturbances
during the deposition process which, if they persist until solidification,
worsen the product quality. In this article, we investigate the stability of a
thin liquid film dragged by a vertical substrate moving against gravity, a flow
configuration found in a variety of coating processes. The receptivity of the
liquid film to three-dimensional disturbances is discussed with Direct
Numerical Simulations (DNS), an in-house non-linear Integral Boundary Layer
(IBL) film model, and Linear Stability Analysis (LSA). The thin film model,
successfully validated with the DNS computations, implements a pseudo-spectral
approach for the capillary terms that allows for investigating non-periodic
surface tension dominated flows. The combination of these numerical tools
allows for describing the mechanisms of capillary and non-linear damping, and
identifying the instability threshold of the coating processes. The results
show that transverse modulations can be beneficial for the damping of
two-dimensional waves within the range of operational conditions considered in
this study, typical of air-knife and slot-die coating.
|
2305.16139v3
|
2023-06-12
|
Realizable Eddy Damped Markovian Anisotropic Closure for Turbulence and Rossby Wave Interactions
|
A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented
for the interaction of two dimensional turbulence and transient waves such as
Rossby waves. The structure of the EDMAC ensures that it is as computationally
efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure but unlike
the EDQNM is guaranteed to be realizable in the presence of transient waves.
Jack Herring's important contributions to laying the foundations of statistical
dynamical closure theories of fluid turbulence are briefly reviewed. The topics
covered include equilibrium statistical mechanics, Eulerian and Lagrangian
statistical dynamical closure theories, and the statistical dynamics of the
interaction of turbulence with topography. The impact of Herring's work is
described and placed in the context of related developments. Some of the
further works that have built on Herring's foundations are discussed. The
relationships between theoretical approaches employed in statistical classical
and quantum field theories, and their overlap, are outlined. The seminal
advances made by the pioneers in strong interaction fluid turbulence are put
into perspective by comparing related developments in strong interaction
quantum filed theory.
|
2306.06921v1
|
2023-06-18
|
Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential
|
We study an inverse problem of determining a time-dependent damping
coefficient and potential appearing in the wave equation in a compact
Riemannian manifold of dimension three or higher. More specifically, we are
concerned with the case of conformally transversally anisotropic manifolds, or
in other words, compact Riemannian manifolds with boundary conformally embedded
in a product of the Euclidean line and a transversal manifold. With an
additional assumption of the attenuated geodesic ray transform being injective
on the transversal manifold, we prove that the knowledge of a certain partial
Cauchy data set determines time-dependent damping coefficient and potential
uniquely.
|
2306.10442v2
|
2023-06-26
|
Blow-up result for a weakly coupled system of wave equations with a scale-invariant damping, mass term and time derivative nonlinearity
|
We study in this article the blow-up of solutions to a coupled semilinear
wave equations which are characterized by linear damping terms in the
\textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and
Tricomi terms. The latter are specifically of great interest from both physical
and mathematical points of view since they allow the speeds of propagation to
be time-dependent ones. However, we assume in this work that both waves are
propagating with the same speeds. Employing this fact together with other
hypotheses on the aforementioned parameters (mass and damping coefficients), we
obtain a new blow-up region for the system under consideration, and we show a
lifespan estimate of the maximal existence time.
|
2306.14768v1
|
2023-06-26
|
Revisiting the damped quantum harmonic oscillator
|
We reanalyse the quantum damped harmonic oscillator, introducing three less
than common features. These are (i) the use of a continuum model of the
reservoir rather than an ensemble of discrete oscillators, (ii) an exact
diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano,
and (iii) the use of the thermofield technique for describing a finite
temperature reservoir. We recover in this way a number of well-known and some,
perhaps, less familiar results. An example of the latter is an ab initio proof
that the oscillator relaxes to the mean-force Gibbs state. We find that special
care is necessary when comparing the damped oscillator with its undamped
counterpart as the former has two distinct natural frequencies, one associated
with short time evolution and the other with longer times.
|
2306.15013v1
|
2023-06-27
|
SPDER: Semiperiodic Damping-Enabled Object Representation
|
We present a neural network architecture designed to naturally learn a
positional embedding and overcome the spectral bias towards lower frequencies
faced by conventional implicit neural representation networks. Our proposed
architecture, SPDER, is a simple MLP that uses an activation function composed
of a sinusoidal multiplied by a sublinear function, called the damping
function. The sinusoidal enables the network to automatically learn the
positional embedding of an input coordinate while the damping passes on the
actual coordinate value by preventing it from being projected down to within a
finite range of values. Our results indicate that SPDERs speed up training by
10x and converge to losses 1,500-50,000x lower than that of the
state-of-the-art for image representation. SPDER is also state-of-the-art in
audio representation. The superior representation capability allows SPDER to
also excel on multiple downstream tasks such as image super-resolution and
video frame interpolation. We provide intuition as to why SPDER significantly
improves fitting compared to that of other INR methods while requiring no
hyperparameter tuning or preprocessing.
|
2306.15242v1
|
2023-07-03
|
Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping
|
We present a new gradient-like dynamical system related to unconstrained
convex smooth multiobjective optimization which involves inertial effects and
asymptotic vanishing damping. To the best of our knowledge, this system is the
first inertial gradient-like system for multiobjective optimization problems
including asymptotic vanishing damping, expanding the ideas laid out in [H.
Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to
Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of
solutions to this system in finite dimensions and further prove that its
bounded solutions converge weakly to weakly Pareto optimal points. In addition,
we obtain a convergence rate of order $O(t^{-2})$ for the function values
measured with a merit function. This approach presents a good basis for the
development of fast gradient methods for multiobjective optimization.
|
2307.00975v3
|
2023-07-05
|
Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping
|
The paper establishes the strong convergence rates of a spatio-temporal full
discretization of the stochastic wave equation with nonlinear damping in
dimension one and two. We discretize the SPDE by applying a spectral Galerkin
method in space and a modified implicit exponential Euler scheme in time. The
presence of the super-linearly growing damping in the underlying model brings
challenges into the error analysis. To address these difficulties, we first
achieve upper mean-square error bounds, and then obtain mean-square convergence
rates of the considered numerical solution. This is done without requiring the
moment bounds of the full approximations. The main result shows that, in
dimension one, the scheme admits a convergence rate of order $\tfrac12$ in
space and order $1$ in time. In dimension two, the error analysis is more
subtle and can be done at the expense of an order reduction due to an
infinitesimal factor. Numerical experiments are performed and confirm our
theoretical findings.
|
2307.01975v1
|
2023-07-12
|
Decoherence effects on lepton number violation from heavy neutrino-antineutrino oscillations
|
We study decoherence effects and phase corrections in heavy
neutrino-antineutrino oscillations (NNOs), based on quantum field theory with
external wave packets. Decoherence damps the oscillation pattern, making it
harder to resolve experimentally. Additionally, it enhances lepton number
violation (LNV) for processes in symmetry-protected low-scale seesaw models by
reducing the destructive interference between mass eigenstates. We discuss a
novel time-independent shift in the phase and derive formulae for calculating
decoherence effects and the phase shift in the relevant regimes, which are the
no dispersion regime and transverse dispersion regime. We find that the phase
shift can be neglected in the parameter region under consideration since it is
small apart from parameter regions with large damping. In the oscillation
formulae, decoherence can be included by an effective damping parameter. We
discuss this parameter and present averaged results, which apply to simulations
of NNOs in the dilepton-dijet channel at the HL-LHC. We show that including
decoherence effects can dramatically change the theoretical prediction for the
ratio of LNV over LNC events.
|
2307.06208v1
|
2023-07-23
|
Visco-elastic damped wave models with time-dependent coefficient
|
In this paper, we study the following Cauchy problem for linear visco-elastic
damped wave models with a general time-dependent coefficient $g=g(t)$:
\begin{equation} \label{EqAbstract} \tag{$\star$} \begin{cases} u_{tt}- \Delta
u + g(t)(-\Delta)u_t=0, &(t,x) \in (0,\infty) \times \mathbb{R}^n, \\ u(0,x)=
u_0(x),\quad u_t(0,x)= u_1(x), &x \in \mathbb{R}^n. \end{cases} \end{equation}
We are interested to study the influence of the damping term $g(t)(-\Delta)u_t$
on qualitative properties of solutions to \eqref{EqAbstract} as decay estimates
for energies of higher order and the parabolic effect. The main tools are
related to WKB-analysis. We apply elliptic as well as hyperbolic WKB-analysis
in different parts of the extended phase space.
|
2307.12340v1
|
2023-07-24
|
Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature
|
It is generally accepted that the phonon gas of a superfluid always enters a
weak coupling regime at sufficiently low temperatures, whatever the strength of
the interactions between the underlying particles (constitutive of the
superfluid). Thus, in this limit, we should always be able to calculate the
damping rate of thermal phonons by applying Fermi's golden rule to the $H\_3$
Hamiltonian of cubic phonon-phonon coupling taken from quantum hydrodynamics,
at least in the case of a convex acoustic branch and in the collisionless
regime (where the eigenfrequency of the considered phonons remains much greater
than the gas thermalization rate). Using the many-body Green's function method,
we predict that, unexpectedly, this is not true in two dimensions, contrary to
the three-dimensional case. We confirm this prediction with classical
phonon-field simulations and a non-perturbative theory in $H\_3$, where the
fourth order is regularized by hand, giving a complex energy to the virtual
phonons of the four-phonon collisional processes. For a weakly interacting
fluid and a phonon mode in the long-wavelength limit, we predict a damping rate
about three times lower than that of the golden rule.
|
2307.12705v1
|
2023-08-01
|
Regularity for the Timoshenko system with fractional damping
|
We study, the Regularity of the Timoshenko system with two fractional
dampings $(-\Delta)^\tau u_t$ and $(-\Delta)^\sigma \psi_t$; both of the
parameters $(\tau, \sigma)$ vary in the interval $[0,1]$. We note that
($\tau=0$ or $\sigma=0$) and ($\tau=1$ or $\sigma=1$) the dampings are called
frictional and viscous, respectively. Our main contribution is to show that the
corresponding semigroup $S(t)=e^{\mathcal{B}t}$, is analytic for
$(\tau,\sigma)\in R_A:=[1/2,1]\times[ 1/2,1]$ and determine the Gevrey's class
$\nu>\dfrac{1}{\phi}$, where $\phi=\left\{\begin{array}{ccc}
\dfrac{2\sigma}{\sigma+1} &{\rm for} & \sigma\leq \tau,\\\\
\dfrac{2\tau}{\tau+1} &{\rm for} & \tau\leq \sigma. \end{array}\right.$ \quad
and \quad $(\tau,\sigma)\in R_{CG}:= (0,1)^2$.
|
2308.00573v2
|
2023-08-16
|
Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system
|
A new framework to obtain time-decay estimates for partially dissipative
hyperbolic systems set on the real line is developed. Under the classical
Shizuta-Kawashima (SK) stability condition, equivalent to the Kalman rank
condition in control theory, the solutions of these systems decay exponentially
in time for high frequencies and polynomially for low ones. This allows to
derive a sharp description of the space-time decay of solutions for large time.
However, such analysis relies heavily on the use of the Fourier transform that
we avoid here, developing the "physical space version" of the hyperbolic
hypocoercivity approach introduced by Beauchard and Zuazua, to prove new
asymptotic results in the linear and nonlinear settings. The new physical space
version of the hyperbolic hypocoercivity approach allows to recover the natural
heat-like time-decay of solutions under sharp rank conditions, without
employing Fourier analysis or $L^1$ assumptions on the initial data. Taking
advantage of this Fourier-free framework, we establish new enhanced time-decay
estimates for initial data belonging to weighted Sobolev spaces. These results
are then applied to the nonlinear compressible Euler equations with linear
damping. We also prove the logarithmic stability of the nonlinearly damped
$p$-system.
|
2308.08280v1
|
2023-09-06
|
Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System
|
In this work, we present a quantization scheme for the damped harmonic
oscillator (QDHO) using a framework known as momentous quantum mechanics. Our
method relies on a semiclassical dynamical system derived from an extended
classical Hamiltonian, where the phase-space variables are given by expectation
values of observables and quantum dispersions. The significance of our study
lies in its potential to serve as a foundational basis for the effective
description of open quantum systems (OQS), and the description of dissipation
in quantum mechanics. By employing the Bateman's dual model as the initial
classical framework, and undergoing quantization, we demonstrate that our
description aligns exceptionally well with the well-established Lindblad master
equation. Furthermore, our approach exhibits robustness and broad applicability
in the context of OQS, rendering it a versatile and powerful tool for studying
various phenomena. We intend to contribute to the advancement of quantum
physics by providing an effective means of quantizing the damped harmonic
oscillator and shedding light on the behavior of open quantum systems.
|
2309.02689v1
|
2023-09-09
|
Secondary cosmic-ray nuclei in the model of Galactic halo with nonlinear Landau damping
|
We employ our recent model of the cosmic-ray (CR) halo by Chernyshov et al.
(2022) to compute the Galactic spectra of stable and unstable secondary nuclei.
In this model, confinement of the Galactic CRs is entirely determined by the
self-generated Alfvenic turbulence whose spectrum is controlled by nonlinear
Landau damping. We analyze the physical parameters affecting propagation
characteristics of CRs, and estimate the best set of free parameters providing
accurate description of available observational data. We also show that
agreement with observations at lower energies may be further improved by taking
into account the effect of ion-neutral damping which operates near the Galactic
disk.
|
2309.04772v1
|
2023-09-20
|
On the damping of tidally driven oscillations
|
Expansions in the oscillation modes of tidally perturbed bodies provide a
useful framework for representing tidally induced flows. However, recent work
has demonstrated that such expansions produce inaccurate predictions for
secular orbital evolution when mode damping rates are computed independently.
We explore the coupling of collectively driven modes by frictional and viscous
dissipation, in tidally perturbed bodies that are both non-rotating and rigidly
rotating. This exploration leads us to propose an alternative approach to
treating the damping of tidally driven oscillations that accounts for
dissipative mode coupling, but which does not require any information beyond
the eigenfunctions and eigenfrequencies of adiabatic modes.
|
2309.11502v1
|
2023-09-25
|
Linearly implicit exponential integrators for damped Hamiltonian PDEs
|
Structure-preserving linearly implicit exponential integrators are
constructed for Hamiltonian partial differential equations with linear constant
damping. Linearly implicit integrators are derived by polarizing the polynomial
terms of the Hamiltonian function and portioning out the nonlinearly of
consecutive time steps. They require only a solution of one linear system at
each time step. Therefore they are computationally more advantageous than
implicit integrators. We also construct an exponential version of the
well-known one-step Kahan's method by polarizing the quadratic vector field.
These integrators are applied to one-dimensional damped Burger's,
Korteweg-de-Vries, and nonlinear Schr{\"o}dinger equations. Preservation of the
dissipation rate of linear and quadratic conformal invariants and the
Hamiltonian is illustrated by numerical experiments.
|
2309.14184v2
|
2023-10-12
|
Plasmon dispersion and Landau damping in the nonlinear quantum regime
|
We study the dispersion properties of electron plasma waves, or plasmons,
which can be excited in quantum plasmas in the nonlinear regime. In order to
describe nonlinear electron response to finite amplitude plasmons, we apply the
Volkov approach to non-relativistic electrons. For that purpose, we use the
Schr\"odinger equation and describe the electron population of a quantum plasma
as a mixture of quantum states. Within the kinetic framework that we are able
to derive from the Volkov solutions, we discuss the role of the wave amplitude
on the nonlinear plasma response. Finally, we focus on the quantum properties
of nonlinear Landau damping and study the contributions of multi-plasmon
absorption and emission processes.
|
2310.08544v1
|
2023-10-29
|
Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity
|
In this article we investigate the asymptotic profile of solutions for the
Cauchy problem of the nonlinear damped beam equation with two variable
coefficients: \[ \partial_t^2 u + b(t) \partial_t u - a(t) \partial_x^2 u +
\partial_x^4 u
= \partial_x \left( N(\partial_x u) \right). \] In the authors' previous
article [17], the asymptotic profile of solutions for linearized problem ($N
\equiv 0$) was classified depending on the assumptions for the coefficients
$a(t)$ and $b(t)$ and proved the asymptotic behavior in effective damping
cases. We here give the conditions of the coefficients and the nonlinear term
in order that the solution behaves as the solution for the heat equation: $b(t)
\partial_t u - a(t) \partial_x^2 u=0$ asymptotically as $t \to \infty$.
|
2310.18878v1
|
2023-11-09
|
Landau Damping in an Electron Gas
|
Material science methods aim at developing efficient computational schemes
for describing complex many-body effects and how they are revealed in
experimentally measurable properties. Bethe-Salpeter equation in the
self-consistent Hartree-Fock basis is often used for this purpose, and in this
paper we employ the real-frequency diagrammatic Monte Carlo framework for
solving the ladder-type Bethe-Salpeter equation for the 3-point vertex function
(and, ultimately, for the system's polarization) to study the effect of
electron-hole Coulomb scattering on Landau damping in the homogeneous electron
gas. We establish how this damping mechanism depends on the Coulomb parameter
$r_s$ and changes with temperature between the correlated liquid and thermal
gas regimes. In a broader context of dielectric response in metals, we also
present the full polarization and the typical dependence of the
exchange-correlation kernel on frequency at finite momentum and temperature
within the same computational framework.
|
2311.05611v2
|
2023-11-11
|
On asymptotic properties of solutions to $σ$-evolution equations with general double damping
|
In this paper, we would like to consider the Cauchy problem for semi-linear
$\sigma$-evolution equations with double structural damping for any $\sigma\ge
1$. The main purpose of the present work is to not only study the asymptotic
profiles of solutions to the corresponding linear equations but also describe
large-time behaviors of globally obtained solutions to the semi-linear
equations. We want to emphasize that the new contribution is to find out the
sharp interplay of ``parabolic like models" corresponding to $\sigma_1 \in
[0,\sigma/2)$ and ``$\sigma$-evolution like models" corresponding to $\sigma_2
\in (\sigma/2,\sigma]$, which together appear in an equation. In this
connection, we understand clearly how each damping term influences the
asymptotic properties of solutions.
|
2311.06660v1
|
2023-11-14
|
Enhanced classical radiation damping of electronic cyclotron motion in the vicinity of the Van Hove singularity in a waveguide
|
We study the damping process of electron cyclotron motion and the resulting
emission in a waveguide using the classical Friedrichs model without relying on
perturbation analysis such as Fermi's golden rule. A classical Van Hove
singularity appears at the lower bound (or cut-off frequency) of the dispersion
associated with each of the electromagnetic field modes in the waveguide. In
the vicinity of the Van Hove singularity, we found that not only is the decay
process associated with the resonance pole enhanced (amplification factor ~
$10^4$) but the branch-point effect is also comparably enhanced. As a result,
the timescale on which most of the decay occurs is dramatically shortened.
Further, this suggests that the non-Markovian branch point effect should be
experimentally observable in the vicinity of the Van Hove singularity. Our
treatment yields a physically-acceptable solution without the problematic
runaway solution that is well known to appear in the traditional treatment of
classical radiation damping based on the Abraham-Lorentz equation.
|
2311.08121v3
|
2023-11-18
|
The temperature dependent Boltzmann equation beyond local equilibrium assumption
|
In this manuscript, we present a temperature dependent Boltzmann equation for
the particles transport through a environmental reservoir, where the
temperature refers to the equilibrium temperature of reservoir, a new damping
force and a inverse damping relaxation time are derived based on the classical
Boltzmann equation, which have obvious influence on the external force and the
relaxation time of transport particles. For comparison, we also define a
non-equilibrium temperature for the transport particle by its distribution
function out of equilibrium, which is different from the equilibrium
temperature of reservoir. There exist heat transfer between the transport
particle and the reservoir, because the whole transport particles are in
non-equilibrium state. Finally, we illustrate them by an example of
one-dimensional transport procedure, the damping force and the non-equilibrium
temperature defined by us are shown numerically.
|
2311.11028v1
|
2023-12-13
|
Integrating Superregenerative Principles in a Compact, Power-Efficient NMR/NQR Spectrometer: A Novel Approach with Pulsed Excitation
|
We present a new approach to Nuclear Quadrupole Resonance (NQR)/Nuclear
Magnetic Resonance (NMR) spectroscopy, the Damp-Enhanced Superregenerative
Nuclear Spin Analyser (DESSA). This system integrates Superregenerative
principles with pulsed sample excitation and detection, offering significant
advancements over traditional Super-Regenerative Receivers (SRRs). Our approach
overcomes certain limitations associated with traditional Super-Regenerative
Receivers (SRRs) by integrating direct digital processing of the oscillator
response delay time (T$_d$) and an electronic damp unit to regulate the
excitation pulse decay time (T$_e$). The essence is combining pulsed excitation
with a reception inspired by, but distinct from, conventional SRRs. The damp
unit allows a rapid termination of the oscillation pulse and the initiation of
detection within microseconds, and direct digital processing avoids the need
for a second lower frequency which is used for quenching in a traditional SRRs,
thereby avoiding the formation of sidebands. We demonstrate the effectiveness
of DESSA on a \ch{NaClO3} sample containing the isotope Chlorine-35 where it
accurately detects the NQR signal with sub-kHz resolution.
|
2312.08491v1
|
2023-12-26
|
Dynamical polarization function, plasmons, their damping and collective effects in semi-Dirac bands
|
We have calculated the dynamical polarization, plasmons and damping rates in
semi-Dirac bands (SDB's) with zero band gap and half-linear, half-parabolic
low-energy spectrum. The obtained plasmon dispersions are strongly anisotropic
and demonstrate some crucial features of both two-dimensional electron gas and
graphene. Such gapless energy dispersions lead to a localized area of undamped
and low-damped plasmons in a limited range of the frequencies and wave vectors.
The calculated plasmon branches demonstrate an increase of their energies for a
finite tilting of the band structure and a fixed Fermi level which could be
used as a signature of a specific tilted spectrum in a semi-Dirac band.
|
2312.16117v1
|
2024-01-09
|
Coherent errors in stabilizer codes caused by quasistatic phase damping
|
Quantum error correction is a key challenge for the development of practical
quantum computers, a direction in which significant experimental progress has
been made in recent years. In solid-state qubits, one of the leading
information loss mechanisms is dephasing, usually modelled by phase flip
errors. Here, we introduce quasistatic phase damping, a more subtle error model
which describes the effect of Larmor frequency fluctuations due to 1/f noise.
We show how this model is different from a simple phase flip error model, in
terms of multi-cycle error correction. Considering the surface code, we provide
numerical evidence for an error threshold, in the presence of quasistatic phase
damping and readout errors. We discuss the implications of our results for spin
qubits and superconducting qubits.
|
2401.04530v2
|
2024-01-19
|
Composite learning backstepping control with guaranteed exponential stability and robustness
|
Adaptive backstepping control provides a feasible solution to achieve
asymptotic tracking for mismatched uncertain nonlinear systems. However,
input-to-state stability depends on high-gain feedback generated by nonlinear
damping terms, and closed-loop exponential stability with parameter convergence
involves a stringent condition named persistent excitation (PE). This paper
proposes a composite learning backstepping control (CLBC) strategy based on
modular backstepping and high-order tuners to compensate for the transient
process of parameter estimation and achieve closed-loop exponential stability
without the nonlinear damping terms and the PE condition. A novel composite
learning mechanism that maximizes the staged exciting strength is designed for
parameter estimation, such that parameter convergence can be achieved under a
condition of interval excitation (IE) or even partial IE that is strictly
weaker than PE. An extra prediction error is employed in the adaptive law to
ensure the transient performance without nonlinear damping terms. The
exponential stability of the closed-loop system is proved rigorously under the
partial IE or IE condition. Simulations have demonstrated the effectiveness and
superiority of the proposed method in both parameter estimation and control
compared to state-of-the-art methods.
|
2401.10785v1
|
2024-01-23
|
Model-Free $δ$-Policy Iteration Based on Damped Newton Method for Nonlinear Continuous-Time H$\infty$ Tracking Control
|
This paper presents a {\delta}-PI algorithm which is based on damped Newton
method for the H{\infty} tracking control problem of unknown continuous-time
nonlinear system. A discounted performance function and an augmented system are
used to get the tracking Hamilton-Jacobi-Isaac (HJI) equation. Tracking HJI
equation is a nonlinear partial differential equation, traditional
reinforcement learning methods for solving the tracking HJI equation are mostly
based on the Newton method, which usually only satisfies local convergence and
needs a good initial guess. Based upon the damped Newton iteration operator
equation, a generalized tracking Bellman equation is derived firstly. The
{\delta}-PI algorithm can seek the optimal solution of the tracking HJI
equation by iteratively solving the generalized tracking Bellman equation.
On-policy learning and off-policy learning {\delta}-PI reinforcement learning
methods are provided, respectively. Off-policy version {\delta}-PI algorithm is
a model-free algorithm which can be performed without making use of a priori
knowledge of the system dynamics. NN-based implementation scheme for the
off-policy {\delta}-PI algorithms is shown. The suitability of the model-free
{\delta}-PI algorithm is illustrated with a nonlinear system simulation.
|
2401.12882v1
|
2024-01-30
|
The nonlinear dynamic behavior of a Rubber-Layer Roller Bearing (RLRB) for vibration isolation
|
In this paper, we study the dynamic behavior of a Rubber-Layer Roller Bearing
(RLRB) interposed between a spring-mass elemental superstructure and a
vibrating base. Thanks to the viscoelastic rolling contact between the rigid
rollers and the rubber layers, the RLRB is able to provide a nonlinear damping
behavior. The effect of the RLRB geometric and material parameters is
investigated under periodic base excitation, showing that both periodic and
aperiodic responses can be achieved. Specifically, since the viscoelastic
damping is non-monotonic (bell shaped), there exist systemdynamic conditions
involving the decreasing portion of the damping curve in which a strongly
nonlinear behavior is experienced. In the second part of the paper, we
investigate the effectiveness of the nonlinear device in terms of seismic
isolation. Focusing on the mean shock of the Central Italy 2016 earthquake, we
opportunely tune the material and geometrical RLRB parameters, showing that a
significant reduction of both the peak and root-mean-square value of the
inertial force acting on the superstructure is achieved, compared to the best
performance of a linear base isolation system.
|
2401.16880v1
|
2024-01-30
|
Poynting-Robertson damping of laser beam driven lightsails
|
Lightsails using Earth-based lasers for propulsion require passive
stabilization to stay within the beam. This can be achieved through the sail's
scattering properties, creating optical restoring forces and torques. Undamped
restoring forces produce uncontrolled oscillations, which could jeopardize the
mission, but it is not obvious how to achieve damping in the vacuum of space.
Using a simple two-dimensional model we show that the Doppler effect and
relativistic aberration of the propelling laser beam create damping terms in
the optical forces and torques. The effect is similar to the Poynting-Robertson
effect causing loss of orbital momentum of dust particles around stars, but can
be enhanced by design of the sail's geometry.
|
2401.16924v1
|
2024-02-29
|
The Equation of Motion for Taut-Line Buzzers
|
Equations of motion are developed for the oscillatory rotation of a disk
suspended between twisted strings kept under tension by a hanging mass, to
which additional forces may be applied. In the absence of forcing, damped
harmonic oscillations are observed to decay with an exponential time envelope
for two different string types. This is consistent with damping caused by
string viscosity, rather than air turbulence, and may be quantified in terms of
a quality factor. To test the proposed equation of motion and model for viscous
damping within the string, we measure both the natural oscillation frequency
and the quality factor for widely varied values of string length, string
radius, disk moment of inertia, and hanging mass. The data are found to scale
in good accord with predictions. A variation where rotational kinetic energy is
converted back and forth to spring potential energy is also discussed.
|
2402.19285v1
|
2024-03-08
|
A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping
|
In this paper, the vibration energy localization in coupled nonlinear
oscillators is investigated, based on the creation of standing solitons. The
main objective is to establish a design methodology for mechanical lattices
using the Nonlinear Schr\"odinger Equation (NLSE) as a guide strategy, even in
the presence of damping. A three-dimensional diagram is used to illustrate
stable parameter regions for damped stationary solitons. Moreover, an analysis
of the influence of the number of oscillators in the system, and a numerical
investigation regarding the stability of solitonic behavior is done. Through
numerical analyses, it is observed that the developed algorithm not only has
the capability to locate the highest amplitudes in the chain of oscillators,
but also to control the intensity at which these amplitudes are located
according to design requirements. The outcomes of the proposed methodology
elucidate the impact that the coupling stiffness has on the stabilization of
the NLSE, as well as the influence of the number of oscillators on the
continuity hypothesis. The developed algorithm holds potential for practical
applications in mechanical engineering since the NLSE is used as a design line
rather than as a consequence of the phenomenon description.
|
2403.05176v1
|
2024-03-08
|
Damping Obliquities of Hot Jupiter Hosts by Resonance Locking
|
When orbiting hotter stars, hot Jupiters are often highly inclined relative
to their host star equator planes. By contrast, hot Jupiters orbiting cooler
stars are more aligned. Prior attempts to explain this correlation between
stellar obliquity and effective temperature have proven problematic. We show
how resonance locking -- the coupling of the planet's orbit to a stellar
gravity mode (g mode) -- can solve this mystery. Cooler stars with their
radiative cores are more likely to be found with g-mode frequencies increased
substantially by core hydrogen burning. Strong frequency evolution in resonance
lock drives strong tidal evolution; locking to an axisymmetric g mode damps
semi-major axes, eccentricities, and as we show for the first time,
obliquities. Around cooler stars, hot Jupiters evolve into spin-orbit alignment
and avoid engulfment. Hotter stars lack radiative cores, and therefore preserve
congenital spin-orbit misalignments. We focus on resonance locks with
axisymmetric modes, supplementing our technical results with simple physical
interpretations, and show that non-axisymmetric modes also damp obliquity.
|
2403.05616v1
|
2024-03-10
|
Linear-in-temperature resistivity and Planckian dissipation arise in a stochastic quantization model of Cooper pairs
|
We suppose that a Cooper pair (CP) will experience a damping force exerted by
the condensed matter. A Langevin equation of a CP in two dimensional condensed
matter is established. Following a method similar to Nelson's stochastic
mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is
derived. If the CPs move with a constant velocity, then the corresponding
direct current (DC) electrical conductivity can be calculated. Therefore, a
Drude like formula of resistivity of CPs is derived. We suppose that the
damping coefficient of CPs in two dimensional cuprate superconductors is a
linear function of temperature. Then the resistivity and scattering rate of CPs
turn out to be also linear-in-temperature. The origin of linear-in-temperature
resistivity and Planckian dissipation in cuprate superconductors may be the
linear temperature dependence of the damping coefficient of CPs.
|
2403.09710v1
|
1995-10-04
|
Microlensing By a Prolate All-Macho Halo
|
It is widely believed that dark matter halos are flattened, that is closer to
oblate than prolate. The evidence cited is based largely on observations of
galaxies which do not look anything like our own and on numerical simulations
which use ad hoc initial conditions. Given what we believe to be a ``reasonable
doubt'' concerning the shape of dark Galactic halo we calculate the optical
depth and event rate for microlensing of stars in the LMC assuming a wide range
of models that include both prolate and oblate halos. We find, in agreement
with previous analysis, that the optical depth for a spherical (E0) halo and
for an oblate (E6) halo are roughly the same, essentially because two competing
effects cancel approximately. However the optical depth for an E6 prolate halo
is reduced by ~35%. This means that an all-Macho prolate halo with reasonable
parameters for the Galaxy is consistent with the published microlensing event
rate.
|
9510023v1
|
1997-04-25
|
Constraints on the density perturbation spectrum from primordial black holes
|
We re-examine the constraints on the density perturbation spectrum, including
its spectral index $n$, from the production of primordial black holes. The
standard cosmology, where the Universe is radiation dominated from the end of
inflation up until the recent past, was studied by Carr, Gilbert and Lidsey; we
correct two errors in their derivation and find a significantly stronger
constraint than they did, $n \lesssim 1.25$ rather than their 1.5. We then
consider an alternative cosmology in which a second period of inflation, known
as thermal inflation and designed to solve additional relic over-density
problems, occurs at a lower energy scale than the main inflationary period. In
that case, the constraint weakens to $n \lesssim 1.3$, and thermal inflation
also leads to a `missing mass' range, $10^{18} g \lesssim M \lesssim 10^{26}
g$, in which primordial black holes cannot form. Finally, we discuss the effect
of allowing for the expected non-gaussianity in the density perturbations
predicted by Bullock and Primack, which can weaken the constraints further by
up to 0.05.
|
9704251v1
|
1998-02-26
|
Inversion of polarimetric data from eclipsing binaries
|
We describe a method for determining the limb polarization and limb darkening
of stars in eclipsing binary systems, by inverting photometric and polarimetric
light curves.
Because of the ill-conditioning of the problem, we use the Backus-Gilbert
method to control the resolution and stability of the recovered solution, and
to make quantitative estimates of the maximum accuracy possible. Using this
method we confirm that the limb polarization can indeed be recovered, and
demonstrate this with simulated data, thus determining the level of
observational accuracy required to achieve a given accuracy of reconstruction.
This allows us to set out an optimal observational strategy, and to critcally
assess the claimed detection of limb polarization in the Algol system.
The use of polarization in stars has been proposed as a diagnostic tool in
microlensing surveys by Simmons et al. (1995), and we discuss the extension of
this work to the case of microlensing of extended sources.
|
9802334v1
|
1998-09-04
|
Cluster-Cluster Strong Lensing: Expectations and Detection Methods
|
We calculate the all-sky number of galaxy clusters that are expected to be
gravitationally lensed by foreground massive clusters. We describe the redshift
and number distributions of clusters using a Press-Schechter analysis, and
model the foreground lensing clusters as singular isothermal spheres. If
Omega_m=0.3 and Omega_Lambda=0.7, we expect ~ 30 cluster-cluster strong lensing
events that involve foreground X-ray luminous clusters with total mass greater
than 7.5 x 10^14 h^-1 M_sun, or X-ray luminosity L_x (2-10 keV) 8 x 10^44 h^-2
ergs s^-1, and background clusters with total mass greater than 10^14 h^-1
M_sun. The number expected in an open universe with Omega_m = 0.3 is less than
\~ 4. Because of uncertainty in sigma_8, the root-mean-square density
fluctuations in spheres of radius 8 h^-1 Mpc, the exact number of such lensing
events is uncertain by a factor of about 5. We examine methods to detect
cluster-cluster lensing events based on optical, X-ray, and Sunyaev-Zel'dovich
effect observations.
|
9809062v3
|
2000-04-14
|
Source Reconstruction as an Inverse Problem
|
Inverse Problem techniques offer powerful tools which deal naturally with
marginal data and asymmetric or strongly smoothing kernels, in cases where
parameter-fitting methods may be used only with some caution. Although they are
typically subject to some bias, they can invert data without requiring one to
assume a particular model for the source. The Backus-Gilbert method in
particular concentrates on the tradeoff between resolution and stability, and
allows one to select an optimal compromise between them. We use these tools to
analyse the problem of reconstructing features of the source star in a
microlensing event, show that it should be possible to obtain useful
information about the star with reasonably obtainable data, and note that the
quality of the reconstruction is more sensitive to the number of data points
than to the quality of individual ones.
|
0004200v1
|
2000-04-18
|
Galaxy Cluster Baryon Fractions, Cluster Surveys and Cosmology
|
The properties of nearby galaxy clusters limit the range of cosmological
parameters consistent with our universe. We describe the limits which arise
from studies of the intracluster medium (ICM) mass fraction fICM and
consideration of the possible sources of systematic error:
Omega_M<0.44h_{50}^{-1/2} at 95% confidence. We emphasize that independent of
Type Ia supernovae (SNe Ia) observations, this cluster study, taken together
with published cosmic microwave background (CMB) anisotropy studies, indicates
a non-zero quintessence or dark energy component Omega_Q>0.
We then discuss future galaxy cluster surveys which will probe the abundance
of galaxy clusters to intermediate and high redshift. We investigate the
sensitivity of these surveys to the cosmological density parameter Omega_M and
the equation of state parameter w of any quintessence component. In particular,
we show that cluster survey constraints from a proposed large solid angle X-ray
survey are comparable in precision and complementary in nature to constraints
expected from future CMB anisotropy and SNe Ia studies.
|
0004244v1
|
2000-05-11
|
Measurement of [OIII] Emission in Lyman Break Galaxies
|
Measurements of [OIII] emission in Lyman Break galaxies (LBGs) at z>3 are
presented. Four galaxies were observed with narrow-band filters using the
Near-IR Camera on the Keck I 10-m telescope. A fifth galaxy was observed
spectroscopically during the commissioning of NIRSPEC, the new infrared
spectrometer on Keck II. The emission-line spectrum is used to place limits on
the metallicity. Comparing these new measurements with others available from
the literature, we find that strong oxygen emission in LBGs may suggest
sub-solar metallicity for these objects. The [OIII]5007 line is also used to
estimate the star formation rate (SFR) of the LBGs. The inferred SFRs are
higher than those estimated from the UV continuum, and may be evidence for dust
extinction.
|
0005254v1
|
2001-03-02
|
Clusters in the Precision Cosmology Era
|
Over the coming decade, the observational samples available for studies of
cluster abundance evolution will increase from tens to hundreds, or possibly to
thousands, of clusters. Here we assess the power of future surveys to determine
cosmological parameters. We quantify the statistical differences among
cosmologies, including the effects of the cosmic equation of state parameter w,
in mock cluster catalogs simulating a 12 sq. deg Sunyaev-Zeldovich Effect
survey and a deep 10^4 sq. deg X-ray survey. The constraints from clusters are
complementary to those from studies of high-redshift Supernovae (SNe), CMB
anisotropies, or counts of high-redshift galaxies. Our results indicate that a
statistical uncertainty of a few percent on both Omega_m and w can be reached
when cluster surveys are used in combination with any of these other datasets.
|
0103049v1
|
2002-07-05
|
New Tests of the Cluster Entropy Floor Hypothesis
|
Recent efforts to account for the observed X-ray luminosity - temperature
relation of galaxy clusters has led to suggestions that the ICM has an apparent
``entropy floor'' at or above the level of 300 keV cm^2. Here, we propose new
tests based on the thermal Sunyaev-Zeldovich effect and on the cluster gas mass
- temperature trend (from X-ray data) to probe the level of excess entropy in
the ICM. We show that these new tests lend further support to the case for a
high entropy floor in massive clusters.
|
0207147v1
|
2003-06-18
|
Kinematic Masses of Super Star Clusters in M82 from High-Resolution Near-Infrared Spectroscopy
|
Using high-resolution (R~22,000) near-infrared (1.51 -- 1.75 microns) spectra
from Keck Observatory, we measure the kinematic masses of two super star
clusters in M82. Cross-correlation of the spectra with template spectra of cool
evolved stars gives stellar velocity dispersions of sigma_r=15.9 +/- 0.8 km/s
for MGG-9 and sigma_r=11.4 +/- 0.8 km/s for MGG-11. The cluster spectra are
dominated by the light of red supergiants, and correlate most closely with
template supergiants of spectral types M0 and M4.5. We fit King models to the
observed profiles of the clusters in archival HST/NICMOS images to measure the
half-light radii. Applying the virial theorem, we determine masses of 1.5 +/-
0.3 x 10^6 M_sun for MGG-9 and 3.5 +/- 0.7 x 10^5 M_sun for MGG-11. Population
synthesis modelling suggests that MGG-9 is consistent with a standard initial
mass function, whereas MGG-11 appears to be deficient in low-mass stars
relative to a standard IMF. There is, however, evidence of mass segregation in
the clusters, in which case the virial mass estimates would represent lower
limits.
|
0306373v1
|
2003-09-10
|
The CMB Quadrupole in a Polarized Light
|
The low quadrupole of the cosmic microwave background (CMB), measured by COBE
and confirmed by WMAP, has generated much discussion recently. We point out
that the well-known correlation between temperature and polarization
anisotropies of the CMB further constrains the low multipole anisotropy data.
This correlation originates from the fact that the low-multipole polarization
signal is sourced by the CMB quadrupole as seen by free electrons during the
relatively recent cosmic history. Consequently, the large-angle temperature
anisotropy data make restrictive predictions for the large-angle polarization
anisotropy, which depend primarily on the optical depth for electron scattering
after cosmological recombination, tau. We show that if current cosmological
models for the generation of large angle anisotropy are correct and the
COBE/WMAP data are not significantly contaminated by non-CMB signals, then the
observed C_te amplitude on the largest scales is discrepant at the 99.8% level
with the observed C_tt for the concordance LCDM model with tau=0.10. Using
tau=0.17, the preferred WMAP model-independent value, the discrepancy is at the
level of 98.5%.
|
0309281v2
|
2003-10-11
|
Statistics of Giant Arcs in Galaxy Clusters
|
We study the expected properties and statistics of giant arcs produced by
galaxy clusters in a LambdaCDM universe and investigate how the characteristics
of CDM clusters determine the properties of the arcs they generate. Due to the
triaxiality and substructure of CDM halos, the giant arc cross section for
individual clusters varies by more than an order of magnitude as a function of
viewing angle. In addition, the shallow density cusps and triaxiality of CDM
clusters cause systematic alignments of giant arcs which should be testable
with larger samples from forthcoming lensing surveys. We compute the predicted
statistics of giant arcs for the LambdaCDM model and compare to results from
previous surveys. The predicted arc statistics are in excellent agreement with
the numbers of giant arcs observed around low redshift (0.2 < z < 0.6) clusters
from the EMSS sample, however there are hints of a possible excess of arcs
observed around high redshift z > 0.6 clusters. This excess, if real, appears
to be due to the presence of highly massive or concentrated clusters at high
redshifts.
|
0310306v1
|
2004-01-23
|
Gravitational Lensing of the Microwave Background by Galaxy Clusters
|
Galaxy clusters will distort the pattern of temperature anisotropies in the
microwave background via gravitational lensing. We create lensed microwave
background maps using clusters drawn from numerical cosmological simulations. A
distinctive dipole-like temperature fluctuation pattern is formed aligned with
the underlying microwave temperature gradient. For a massive cluster, the
characteristic angular size of the temperature distortion is a few arcminutes
and the characteristic amplitude a few micro-Kelvin. We demonstrate a simple
technique for estimating the lensing deflection induced by the cluster;
microwave background lensing measurements have the potential to determine the
mass distribution for some clusters with good accuracy on angular scales up to
a few arcminutes. Future high-resolution and high-sensitivity microwave
background maps will have the capability to detect lensing by clusters; we
discuss various systematic limitations on probing cluster masses using this
technique.
|
0401519v2
|
2004-04-15
|
Is the slope of the intrinsic Baldwin effect constant?
|
We investigate the relationship between emission-line strength and continuum
luminosity in the best-studied nearby Seyfert 1 galaxy NGC5548. Our analysis of
13 years of ground-based optical monitoring data reveals significant
year-to-year variations in the observed H-beta emission-line response in this
source. More specifically, we confirm the result of Gilbert and Peterson (2003)
of a non-linear relationship between the continuum and H-beta emission-line
fluxes. Furthermore, we show that the slope of this relation is not constant,
but rather decreases as the continuum flux increases. Both effects are
consistent with photoionisation model predictions of a luminosity-dependent
response in this line.
|
0404296v1
|
2005-08-04
|
Gravitino, Axino, Kaluza-Klein Graviton Warm and Mixed Dark Matter and Reionisation
|
Stable particle dark matter may well originate during the decay of long-lived
relic particles, as recently extensively examined in the cases of the axino,
gravitino, and higher-dimensional Kaluza-Klein (KK) graviton. It is shown that
in much of the viable parameter space such dark matter emerges naturally
warm/hot or mixed. In particular, decay produced gravitinos (KK-gravitons) may
only be considered cold for the mass of the decaying particle in the several
TeV range, unless the decaying particle and the dark matter particle are almost
degenerate. Such dark matter candidates are thus subject to a host of
cosmological constraints on warm and mixed dark matter, such as limits from a
proper reionisation of the Universe, the Lyman-alpha forest, and the abundance
of clusters of galaxies.. It is shown that constraints from an early
reionsation epoch, such as indicated by recent observations, may potentially
limit such warm/hot components to contribute only a very small fraction to the
dark matter.
|
0508141v2
|
1999-08-10
|
Magnetic relaxation in a classical spin chain as model for nanowires
|
With decreasing particle size, different mechanisms dominate the thermally
activated magnetization reversal in ferromagnetic particles. We investigate
some of these mechanisms for the case of elongated, single-domain nanoparticles
which we describe by a classical Heisenberg spin chain driven by an external
magnetic field. For sufficiently small system size the magnetic moments rotate
coherently. With increasing size a crossover to a reversal due to
soliton-antisoliton nucleation sets in. For even larger systems many of these
soliton-antisoliton pairs nucleate at the same time. These effects give rise to
a complex size dependence of the energy barriers and characteristic time scales
of the relaxation. We study these quantities using Monte Carlo simulations as
well as a direct integration of the Landau-Lifshitz-Gilbert equation of motion
with Langevin dynamics and we compare our results with asymptotic solutions for
the escape rate following from the Fokker-Planck equation. Also, we investigate
the crossover from coherent rotation to soliton-antisoliton nucleation and
multi-droplet nucleation, especially its dependence on the system size, the
external field and the anisotropy of the system.
|
9908150v1
|
2000-07-17
|
Fine-grid Simulations of Thermally Activated Switching in Nanoscale Magets
|
Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal
fluctuations is used to study the dynamic response of single-domain nanomagnets
to rapid changes in the applied magnetic field. The simulation can resolve
magnetization patterns within nanomagnets and uses the Fast Multipole method to
calculate dipole-dipole interactions efficiently. The thermal fluctuations play
an essential part in the reversal process whenever the applied field is less
than the zero-temperature coercive field. In this situation pillar-shaped
nanomagnets are found to reverse through a local curling mode that involves the
formation and propagation of a domain wall. Tapering the ends of the pillars to
reduce pole-avoidance effects changes the energies involved but not the
fundamental process. The statistical distribution of switching times is well
described by the independent nucleation and subsequent growth of regions of
reversed magnetization at both ends of the pillar.
|
0007279v1
|
2001-01-31
|
Langevin Simulation of Thermally Activated Magnetization Reversal in Nanoscale Pillars
|
Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model
incorporating thermal fluctuations and dipole-dipole interactions (calculated
by the Fast Multipole Method) are presented for systems composed of nanoscale
iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated
under sinusoidally varying fields are obtained, while the coercive field is
estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 K. Thermal
effects are essential to the relaxation of magnetization trapped in a
metastable orientation, such as happens after a rapid reversal of an external
magnetic field less than the coercive value. The distribution of switching
times is compared to a simple analytic theory that describes reversal with
nucleation at the ends of the nanomagnets. Results are also presented for
arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a
separation of 300 nm, where the field from neighboring pillars is only $\sim$ 1
Oe, the interactions have a significant effect on the switching of the magnets.
|
0101477v2
|
2001-05-04
|
On a common circle: natural scenes and Gestalt rules
|
To understand how the human visual system analyzes images, it is essential to
know the structure of the visual environment. In particular, natural images
display consistent statistical properties that distinguish them from random
luminance distributions. We have studied the geometric regularities of oriented
elements (edges or line segments) present in an ensemble of visual scenes,
asking how much information the presence of a segment in a particular location
of the visual scene carries about the presence of a second segment at different
relative positions and orientations. We observed strong long-range correlations
in the distribution of oriented segments that extend over the whole visual
field. We further show that a very simple geometric rule, cocircularity,
predicts the arrangement of segments in natural scenes, and that different
geometrical arrangements show relevant differences in their scaling properties.
Our results show similarities to geometric features of previous physiological
and psychophysical studies. We discuss the implications of these findings for
theories of early vision.
|
0105097v1
|
2002-10-11
|
Fluctuations and Dissipation of Coherent Magnetization
|
A quantum mechanical model is used to derive a generalized Landau-Lifshitz
equation for a magnetic moment, including fluctuations and dissipation. The
model reproduces the Gilbert-Brown form of the equation in the classical limit.
The magnetic moment is linearly coupled to a reservoir of bosonic degrees of
freedom. Use of generalized coherent states makes the semiclassical limit more
transparent within a path-integral formulation. A general
fluctuation-dissipation theorem is derived. The magnitude of the magnetic
moment also fluctuates beyond the Gaussian approximation. We discuss how the
approximate stochastic description of the thermal field follows from our
result. As an example, we go beyond the linear-response method and show how the
thermal fluctuations become anisotropy-dependent even in the uniaxial case.
|
0210273v2
|
2002-11-18
|
Field dependence of magnetization reversal by spin transfer
|
We analyse the effect of the applied field (Happl) on the current-driven
magnetization reversal in pillar-shaped Co/Cu/Co trilayers, where we observe
two different types of transition between the parallel (P) and antiparallel
(AP) magnetic configurations of the Co layers. If Happl is weaker than a rather
small threshold value, the transitions between P and AP are irreversible and
relatively sharp. For Happl exceding the threshold value, the same transitions
are progressive and reversible. We show that the criteria for the stability of
the P and AP states and the experimentally observed behavior can be precisely
accounted for by introducing the current-induced torque of the spin transfer
models in a Landau-Lifschitz-Gilbert equation. This approach also provides a
good description for the field dependence of the critical currents.
|
0211371v1
|
2003-10-18
|
NMR Investigation of the Organic Conductor lambda-(BETS)2FeCl4
|
The two-dimensional organic conductor lambda-(BETS)2FeCl4 has an unusual
phase diagram as a function of temperature and magnetic field that includes a
paramagnetic metal (PM) phase, an antiferromagnetic insulating (AFI) phase, and
a field-induced superconducting phase [S. Uji, H. Kobayashi, L. Balicas, and
James S. Brooks, Adv. Mater. 14, 243 (2002), and cited references]. Here, we
report a preliminary investigation of the PM and AFI phases at 9.0 T over the
temperature range 2.0-180 K that uses proton NMR measurements of the spectrum,
the spin-lattice relaxation rate (1/T1), and the spin echo decay rate (1/T2).
The sample is asmall single crystal whose mass is approximately 3 micrograms
(approximately 2E16 protons). Its small size creates several challenges that
include detecting small signals and excluding parasitic proton signals that are
not from the sample [H. N. Bachman and I. F. Silvera, J. Mag. Res. 162, 417
(2003)]. These strategies and other techniques used to obtain viable signals
are described.
|
0310433v1
|
2004-04-22
|
Non-collinear magnetic structures: a possible cause for current induced switching
|
Current induced switching in Co/Cu/Co trilayers is described in terms of
ab-initio determined magnetic twisting energies and corresponding sheet
resistances. In viewing the twisting energy as an energy flux the
characteristic time thereof is evaluated by means of the
Landau-Lifshitz-Gilbert equation using ab-initio parameters. The obtained
switching times are in very good agreement with available experimental data. In
terms of the calculated currents, scalar quantities since a classical Ohm's law
is applied, critical currents needed to switch magnetic configurations from
parallel to antiparallel and vice versa can unambiguously be defined. It is
found that the magnetoresistance viewed as a function of the current is
essentially determined by the twisting energy as a function of the relative
angle between the orientations of the magnetization in the magnetic slabs,
which in turn can also explain in particular cases the fact that after having
switched off the current the system remains in the switched magnetic
configuration. For all ab-initio type calculations the fully relativistic
Screened Korringa-Kohn-Rostoker method and the corresponding Kubo-Greenwood
equation in the context of density functional theory are applied.
|
0404534v1
|
2004-06-21
|
Basic considerations for magnetization dynamics in the combined presence of spin-transfer torques and thermal fluctuations
|
This article reviews basic theoretical features of Gilbert magnetization
dynamics of a single domain magnetic film in the presence of Slonczewski
spin-transfer torques, with and without thermal fluctuations taken into
account. Rather than showing results of detailed numerical calculations, the
discussion here is restricted to basic analytical results and conclusions which
can mostly be derived from simply the form of the equations of motion, as well
as elementary considerations based on classical stability analysis and the
fluctuation-dissipation theorem. The presents work describes how interesting
features of spin-transfer may be viewed as arising from non-equilibrium
thermodynamics that are a direct consequence of the nonreciprocal nature of
spin-transfer torques. The present article discusses fairly general results for
spin-torque induced instability without thermal fluctuations, as well as the
case of thermally activated magnetization reversal in uniaxial devices in the
combined presence of external fields, thermal fluctuations, and spin-transfer
torques. The results will be discussed and briefly compared and contrasted with
that of prior work.
|
0406486v1
|
2004-06-24
|
Thermal Effects on the Magnetic Field Dependence of Spin Transfer Induced Magnetization Reversal
|
We have developed a self-aligned, high-yield process to fabricate CPP
(current perpendicular to the plane) magnetic sensors of sub 100 nm dimensions.
A pinned synthetic antiferromagnet (SAF) is used as the reference layer which
minimizes dipole coupling to the free layer and field induced rotation of the
reference layer. We find that the critical currents for spin transfer induced
magnetization reversal of the free layer vary dramatically with relatively
small changes the in-plane magnetic field, in contrast to theoretical
predictions based on stability analysis of the Gilbert equations of
magnetization dynamics including Slonczewski-type spin-torque terms. The
discrepancy is believed due to thermal fluctuations over the time scale of the
measurements. Once thermal fluctuations are taken into account, we find good
quantitative agreement between our experimental results and numerical
simulations.
|
0406574v1
|
2004-07-23
|
Micromagnetic understanding of current-driven domain wall motion in patterned nanowires
|
In order to explain recent experiments reporting a motion of magnetic domain
walls (DW) in nanowires carrying a current, we propose a modification of the
spin transfer torque term in the Landau-Lifchitz-Gilbert equation. We show that
it explains, with reasonable parameters, the measured DW velocities as well as
the variation of DW propagation field under current. We also introduce
coercivity by considering rough wires. This leads to a finite DW propagation
field and finite threshold current for DW propagation, hence we conclude that
threshold currents are extrinsic. Some possible models that support this new
term are discussed.
|
0407628v2
|
2004-08-07
|
Hysteresis multicycles in nanomagnet arrays
|
We predict two new physical effects in arrays of single-domain nanomagnets by
performing simulations using a realistic model Hamiltonian and physical
parameters. First, we find hysteretic multicycles for such nanomagnets. The
simulation uses continuous spin dynamics through the Landau-Lifshitz-Gilbert
(LLG) equation. In some regions of parameter space, the probability of finding
a multicycle is as high as ~0.6. We find that systems with larger and more
anisotropic nanomagnets tend to display more multicycles. This result
demonstrates the importance of disorder and frustration for multicycle
behavior. We also show that there is a fundamental difference between the more
realistic vector LLG equation and scalar models of hysteresis, such as Ising
models. In the latter case, spin and external field inversion symmetry is
obeyed but in the former it is destroyed by the dynamics, with important
experimental implications.
|
0408158v1
|
2004-12-03
|
High frequency magnetic permeability of nanocomposite film
|
The high frequency magnetic permeability of nanocomposite film consisting of
the single-domain spherical ferromagnetic particles in the dielectric matrix is
studied. The permeability is assumed to be determined by rotation of the
ferromagnetic inclusion magnetic moments around equilibrium direction in AC
magnetic field. The composite is modeled by a cubic array of ferromagnetic
particles. The magnetic permeability tensor is calculated by solving the
Landau-Lifshits-Gilbert equation accounting for the dipole interaction of
magnetic particles. The permeability tensor components are found as functions
of the frequency, temperature, ferromagnetic inclusions density and magnetic
anisotropy. The obtained results show that nanocomposite films could have
rather high value of magnetic permeability in the microwave range.
|
0412073v1
|
2005-01-07
|
Dielectric resonances of ordered passive arrays
|
The electrical and optical properties of ordered passive arrays, constituted
of inductive and capacitive components, are usually deduced from Kirchhoff's
rules. Under the assumption of periodic boundary conditions, comparable results
may be obtained via an approach employing transfer matrices. In particular,
resonances in the dielectric spectrum are demonstrated to occur if all
eigenvalues of the transfer matrix of the entire array are unity. The latter
condition, which is shown to be equivalent to the habitual definition of a
resonance in impedance for an array between electrodes, allows for a convenient
and accurate determination of the resonance frequencies, and may thus be used
as a tool for the design of materials with a specific dielectric response. For
the opposite case of linear arrays in a large network, where periodic boundary
condition do not apply, several asymptotic properties are derived. Throughout
the article, the derived analytic results are compared to numerical models,
based on either Exact Numerical Renormalisation or the spectral method.
|
0501137v1
|
2005-07-27
|
"Stochastic Modeling of Coercivity " - A Measure of Non-equilibrium State
|
A typical coercivity versus particle size curve for magnetic nanoparticles
has been explained by using the Gilbert equation followed by the corresponding
Fokker Plank equation. Kramer's treatment has been employed to explain the
increase in coercivity in the single domain region. The single to multi-domain
transformation has been assumed to explain the decrease in coercive field
beyond a certain particle size. The justification for using Langevin theory of
paramagnetism (including anisotropy energy) to fit the M vs H curve is
discussed. The super-symmetric Hamiltonian approach is used to find out the
relaxation time for the spins (making an angle greater than $90^0$ with applied
field) at domain wall. The main advantage of our technique is that we can
easily take into account the time of measurement as we usually do in realistic
measurement.
|
0507640v1
|
2005-09-13
|
Synchronization of spin-transfer oscillators driven by stimulated microwave currents
|
We have simulated the non-linear dynamics of networks of spin-transfer
oscillators. The oscillators are magnetically uncoupled but electrically
connected in series. We use a modified Landau-Lifschitz- Gilbert equation to
describe the motion of each oscillator in the presence of the oscillations of
all the others. We show that the oscillators of the network can be synchronized
not only in frequency but also in phase. The coupling is due to the microwave
components of the current induced in each oscillator by the oscillations in all
the other oscillators. Our results show how the emitted microwave power of
spin-transfer oscillators can be considerably enhanced by current-induced
synchronization in an electrically connected network. We also discuss the
possible application of our synchronization mechanism to the interpretation of
the surprisingly narrow microwave spectrum in some isolated spin-transfer
oscillators.
|
0509326v2
|
2005-11-04
|
Synchronized Magnetization Oscillations in F/N/F Nanopillars
|
Current-induced magnetization dynamics in a trilayer structure composed of
two ferromagnetic free layers and a nonmagnetic spacer is examined. Both free
layers are treated as a monodomain magnetic body with an uniform agnetization.
The dynamics of the two magnetizations is modeled by modified
Landau-Lifshitz-Gilbert equations with spin-transfer torque terms. By solving
the equations simultaneously, we discuss their various solutions in detail. We
show that there exists the synchronous motion of two magnetizations among the
various solutions; the magnetizations are resonantly coupled via spin-transfer
torques and perform precessional motions with the same period. The condition to
excite the synchronous motion depends on the difference between the intrinsic
frequencies of the two ferromagnetic free layers as well as the magnitude of
current.
|
0511095v1
|
2006-01-27
|
Dynamics of thin-film spin-flip transistors with perpendicular source-drain magnetizations
|
A "spin-flip transistor" is a lateral spin valve consisting of ferromagnetic
source drain contacts to a thin-film normal-metal island with an electrically
floating ferromagnetic base contact on top. We analyze the
\emph{dc}-current-driven magnetization dynamics of spin-flip transistors in
which the source-drain contacts are magnetized perpendicularly to the device
plane by magnetoelectronic circuit theory and the macrospin
Landau-Lifshitz-Gilbert equation. Spin flip scattering and spin pumping effects
are taken into account. We find a steady-state rotation of the base
magnetization at GHz frequencies that is tuneable by the source-drain bias. We
discuss the advantages of the lateral structure for high-frequency generation
and actuation of nanomechanical systems over recently proposed nanopillar
structures.
|
0601630v1
|
2007-03-17
|
Large-amplitude coherent spin waves exited by spin-polarized current in nanoscale spin valves
|
We present spectral measurements of spin-wave excitations driven by direct
spinpolarized current in the free layer of nanoscale
Ir20Mn80/Ni80Fe20/Cu/Ni80Fe20 spin valves. The measurements reveal that
large-amplitude coherent spin wave modes are excited over a wide range of bias
current. The frequency of these excitations exhibits a series of jumps as a
function of current due to transitions between different localized nonlinear
spin wave modes of the Ni80Fe20 nanomagnet. We find that micromagnetic
simulations employing the Landau-Lifshitz-Gilbert equation of motion augmented
by the Slonczewski spin torque term (LLGS) accurately describe the frequency of
the current-driven excitations including the mode transition behavior. However
LLGS simulations give qualitatively incorrect predictions for the amplitude of
excited spin waves as a function of current.
|
0703458v2
|
2001-12-11
|
A Data Mining Framework for Optimal Product Selection in Retail Supermarket Data: The Generalized PROFSET Model
|
In recent years, data mining researchers have developed efficient association
rule algorithms for retail market basket analysis. Still, retailers often
complain about how to adopt association rules to optimize concrete retail
marketing-mix decisions. It is in this context that, in a previous paper, the
authors have introduced a product selection model called PROFSET. This model
selects the most interesting products from a product assortment based on their
cross-selling potential given some retailer defined constraints. However this
model suffered from an important deficiency: it could not deal effectively with
supermarket data, and no provisions were taken to include retail category
management principles. Therefore, in this paper, the authors present an
important generalization of the existing model in order to make it suitable for
supermarket data as well, and to enable retailers to add category restrictions
to the model. Experiments on real world data obtained from a Belgian
supermarket chain produce very promising results and demonstrate the
effectiveness of the generalized PROFSET model.
|
0112013v1
|
2005-02-22
|
The QuarkNet/Grid Collaborative Learning e-Lab
|
We describe a case study that uses grid computing techniques to support the
collaborative learning of high school students investigating cosmic rays.
Students gather and upload science data to our e-Lab portal. They explore those
data using techniques from the GriPhyN collaboration. These techniques include
virtual data transformations, workflows, metadata cataloging and indexing, data
product provenance and persistence, as well as job planners. Students use web
browsers and a custom interface that extends the GriPhyN Chiron portal to
perform all of these tasks. They share results in the form of online posters
and ask each other questions in this asynchronous environment. Students can
discover and extend the research of other students, modeling the processes of
modern large-scale scientific collaborations. Also, the e-Lab portal provides
tools for teachers to guide student work throughout an investigation.
http://quarknet.uchicago.edu/elab/cosmic
|
0502089v1
|
2006-10-11
|
Properties of codes in rank metric
|
We study properties of rank metric and codes in rank metric over finite
fields. We show that in rank metric perfect codes do not exist. We derive an
existence bound that is the equivalent of the Gilbert--Varshamov bound in
Hamming metric. We study the asymptotic behavior of the minimum rank distance
of codes satisfying GV. We derive the probability distribution of minimum rank
distance for random and random $\F{q}$-linear codes. We give an asymptotic
equivalent of their average minimum rank distance and show that random
$\F{q}$-linear codes are on GV bound for rank metric.
We show that the covering density of optimum codes whose codewords can be
seen as square matrices is lower bounded by a function depending only on the
error-correcting capability of the codes. We show that there are quasi-perfect
codes in rank metric over fields of characteristic 2.
|
0610057v1
|
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