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2023-09-29 | A Fast second-order solver for stiff multifluid dust and gas hydrodynamics | We present MDIRK: a Multifluid second-order Diagonally-Implicit Runge-Kutta
method to study momentum transfer between gas and an arbitrary number ($N$) of
dust species. The method integrates the equations of hydrodynamics with an
Implicit Explicit (IMEX) scheme and solves the stiff source term in the
momentum equation with a diagonally-implicit asymptotically stable Runge-Kutta
method (DIRK). In particular, DIRK admits a simple analytical solution that can
be evaluated with $\mathcal{O}(N)$ operations, instead of standard matrix
inversion, which is $\mathcal{O}(N)^3$. Therefore the analytical solution
significantly reduces the computational cost of the multifluid method, making
it suitable for studying the dynamics of systems with particle-size
distributions. We demonstrate that the method conserves momentum to machine
precision and converges to the correct equilibrium solution with constant
external acceleration. To validate our numerical method we present a series of
simple hydrodynamic tests, including damping of sound waves, dusty shocks, a
multi-fluid dusty Jeans instability, and a steady-state gas-dust drift
calculation. The simplicity of MDIRK lays the groundwork to build fast
high-order asymptotically stable multifluid methods. | 2310.04435v3 |
2023-10-19 | Error-mitigated fermionic classical shadows on noisy quantum devices | Efficiently estimating the expectation values of fermionic Hamiltonians,
including $k$-particle reduced density matrices ($k$-RDMs) of an $n$-mode
fermionic state, is crucial for quantum simulations of a wealth of physical
systems from the fields of many-body physics, chemistry, and materials. Yet,
conventional quantum state tomography methods are too costly in terms of their
resource requirements. Classical shadow (CS) algorithms have been proposed as a
solution to address this task by substantially reducing the number of copies of
quantum states. However, the implementation of these algorithms faces a
significant challenge due to the inherent noise in near-term quantum devices,
leading to inaccuracies in gate operations. To address this challenge, we
propose an error-mitigated CS algorithm for fermionic systems. For $n$-qubit
quantum systems, our algorithm, which employs the easily prepared initial state
$|0^n\rangle\!\langle 0^n|$ assumed to be noiseless, provably efficiently
estimates all elements of $k$-RDMs with $\widetilde{\mathcal O}(kn^k)$ scaled
copies of quantum states and $\widetilde{\mathcal O}(\sqrt{n})$ scaled
calibration measurements. It does so even in the presence of gate or
measurement noise such as depolarizing, amplitude damping, or $X$-rotation
noise with at most a constant noise strength. Furthermore, our algorithm
exhibits scaling comparable to previous CS algorithms for fermionic systems
with respect to the number of quantum state copies, while also demonstrating
enhanced resilience to noise. We numerically demonstrate the performance of our
algorithm in the presence of these noise sources, and its performance under
Gaussian unitary noise. Our results underscore the potential utility of
implementing our algorithm on near-term quantum devices. | 2310.12726v2 |
2023-11-02 | Phase space noncommutativity, power-law inflation and quantum cosmology | Considering an arbitrary dimensional FLRW universe in the framework of a
generalized S\'{a}ez--Ballester (SB) theory, we establish a noncommutative (NC)
cosmological model. We concentrate on the predictions of NC model and compare
them with their commutative counterparts in both the classical and quantum
regimes. For the classic case, taking a very small NC parameter, we apply two
different methods to analyze the model features. First, we show through
numerical analysis that our NC model is a successful inflationary model capable
of overcoming the graceful exit and horizon problems. Furthermore, the NC
traces are visible the late time, which supports the UV/IR mixing
characteristic of the NC models. In the second method, we show that our NC
model can correspond to the previously developed NC inflationary models. In the
commutative quantum case, we obtain an exact wave function and then use the WKB
approximation to show that the solutions of the corresponding classical regime
are recovered. Finally, with regard to the NC quantum level, we focus on the
special case for which we show that a constant of motion exists. The latter
helps us to conveniently transform the corresponding complicated NC-WDW
equation into an ordinary differential equation, which can be easily solved
numerically for the general case or analytically for some special cases. The
resultant solutions show a damping behavior in the wave function associated
with the proposed NC model, which may be important in determining the viable
initial states for the very early universe. | 2311.01627v1 |
2023-11-04 | Electronic quantum wires in extended quasiparticle picture | A one-dimensional quantum wire of Fermions is considered and ground state
properties are calculated in the high density regime within the extended
quasiparticle picture and Born approximation. Expanding the two-particle Green
functions determines the selfenergy and the polarization as well as the
response function on the same footing. While the on-shell selfenergies are
strictly zero due to Pauli-blocking of elastic scattering, the off-shell
behaviour shows a rich structure of a gap in the damping of excitation which is
closed when the momentum approaches the Fermi one. The consistent spectral
function is presented completing the first two energy-weighted sum rules. The
excitation spectrum shows a splitting due to holons and antiholons as non-Fermi
liquid behaviour. A renormalization procedure is proposed by subtracting an
energy constant to render the Fock exchange energy finite. The effective mass
derived from meanfield shows a dip as onset of Peierls instability. The
correlation energy is calculated with the help of the extended quasiparticle
picture which accounts for off-shell effects. The corresponding response
function leads to the same correlation energy as the selfenergy in agreement
with perturbation theory. The reduced density matrix or momentum distribution
is calculated with the help of a Pad\'e regularization repairing deficiencies
of the perturbation theory. A seemingly finite step at the Fermi energy
indicating Fermi-liquid behaviour is repaired in this way. | 2311.02414v1 |
2023-12-01 | Large enhancement of spin-orbit torques under a MHz modulation due to phonon-magnon coupling | The discovery of spin-orbit torques (SOTs) generated through the spin Hall or
Rashba effects provides an alternative write approach for magnetic
random-access memory (MRAM), igniting the development of spin-orbitronics in
recent years. Quantitative characterization of SOTs highly relies on the
SOT-driven ferromagnetic resonance (ST-FMR), where a modulated microwave
current is used to generate ac SOTs and the modulation-frequency is usually
less than 100 kHz (the limit of conventional lock-in amplifiers). Here we have
investigated the SOT of typical SOT material/ferromagnet bilayers in an
extended modulation-frequency range, up to MHz, by developing the ST-FMR
measurement. Remarkably, we found that the measured SOTs are enhanced about
three times in the MHz range, which cannot be explained according to present
SOT theory. We attribute the enhancement of SOT to additional magnon
excitations due to phonon-magnon coupling, which is also reflected in the
slight changes of resonant field and linewidth in the acquired ST-FMR spectra,
corresponding to the modifications of effective magnetization and damping
constant, respectively. Our results indicate that the write current of SOT-MRAM
may be reduced with the assistant of phonon-magnon coupling. | 2401.02967v1 |
2024-01-25 | Photon propagation in a charged Bose-Einstein condensate | We consider the propagation of photons in the background of a Bose-Einstein
(BE) condensate of a charged scalar field, by extending a method recently
proposed to treat the propagation of fermions in a BE condensate. We determine
the dispersion relations of the collective modes of the system, as well as the
photon polarization tensor and the dielectric constant that result after the
symmetry breaking associated with the BE condensation in the model. Two modes
correspond to the transverse photon polarizations, and their dispersion
relations have the usual form of the transverse photons in a plasma. The other
two modes, which we denote as the $(\pm)$ modes, are combinations of the
longitudinal photon and the massive scalar field. The dispersion relation of
the $(-)$ mode decreases as a function of the momentum in a given range, and
the corresponding group velocity is negative in that range. We also determine
the wavefunctions of the $(\pm)$ modes, which can be used to obtain the
corrections to the dispersion relations (e.g., imaginary parts due the damping
effects) and/or the effects of scattering, due to the interactions with the
excitations of the system. The results can be useful in various physical
contexts that have been considered in the literature involving the
electrodynamics of a charged scalar BE condensate. | 2401.13896v1 |
2024-01-26 | Well-posedness and stability of the Navier-Stokes-Maxwell equations | The paper is devoted to studying the well-posedness and stability of the
generalized Navier-Stokes-Maxwell (NSM) equations with the standard Ohm's law
in $\mathbb{R}^d$ for $d \in \{2,3\}$. More precisely, the global
well-posedness is established in case of fractional Laplacian velocity
$(-\Delta)^\alpha v$ with $\alpha = \frac{d}{2}$ for suitable data. In
addition, the local well-posedness in the inviscid case is also provided for
sufficient smooth data, which allows us to study the inviscid limit of
associated positive viscosity solutions in the case $\alpha = 1$, where an
explicit bound on the difference is given. On the other hand, in the case
$\alpha = 0$ the stability near a magnetohydrostatic equilibrium with a
constant (or equivalently bounded) magnetic field is also obtained in which
nonhomogeneous Sobolev norms of the velocity and electric fields, and the
$L^\infty$ norm of the magnetic field converge to zero as time goes to infinity
with an implicit rate. In this velocity damping case, the situation is
different both in case of the two and a half, and three-dimensional
magnetohydrodynamics (MHD) system, where an explicit rate of convergence in
infinite time is computed for both the velocity and magnetic fields in
nonhomogeneous Sobolev norms. Therefore, there is a gap between NSM and MHD in
terms of the norm convergence of the magnetic field and the rate of decaying in
time, even the latter equations can be proved as a limiting system of the
former one in the sense of distributions as the speed of light tends to
infinity. | 2401.14839v2 |
2024-03-14 | The effect of spatially-varying collision frequency on the development of the Rayleigh-Taylor instability | The Rayleigh-Taylor (RT) instability is ubiquitously observed, yet has
traditionally been studied using ideal fluid models. Collisionality can vary
strongly across the fluid interface, and previous work demonstrates the
necessity of kinetic models to completely capture dynamics in certain
collisional regimes. Where previous kinetic simulations used spatially- and
temporally-constant collision frequency, this work presents 5-dimensional (two
spatial, three velocity dimensions) continuum-kinetic simulations of the RT
instability using a more realistic spatially-varying collision frequency. Three
cases of collisional variation are explored for two Atwood numbers: low to
intermediate, intermediate to high, and low to high. The low to intermediate
case exhibits no RT instability growth, while the intermediate to high case is
similar to a fluid limit kinetic case with interface widening biased towards
the lower collisionality region. A novel contribution of this work is the low
to high collisionality case that shows significantly altered instability growth
through upward movement of the interface and damped spike growth due to
increased free-streaming particle diffusion in the lower region. Contributions
to the energy-flux from the non-Maxwellian portions of the distribution
function are not accessible to fluid models and are greatest in magnitude in
the spike and regions of low collisionality. Increasing the Atwood number
results in greater RT instability growth and reduced upward interface movement.
Deviation of the distribution function from Maxwellian is inversely
proportional to collision frequency and concentrated around the fluid
interface. The linear phase of RT instability growth is well-described by
theoretical linear growth rates accounting for viscosity and diffusion. | 2403.09591v1 |
2002-02-21 | Mechanisms of spin-polarized current-driven magnetization switching | The mechanisms of the magnetization switching of magnetic multilayers driven
by a current are studied by including exchange interaction between local
moments and spin accumulation of conduction electrons. It is found that this
exchange interaction leads to two additional terms in the
Landau-Lifshitz-Gilbert equation: an effective field and a spin torque. Both
terms are proportional to the transverse spin accumulation and have comparable
magnitudes. | 0202363v1 |
1991-12-02 | Perturbations of a Stringy Black Hole | We extend the three dimensional stringy black hole of Horne and Horowitz to
four dimensions. After a brief discussion of the global properties of the
metric, we discuss the stability of the background with respect to small
perturbations, following the methods of Gilbert and of Chandrasekhar. The
potential for axial perturbations is found to be positive definite. | 9112001v2 |
1996-05-06 | Finitely presented subgroups of automatic groups and their isoperimetric functions | We describe a general technique for embedding certain amalgamated products
into direct products. This technique provides us with a way of constructing a
host of finitely presented subgroups of automatic groups which are not even
asynchronously automatic. We can also arrange that such subgroups satisfy, at
best, an exponential isoperimetric inequality. | 9605201v1 |
1999-07-22 | Constructing Hyperbolic Manifolds | In this paper we show how to obtain representations of Coxeter groups acting
on H^n to certain classical groups. We determine when the kernel of such a
representation is torsion-free and thus the quotient a hyperbolic n-manifold. | 9907139v1 |
2002-02-06 | Quaternionic equation for electromagnetic fields in inhomogeneous media | We show that the Maxwell equations for arbitrary inhomogeneous media are
equivalent to a single quaternionic equation which can be considered as a
generalization of the Vekua equation for generalized analytic functions. | 0202010v1 |
1996-02-29 | Error Correction in Quantum Communication | We show how procedures which can correct phase and amplitude errors can be
directly applied to correct errors due to quantum entanglement. We specify
general criteria for quantum error correction, introduce quantum versions of
the Hamming and the Gilbert-Varshamov bounds and comment on the practical
implementation of quantum codes. | 9602022v1 |
2007-05-19 | Log-periodic drift oscillations in self-similar billiards | We study a particle moving at unit speed in a self-similar Lorentz billiard
channel; the latter consists of an infinite sequence of cells which are
identical in shape but growing exponentially in size, from left to right. We
present numerical computation of the drift term in this system and establish
the logarithmic periodicity of the corrections to the average drift. | 0705.2790v1 |
2008-04-26 | Asymptotic Bound on Binary Self-Orthogonal Codes | We present two constructions for binary self-orthogonal codes. It turns out
that our constructions yield a constructive bound on binary self-orthogonal
codes. In particular, when the information rate R=1/2, by our constructive
lower bound, the relative minimum distance \delta\approx 0.0595 (for GV bound,
\delta\approx 0.110). Moreover, we have proved that the binary self-orthogonal
codes asymptotically achieve the Gilbert-Varshamov bound. | 0804.4194v1 |
2009-05-04 | Self-organized quantum transitions in a spin-electron coupled system | We investigate quantum dynamics of the excited electronic states in the
double-exchange model at half-filling by solving coupled equations for the
quantum evolution of electrons and Landau-Lifshits-Gilbert equation for
classical spins. The non-adiabatic quantum transitions driving the relaxation
are coordinated through the self-organized space-time structure of the
electron/spin dynamics leading to a resonant precession analogous to the ESR
process. | 0905.0311v1 |
2009-05-04 | Oscillating Ponomarenko dynamo in the highly conducting limit | This paper considers dynamo action in smooth helical flows in cylindrical
geometry, otherwise known as Ponomarenko dynamos, with periodic time
dependence. An asymptotic framework is developed that gives growth rates and
frequencies in the highly conducting limit of large magnetic Reynolds number,
when modes tend to be localized on resonant stream surfaces. This theory is
validated by means of numerical simulations. | 0905.0415v1 |
2009-12-24 | Scenarios of Gravitino Dark Matter and their Cosmological and Particle Physics Implications | I report on some scenarios where the gravitino is the dark matter and the
supersymmetry breaking mediated by a gauge sector. | 0912.4885v1 |
2010-07-20 | Factoring Permutation Matrices Into a Product of Tridiagonal Matrices | Gilbert Strang posited that a permutation matrix of bandwidth $w$ can be
written as a product of $N < 2w$ permutation matrices of bandwidth 1. A proof
employing a greedy ``parallel bubblesort'' algorithm on the rows of the
permutation matrix is detailed and further points of interest are elaborated. | 1007.3467v1 |
2011-05-26 | Qu'est-ce qu'une espèce de structures? Genèse et description | This is an overview (in french) of the Theory of Species for a general
audience. Basic notions are introduced in a non too technical manner, with an
explanation of why should one approach the notion of discrete structures in
this particular way. | 1105.5406v1 |
2011-12-16 | Reply to the comment of T.Gilbert and D.P.Sanders on "Capturing correlations in chaotic diffusion by approximation methods" | This is a reply to the comment by Gilbert and Sanders [arXiv:1111.6271
(2011)]. We point out that their comment is a follow-up of a previous
discussion which we briefly summarize before we refute their new criticism. | 1112.3927v1 |
2012-03-24 | A new look at finitely generated metabelian groups | A group is metabelian if its commutator subgroup is abelian. For finitely
generated metabelian groups, classical commutative algebra, algebraic geometry
and geometric group theory, especially the latter two subjects, can be brought
to bear on their study. The object of this paper is to describe some of the new
ideas and open problems that arise. | 1203.5431v1 |
2012-06-05 | A convergent and precise finite element scheme for Landau-Lifschitz-Gilbert equation | In this paper, we rigorously study an order 2 scheme that was previously
proposed by some of the authors. A slight modification is proposed that enables
us to prove the convergence of the scheme while simplifying in the same time
the inner iteration. | 1206.0997v1 |
2013-01-20 | Residual properties of groups defined by basic commutators | In this paper we study the residual nilpotence of groups defined by basic
commutators. We prove that the so-called Hydra groups as well as certain of
their generalizations and quotients are, in the main, residually torsion-free
nilpotent. By way of contrast we give an example of a group defined by two
basic commutators which is not residually torsion-free nilpotent. | 1301.4629v2 |
2013-03-21 | Anisimov's Theorem for inverse semigroups | The idempotent problem of a finitely generated inverse semigroup is the
formal language of all words over the generators representing idempotent
elements. This note proves that a finitely generated inverse semigroup with
regular idempotent problem is necessarily finite. This answers a question of
Gilbert and Noonan Heale, and establishes a generalisation to inverse
semigroups of Anisimov's Theorem for groups. | 1303.5239v1 |
2013-10-13 | Underwater Gas Expansion and Deflagration | The underwater combustion of a propane-air mixture in an acrylic cylinder is
captured on video from multiple angles. This experiment is designed to provide
visual data and pressure time-histories for future CFD validation studies. | 1310.3523v1 |
2014-03-12 | A semi-discrete scheme for the stochastic Landau-Lifshitz equation | We propose a new convergent time semi-discrete scheme for the stochastic
Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does
not require the resolution of a nonlinear problem at each time step. Using a
martingale approach, we prove the convergence in law of the scheme up to a
subsequence. | 1403.3016v1 |
2014-03-17 | Quantum codes from affine variety codes and their subfield-subcodes | We use affine variety codes and their subfield-subcodes for obtaining quantum
stabilizer codes via the CSS code construction. With this procedure, we get
codes with good parameters and a code whose parameters exceed the CSS quantum
Gilbert-Varshamov bound given by Feng and Ma. | 1403.4060v2 |
2015-10-19 | Decomposability of Finitely Generated Torsion-free Nilpotent Groups | We describe an algorithm for deciding whether or not a given finitely
generated torsion-free nilpotent group is decomposable as the direct product of
nontrivial subgroups. | 1510.05632v2 |
2016-02-27 | On automatic subsets of the Gaussian integers | Suppose that $a$ and $b$ are multiplicatively independent Gaussian integers,
that are both of modulus~$\geq \sqrt 5$. We prove that there exist a $X\subset
\mathbb Z[i]$ which is $a$-automatic but not $b$-automatic. This settles a
problem of Allouche, Cateland, Gilbert, Peitgen, Shallit, and Skordev. | 1602.08579v3 |
2016-09-22 | Manipulation of magnetic Skyrmions with a Scanning Tunneling Microscope | The dynamics of a single magnetic Skyrmion in an atomic spin system under the
influence of Scanning Tunneling Microscope is investigated by computer
simulations solving the Landau-Lifshitz-Gilbert equation. Two possible
scenarios are described: manipulation with aid of a spin-polarized tunneling
current and by an electric field created by the scanning tunneling microscope.
The dynamics during the creation and annihilation process is studied and the
possibility to move single Skyrmions is showed. | 1609.06797v1 |
2016-11-03 | Quantile Reinforcement Learning | In reinforcement learning, the standard criterion to evaluate policies in a
state is the expectation of (discounted) sum of rewards. However, this
criterion may not always be suitable, we consider an alternative criterion
based on the notion of quantiles. In the case of episodic reinforcement
learning problems, we propose an algorithm based on stochastic approximation
with two timescales. We evaluate our proposition on a simple model of the TV
show, Who wants to be a millionaire. | 1611.00862v1 |
2017-01-30 | Elementary equivalence vs commensurability for hyperbolic groups | We study to what extent torsion-free (Gromov)-hyperbolic groups are
elementarily equivalent to their finite index subgroups. In particular, we
prove that a hyperbolic limit group either is a free product of cyclic groups
and surface groups, or admits infinitely many subgroups of finite index which
are pairwise non elementarily equivalent. | 1701.08853v1 |
2017-08-01 | Imaging from the Inside Out: Inverse Scattering with Photoactivated Internal Sources | We propose a method to reconstruct the optical properties of a scattering
medium with subwavelength resolution. The method is based on the solution to
the inverse scattering problem with photoactivated internal sources. Numerical
simulations of three-dimensional structures demonstrate that a resolution of
approximately $\lambda/25$ is achievable. | 1708.00128v1 |
2017-09-22 | On self-dual four circulant codes | Four circulant codes form a special class of $2$-generator, index $4$,
quasi-cyclic codes. Under some conditions on their generator matrices they can
be shown to be self-dual. Artin primitive root conjecture shows the existence
of an infinite subclass of these codes satisfying a modified Gilbert-Varshamov
bound. | 1709.07548v1 |
2008-11-14 | Scott and Swarup's regular neighbourhood as a tree of cylinders | Let G be a finitely presented group. Scott and Swarup have constructed a
canonical splitting of G which encloses all almost invariant sets over
virtually polycyclic subgroups of a given length. We give an alternative
construction of this regular neighbourhood, by showing that it is the tree of
cylinders of a JSJ splitting. | 0811.2389v1 |
2016-03-02 | On self-dual double circulant codes | Self-dual double circulant codes of odd dimension are shown to be dihedral in
even characteristic and consta-dihedral in odd characteristic. Exact counting
formulae are derived for them and used to show they contain families of codes
with relative distance satisfying a modified Gilbert-Varshamov bound. | 1603.00762v1 |
2020-03-02 | Improved Gilbert-Varshamov Bound for Entanglement-Assisted Asymmetric Quantum Error Correction by Symplectic Orthogonality | We propose and prove an existential theorem for entanglement-assisted
asymmetric quantum error correction. Then we demonstrate its superiority over
the conventional one. | 2003.00668v2 |
2021-05-14 | Very regular solution to Landau-Lifshitz system with spin-polarized transport | In this paper, we provide a precise description of the compatibility
conditions for the initial data so that one can show the existence and
uniqueness of regular short-time solution to the Neumann initial-boundary
problem of a class of Landau-Lifshitz-Gilbert system with spin-polarized
transport, which is a strong nonlinear coupled parabolic system with non-local
energy. | 2105.06616v1 |
2009-07-15 | Barnett Effect in Thin Magnetic Films and Nanostructures | The Barnett effect refers to the magnetization induced by rotation of a
demagnetized ferromagnet. We describe the location and stability of stationary
states in rotating nanostructures using the Landau-Lifshitz-Gilbert equation.
The conditions for an experimental observation of the Barnett effect in
different materials and sample geometries are discussed. | 0907.2648v1 |
2013-11-14 | The dimension of the leafwise reduced cohomology | Geometric conditions are given so that the leafwise reduced cohomology is of
infinite dimension, specially for foliations with dense leaves on closed
manifolds. The main new definition involved is the intersection number of
subfoliations with "appropriate coefficients". The leafwise reduced cohomology
is also described for homogeneous foliations with dense leaves on closed
nilmanifolds. | 1311.3518v1 |
2018-02-21 | Enhanced global signal of neutral hydrogen due to excess radiation at cosmic dawn | We revisit the global 21cm signal calculation incorporating a possible radio
background at early times, and find that the global 21cm signal shows a much
stronger absorption feature, which could enhance detection prospects for future
21 cm experiments. In light of recent reports of a possible low-frequency
excess radio background, we propose that detailed 21 cm calculations should
include a possible early radio background. | 1802.07432v1 |
2019-03-22 | Nonlinear Iterative Hard Thresholding for Inverse Scattering | We consider the inverse scattering problem for sparse scatterers. An image
reconstruction algorithm is proposed that is based on a nonlinear
generalization of iterative hard thresholding. The convergence and error of the
method was analyzed by means of coherence estimates and compared to numerical
simulations. | 1903.10875v1 |
2019-04-06 | Phenomenological description of the dynamics of bipartite antiferromagnets in the limit of strong exchange | The equation of motion of the staggered order parameter is derived in a
step-by-step manner from the coupled Landau-Lifshitz-Gilbert dynamics of
bipartite spin moments in the limit of strong antiferromagnetic exchange
coupling. | 1904.03529v4 |
2019-04-19 | Variational approximation of functionals defined on $1$-dimensional connected sets in $\mathbb{R}^n$ | In this paper we consider the Euclidean Steiner tree problem and, more
generally, (single sink) Gilbert--Steiner problems as prototypical examples of
variational problems involving 1-dimensional connected sets in $\mathbb{R}^n$.
Following the the analysis for the planar case presented in [4], we provide a
variational approximation through Ginzburg--Landau type energies proving a
$\Gamma$-convergence result for $n \geq 3$. | 1904.09328v1 |
2020-07-14 | Competitively Pricing Parking in a Tree | Motivated by demand-responsive parking pricing systems we consider
posted-price algorithms for the online metrical matching problem and the online
metrical searching problem in a tree metric. Our main result is a poly-log
competitive posted-price algorithm for online metrical searching. | 2007.07294v2 |
2022-09-23 | Limiting Distributions of Sums with Random Spectral Weights | This paper studies the asymptotic properties of weighted sums of the form
$Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random
variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or
singular values in the classic Erd\H{o}s-R\'enyi-Gilbert model. In particular,
we prove central limit-type theorems for the sequences $n^{-1}Z_n$ with varying
conditions imposed on $X_1, X_2, \ldots, X_n$. | 2209.11389v1 |
2023-09-16 | Expansion of the Critical Intensity for the Random Connection Model | We derive an asymptotic expansion for the critical percolation density of the
random connection model as the dimension of the encapsulating space tends to
infinity. We calculate rigorously the first expansion terms for the Gilbert
disk model, the hyper-cubic model, the Gaussian connection kernel, and a
coordinate-wise Cauchy kernel. | 2309.08830v1 |
2024-03-14 | Remarks on the rate of linear vortex symmetrization | We reformulate results from the paper ``Linear vortex symmetrization: The
spectral density function" by Ionescu and the author in simplified forms and
derive rigorously the bounds given in Bassom and Gilbert (J. Fluid Mech.,
1998), which provided interesting insights on the vortex symmetrization
phenomenon. | 2403.09397v1 |
2003-10-29 | Comparing Chemical Abundances of the Damped Lya Systems and Metal-Poor Stars | I briefly draw comparisons between the fields of damped Lya and metal-poor
stellar abundances. In particular, I examine their complementary
age-metallicity relations and comparisons between the damped Lya and dwarf
galaxy abundance patterns. Regarding the latter, I describe a series of
problems concerning associating high z damped Lya systems with present-day
dwarfs. | 0310850v1 |
2006-12-01 | Stochastic excitation and damping of solar-type oscillations | A review on acoustic mode damping and excitation in solar-type stars is
presented. Current models for linear damping rates are discussed in the light
of recent low-degree solar linewidth measurements with emphasis on the
frequency-dependence of damping rates of low-order modes. Recent developments
in stochastic excitation models are reviewed and tested against the latest
high-quality data of solar-like oscillations, such as from alpha Cen A, and
against results obtained from hydrodynamical simulations. | 0612024v1 |
1997-08-11 | A theoretical study on the damping of collective excitations in a Bose-Einstein condensate | We study the damping of low-lying collective excitations of condensates in a
weakly interacting Bose gas model within the framework of imaginary time path
integral. A general expression of the damping rate has been obtained in the low
momentum limit for both the very low temperature regime and the higher
temperature regime. For the latter, the result is new and applicable to recent
experiments. Theoretical predictions for the damping rate are compared with the
experimental values. | 9708080v3 |
1997-09-24 | Damping in dilute Bose gases: a mean-field approach | Damping in a dilute Bose gas is investigated using a mean-field approximation
which describes the coupled oscillations of condensate and non-condensate atoms
in the collisionless regime. Explicit results for both Landau and Beliaev
damping rates are given for non-uniform gases. In the case of uniform systems
we obtain results for the damping of phonons both at zero and finite
temperature. The isothermal compressibility of a uniform gas is also discussed. | 9709259v1 |
2000-09-01 | Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud | We calculate the damping of condensate collective excitations at finite
temperatures arising from the lack of equilibrium between the condensate and
thermal atoms. We neglect the non-condensate dynamics by fixing the thermal
cloud in static equilibrium. We derive a set of generalized Bogoliubov
equations for finite temperatures that contain an explicit damping term due to
collisional exchange of atoms between the two components. We have numerically
solved these Bogoliubov equations to obtain the temperature dependence of the
damping of the condensate modes in a harmonic trap. We compare these results
with our recent work based on the Thomas-Fermi approximation. | 0009021v2 |
2000-11-20 | Cavity assisted quasiparticle damping in a Bose-Einstein condensate | We consider an atomic Bose-Einstein condensate held within an optical cavity
and interacting with laser fields. We show how the interaction of the cavity
mode with the condensate can cause energy due to excitations to be coupled to a
lossy cavity mode, which then decays, thus damping the condensate, how to
choose parameters for damping specific excitations, and how to target a range
of different excitations to potentially produce extremely cold condensates. | 0011341v2 |
2002-12-16 | The nonlinear damping of Bose-Einstein condensate oscillations at ultra-low temperatures | We analyze the damping of the transverse breathing mode in an elongated trap
at ultralow temperatures. The damping occurs due to the parametric resonance
entailing the energy transfer to the longitudinal degrees of freedom. It is
found that the nonlinear coupling between the transverse and discrete
longitudinal modes can result in an anomalous behavior of the damping as a
function of time with the partially reversed pumping of the breathing mode. The
picture revealed explains the results observed in [16]. | 0212377v2 |
2004-08-27 | Tunable magnetization damping in transition metal ternary alloys | We show that magnetization damping in Permalloy, Ni80Fe20 (``Py''), can be
enhanced sufficiently to reduce post-switching magnetization precession to an
acceptable level by alloying with the transition metal osmium (Os). The damping
increases monotonically upon raising the Os-concentration in Py, at least up to
9% of Os. Other effects of alloying with Os are suppression of magnetization
and enhancement of in-plane anisotropy. Magnetization damping also increases
significantly upon alloying with the five other transition metals included in
this study (4d-elements: Nb, Ru, Rh; 5d-elements: Ta, Pt) but never as strongly
as with Os. | 0408608v1 |
2005-03-06 | Nonlinear damping in nanomechanical beam oscillator | We investigate the impact of nonlinear damping on the dynamics of a
nanomechanical doubly clamped beam. The beam is driven into nonlinear regime
and the response is measured by a displacement detector. For data analysis we
introduce a nonlinear damping term to Duffing equation. The experiment shows
conclusively that accounting for nonlinear damping effects is needed for
correct modeling of the nanomechanical resonators under study. | 0503130v2 |
2006-05-23 | The origin of increase of damping in transition metals with rare earth impurities | The damping due to rare earth impurities in transition metals is discussed in
the low concentration limit. It is shown that the increase in damping is mainly
due to the coupling of the orbital moments of the rare earth impurities and the
conduction $p$-electrons. It is shown that an itinerant picture for the host
transition ions is needed to reproduce the observed dependence of the damping
on the total angular moment of the rare earths. | 0605583v1 |
2001-05-14 | Simplified models of electromagnetic and gravitational radiation damping | In previous work the authors analysed the global properties of an approximate
model of radiation damping for charged particles. This work is put into context
and related to the original motivation of understanding approximations used in
the study of gravitational radiation damping. It is examined to what extent the
results obtained previously depend on the particular model chosen. Comparisons
are made with other models for gravitational and electromagnetic fields. The
relation of the kinetic model for which theorems were proved to certain
many-particle models with radiation damping is exhibited. | 0105045v1 |
1994-06-07 | Damping Rate of a Yukawa Fermion at Finite Temperature | The damping of a massless fermion coupled to a massless scalar particle at
finite temperature is considered using the Braaten-Pisarski resummation
technique. First the hard thermal loop diagrams of this theory are extracted
and effective Green's functions are constructed. Using these effective Green's
functions the damping rate of a soft Yukawa fermion is calculated. This rate
provides the most simple example for the damping of a soft particle. To leading
order it is proportional to $g^2T$, whereas the one of a hard fermion is of
higher order. | 9406242v1 |
2006-05-02 | Moduli decay in the hot early Universe | We consider moduli fields interacting with thermalized relativistic matter.
We determine the temperature dependence of their damping rate and find it is
dominated by thermal effects in the high temperature regime, i.e. for
temperatures larger than their mass. For a simple scalar model the damping rate
is expressed through the known matter bulk viscosity. The high temperature
damping rate is always smaller than the Hubble rate, so that thermal effects
are not sufficient for solving the cosmological moduli problem. | 0605030v2 |
2006-11-27 | Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${{\mathbb R}^2}$ | We consider the zero viscosity limit of long time averages of solutions of
damped and driven Navier-Stokes equations in ${\mathbb R}^2$. We prove that the
rate of dissipation of enstrophy vanishes. Stationary statistical solutions of
the damped and driven Navier-Stokes equations converge to renormalized
stationary statistical solutions of the damped and driven Euler equations.
These solutions obey the enstrophy balance. | 0611782v1 |
2001-11-25 | The Landau Damping Effect and Complex-valued Nature of Physical Quantities | Within the framework of the hypothesis offered by authors about
complex-valued nature of physical quantities, the effect of the Landau damping
has been explored with assumption that not only frequency can be a small
imaginary component but also a wave vector. The numerical solution of the
obtained dispersion equation testifies that uncollisional damping is
accompanied in a certain region of space by antidumping of waves, and in
particular situations antidumping may prevail over damping. It is possible that
this effect may explain the experimental difficulties connected with inhibition
of instabilities of plasma in the problem of controllable thermonuclear fusion. | 0111176v1 |
2005-10-14 | Nontrapping arrest of Langmuir wave damping near the threshold amplitude | Evolution of a Langmuir wave is studied numerically for finite amplitudes
slightly above the threshold which separates damping from nondamping cases.
Arrest of linear damping is found to be a second-order effect due to ballistic
evolution of perturbations, resonant power transfer between field and
particles, and organization of phase space into a positive slope for the
average distribution function $f_{av}$ around the resonant wave phase speed
$v_\phi$. Near the threshold trapping in the wave potential does not arrest
damping or saturate the subsequent growth phase. | 0510131v3 |
2000-06-22 | Decoherence and Entanglement in Two-mode Squeezed Vacuum States | I investigate the decoherence of two-mode squeezed vacuum states by analyzing
the relative entropy of entanglement. I consider two sources of decoherence:
(i) the phase damping and (ii) the amplitude damping due to the coupling to the
thermal environment. In particular, I give the exact value of the relative
entropy of entanglement for the phase damping model. For the amplitude damping
model, I give an upper bound for the relative entropy of entanglement, which
turns out to be a good approximation for the entanglement measure in usual
experimental situations. | 0006100v1 |
2006-08-02 | Damped Population Oscillation in a Spontaneously Decaying Two-Level Atom Coupled to a Monochromatic Field | We investigate the time evolution of atomic population in a two-level atom
driven by a monochromatic radiation field, taking spontaneous emission into
account. The Rabi oscillation exhibits amplitude damping in time caused by
spontaneous emission. We show that the semiclassical master equation leads in
general to an overestimation of the damping rate and that a correct
quantitative description of the damped Rabi oscillation can thus be obtained
only with a full quantum mechanical theory. | 0608020v1 |
2008-12-18 | Dipole Oscillations of a Fermi Gas in a Disordered Trap: Damping and Localization | We theoretically study the dipole oscillations of an ideal Fermi gas in a
disordered trap. We show that even weak disorder induces strong damping of the
oscillations and we identify a metal-insulator crossover. For very weak
disorder, we show that damping results from a dephasing effect related to weak
random perturbations of the energy spectrum. For increasing disorder, we show
that the Fermi gas crosses over to an insulating regime characterized by
strong-damping due to the proliferation of localized states. | 0812.3501v2 |
2009-03-11 | Confronting the damping of the baryon acoustic oscillations with observation | We investigate the damping of the baryon acoustic oscillations in the matter
power spectrum due to the quasinonlinear clustering and redshift-space
distortions by confronting the models with the observations of the Sloan
Digital Sky Survey luminous red galaxy sample. The chi-squared test suggests
that the observed power spectrum is better matched by models with the damping
of the baryon acoustic oscillations rather than the ones without the damping. | 0903.1883v1 |
2009-04-10 | Spectral deviations for the damped wave equation | We prove a Weyl-type fractal upper bound for the spectrum of the damped wave
equation, on a negatively curved compact manifold. It is known that most of the
eigenvalues have an imaginary part close to the average of the damping
function. We count the number of eigenvalues in a given horizontal strip
deviating from this typical behaviour; the exponent that appears naturally is
the `entropy' that gives the deviation rate from the Birkhoff ergodic theorem
for the geodesic flow. A Weyl-type lower bound is still far from reach; but in
the particular case of arithmetic surfaces, and for a strong enough damping, we
can use the trace formula to prove a result going in this direction. | 0904.1736v1 |
2009-10-26 | Pressure Fronts in 1D Damped Nonlinear Lattices | The propagation of pressure fronts (impact solutions) in 1D chains of atoms
coupled by anharmonic potentials between nearest neighbor and submitted to
damping forces preserving uniform motion, is investigated. Travelling fronts
between two regions at different uniform pressures are found numerically and
well approximate analytically. It is proven that there are three analytical
relations between the impact velocity, the compression, the front velocity and
the energy dissipation which only depend on the coupling potential and are
\textit{independent} of the damping. Such travelling front solutions cannot
exist without damping. | 0910.4890v1 |
2010-01-12 | Decoherence and damping in ideal gases | The particle and current densities are shown to display damping and undergo
decoherence in ideal quantum gases. The damping is read off from the equations
of motion reminiscent of the Navier-Stokes equations and shows some formal
similarity with Landau damping. The decoherence leads to consistent density and
current histories with characteristic length and time scales given by the ideal
gas. | 1001.1803v2 |
2010-05-14 | The effect of spin magnetization in the damping of electron plasma oscillations | The effect of spin of particles in the propagation of plasma waves is studied
using a semi-classical kinetic theory for a magnetized plasma. We focus in the
simple damping effects for the electrostatic wave modes besides Landau damping.
Without taking into account more quantum effects than spin contribution to
Vlasov's equation, we show that spin produces a new damping or instability
which is proportional to the zeroth order magnetization of the system. This
correction depends on the electromagnetic part of the wave which is coupled
with the spin vector. | 1005.2573v1 |
2010-06-01 | Recent Progress on a Manifold Damped and Detuned Structure for CLIC | A damped detuned structure for the main X-band linacs of CLIC is being
investigated as an alternative design to the present baseline heavily damped
structure. In our earlier designs we studied detuned structures, operating at
11.994 GHz, with a range of dipole bandwidths in order to ensure the structure
satisfies beam dynamics and rf breakdown constraints. Here we report on the
development of a damped and detuned structure which satisfies both constraints.
Preparations for high power testing of the structure are also discussed | 1006.0087v1 |
2010-07-21 | Finite temperature damping of collective modes of a BCS-BEC crossover superfluid | A new mechanism is proposed to explain the puzzling damping of collective
excitations, which was recently observed in the experiments of strongly
interacting Fermi gases below the superfluid critical temperature on the
fermionic (BCS) side of Feshbach resonance. Sound velocity, superfluid density
and damping rate are calculated with effective field theory. We find that a
dominant damping process is due to the interaction between superfluid phonons
and thermally excited fermionic quasiparticles, in contrast to the previously
proposed pair-breaking mechanism. Results from our effective model are compared
quantitatively with recent experimental findings, showing a good agreement. | 1007.3694v2 |
2010-08-04 | Confinement induced by fermion damping in three-dimensional QED | The three-dimensional non-compact QED is known to exhibit weak confinement
when fermions acquire a finite mass via the mechanism of dynamical chiral
symmetry breaking. In this paper, we study the effect of fermion damping caused
by elastic scattering on the classical potential between fermions. By
calculating the vacuum polarization function that incorporates the fermion
damping effect, we show that fermion damping can induce a weak confinement even
when the fermions are massless and the chiral symmetry is not broken. | 1008.0736v2 |
2011-06-22 | Highly Damped Quasinormal Modes and the Small Scale Structure of Quantum Corrected Black Hole Exteriors | Quasinormal modes provide valuable information about the structure of
spacetime outside a black hole. There is also a conjectured relationship
between the highly damped quasinormal modes and the semi-classical spectrum of
the horizon area/entropy. In this paper, we show that for spacetimes
characterized by more than one scale, the "infinitely damped" modes in
principle probe the structure of spacetime outside the horizon at the shortest
length scales. We demonstrate this with the calculation of the highly damped
quasinormal modes of the non-singular, single horizon, quantum corrected black
hole derived in [14]. | 1106.4357v1 |
2012-06-14 | Damping of optomechanical disks resonators vibrating in air | We report on miniature GaAs disk optomechanical resonators vibrating in air
in the radiofrequency range. The flexural modes of the disks are studied by
scanning electron microscopy and optical interferometry, and correctly modeled
with the elasticity theory for annular plates. The mechanical damping is
systematically measured, and confronted with original analytical models for air
damping. Formulas are derived that correctly reproduce both the mechanical
modes and the damping behavior, and can serve as design tools for
optomechanical applications in fluidic environment. | 1206.3032v1 |
2012-07-09 | A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations | In this paper, we establish a generalized H{\"o}lder's or interpolation
inequality for weighted spaces in which the weights are non-necessarily
homogeneous. We apply it to the stabilization of some damped wave-like
evolution equations. This allows obtaining explicit decay rates for smooth
solutions for more general classes of damping operators. In particular, for
$1-d$ models, we can give an explicit decay estimate for pointwise damping
mechanisms supported on any strategic point. | 1207.2030v2 |
2012-07-10 | Conformation dependent damping and generalization of fluctuation-dissipation relation | Damping on an object generally depends on its conformation (shape size etc.).
We consider the Langevin dynamics of a model system with a conformation
dependent damping and generalize the fluctuation dissipation relation to fit in
such a situation. We derive equilibrium distribution function for such a case
which converges to the standard Boltzmann form at the limit of uniform damping.
The results can have implications, in general, for barrier overcoming processes
where standard Boltzmann statistics is slow. | 1207.2218v2 |
2013-04-07 | Phenomenological model of anomalous magnon softening and damping in half-metallic manganites | To describe anomalous zone-boundary softening and damping of magnons in
manganites we present a phenomenological two-fluid model containing
ferromagnetic Fermi-liquid and non-Fermi-liquid components. The Fermi-liquid
component accounts for softening of zone-boundary magnons and for the Landau
damping of magnons in the Stoner continuum arising at low frequencies due to
zero-point effects. Coupling of the Fermi-liquid and non-Fermi-liquid fluids
yields conventional long wavelength magnons damped due to their coupling with
longitudinal spin fluctuations. | 1304.1983v1 |
2013-04-25 | Determination of Transverse Density Structuring from Propagating MHD Waves in the Solar Atmosphere | We present a Bayesian seismology inversion technique for propagating
magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The
technique uses theoretical predictions for the spatial damping of propagating
kink waves in transversely inhomogeneous coronal waveguides. It combines wave
amplitude damping length scales along the waveguide with theoretical results
for resonantly damped propagating kink waves to infer the plasma density
variation across the oscillating structures. Provided the spatial dependence of
the velocity amplitude along the propagation direction is measured and the
existence of two different damping regimes is identified, the technique would
enable us to fully constrain the transverse density structuring, providing
estimates for the density contrast and its transverse inhomogeneity length
scale. | 1304.6869v1 |
2013-07-08 | Optimal decay rate of the bipolar Euler-Poisson system with damping in $\mathbb{R}^3$ | By rewriting a bipolar Euler-Poisson equations with damping into an Euler
equation with damping coupled with an Euler-Poisson equation with damping, and
using a new spectral analysis, we obtain the optimal decay results of the
solutions in $L^2$-norm, which improve theose in \cite{Li3, Wu3}. More
precisely, the velocities $u_1,u_2$ decay at the $L^2-$rate $(1+t)^{-{5}{4}}$,
which is faster than the normal $L^2-$rate $(1+t)^{-{3}{4}}$ for the Heat
equation and the Navier-Stokes equations. In addition, the disparity of two
densities $\rho_1-\rho_2$ and the disparity of two velocities $u_1-u_2$ decay
at the $L^2$-rate $(1+t)^{-2}$. | 1307.2081v1 |
2013-07-27 | Symmetry considerations on radiation damping | It is well known that a direct Lagrangian description of radiation damping is
still missing. In this paper we will use a specific approach of this problem
which is the standard way to treat the radiation damping problem. The
objectives here are to construct: a N=2 supersymmetric extension for the model
describing the radiation damping on the noncommutative plane with electric and
magnetic interactions; a dualization analysis of the original action; the
supercharge algebra and the total Hamiltonian for the system. | 1307.7319v1 |
2014-02-10 | Damping of a nanocantilever by paramagnetic spins | We compute damping of mechanical oscillations of a cantilever that contains
flipping paramagnetic spins. This kind of damping is mandated by the dynamics
of the total angular momentum, spin + mechanical. Rigorous expression for the
damping rate is derived in terms of measurable parameters. The effect of spins
on the quality factor of the cantilever can be significant in cantilevers of
small length that have large concentration of paramagnetic spins of atomic
and/or nuclear origin. | 1402.2326v1 |
2014-02-20 | Long-time behavior of solutions of a BBM equation with generalized damping | We study the long-time behavior of the solution of a damped BBM equation $u_t
+ u_x - u_{xxt} + uu_x + \mathscr{L}_{\gamma}(u) = 0$. The proposed dampings
$\mathscr{L}_{\gamma}$ generalize standards ones, as parabolic
($\mathscr{L}_{\gamma}(u)=-\Delta u$) or weak damping
($\mathscr{L}_{\gamma}(u)=\gamma u$) and allows us to consider a greater range.
After establish the local well-posedness in the energy space, we investigate
some numerical properties. | 1402.5009v1 |
2014-02-24 | N=2 supersymmetric radiation damping problem on a noncommutative plane | It is well known that a direct Lagrangian description of radiation damping is
still missing. In this paper a specific approach of this problem was used,
which is the standard way to treat the radiation damping problem. A $N=2$
supersymmetric extension for the model describing the radiation damping on the
noncommutative plane with electric and magnetic interactions was obtained. The
entire supercharge algebra and the total Hamiltonian for the system were
analyzed. Finally, noncommutativity features were introduced and its
consequences were explored.. | 1402.6996v1 |
2014-11-03 | Renormalized solutions to the continuity equation with an integrable damping term | We consider the continuity equation with a nonsmooth vector field and a
damping term. In their fundamental paper, DiPerna and Lions proved that, when
the damping term is bounded in space and time, the equation is well posed in
the class of distributional solutions and the solution is transported by
suitable characteristics of the vector field. In this paper, we prove existence
and uniqueness of renormalized solutions in the case of an integrable damping
term, employing a new logarithmic estimate inspired by analogous ideas of
Ambrosio, Lecumberry, and Maniglia, Crippa and De Lellis in the Lagrangian
case. | 1411.0451v1 |
2015-03-20 | Applying a formula for generator redispatch to damp interarea oscillations using synchrophasors | If an interarea oscillatory mode has insufficient damping, generator
redispatch can be used to improve its damping. We explain and apply a new
analytic formula for the modal sensitivity to rank the best pairs of generators
to redispatch. The formula requires some dynamic power system data and we show
how to obtain that data from synchrophasor measurements. The application of the
formula to damp interarea modes is explained and illustrated with interarea
modes of the New England 10-machine power system. | 1503.06144v2 |
2016-01-21 | Codeword Stabilized Quantum Codes for Asymmetric Channels | We discuss a method to adapt the codeword stabilized (CWS) quantum code
framework to the problem of finding asymmetric quantum codes. We focus on the
corresponding Pauli error models for amplitude damping noise and phase damping
noise. In particular, we look at codes for Pauli error models that correct one
or two amplitude damping errors. Applying local Clifford operations on graph
states, we are able to exhaustively search for all possible codes up to length
$9$. With a similar method, we also look at codes for the Pauli error model
that detect a single amplitude error and detect multiple phase damping errors.
Many new codes with good parameters are found, including nonadditive codes and
degenerate codes. | 1601.05763v1 |
2016-02-08 | On Boundary Damped Inhomogeneous Timoshenko Beams and Related Problems | We consider the model equations for the Timoshenko beam as a first order
system in the framework of evolutionary equations. The focus is on boundary
damping, which is implemented as a dynamic boundary condition. A change of
material laws allows to include a large class of cases of boundary damping. By
choosing a particular material law, it is shown that the first order approach
to Sturm-Liouville problems with boundary damping is also covered. | 1602.02521v1 |
2016-02-13 | Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain | In this paper, we consider the asymptotic behavior of solutions to the wave
equation with space-dependent damping in an exterior domain. We prove that when
the damping is effective, the solution is approximated by that of the
corresponding heat equation as time tends to infinity. Our proof is based on
semigroup estimates for the corresponding heat equation and weighted energy
estimates for the damped wave equation. The optimality of the decay late for
solutions is also established. | 1602.04318v1 |
2016-02-29 | Robust quantum state recovery from amplitude damping within a mixed states framework | Due to the interaction with the environment, a quantum state is subjected to
decoherence which becomes one of the biggest problems for practical quantum
computation. Amplitude damping is one of the most important decoherence
processes. Here, we show that general two-qubit mixed states undergoing an
amplitude damping can be almost completely restored using a reversal procedure.
This reversal procedure through CNOT and Hadamard gates, could also protect the
entanglement of two-qubit mixed states, when it undergoes general amplitude
damping. Moreover, in the presence of uncertainty in the underlying system, we
propose a robust recovering method with optimal characteristics of the problem. | 1602.08865v1 |
2016-07-21 | Protecting and enhancing spin squeezing under decoherence using weak measurement | We propose an efficient method to protect spin squeezing under the action of
amplitude-damping, depolarizing and phase-damping channels based on measurement
reversal from weak measurement, and consider an ensemble of N independent
spin-1/2 particles with exchange symmetry. We find that spin squeezing can be
enhanced greatly under three different decoherence channels and spin-squeezing
sudden death (SSSD) can be avoided undergoing amplitude damping and
phase-damping channels. | 1607.06530v2 |
2016-09-05 | Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain | This paper is concerned with weighted energy estimates and diffusion
phenomena for the initial-boundary problem of the wave equation with
space-dependent damping term in an exterior domain. In this analysis, an
elliptic problem was introduced by Todorova and Yordanov. This attempt was
quite useful when the coefficient of the damping term is radially symmetric. In
this paper, by modifying their elliptic problem, we establish weighted energy
estimates and diffusion phenomena even when the coefficient of the damping term
is not radially symmetric. | 1609.01063v2 |
2016-11-16 | Finite-orbit-width effects on the geodesic acoustic mode in the toroidally rotating tokamak plasma | The Landau damping of geodesic acoustic mode (GAM) in a torodial rotating
tokamak plasma is analytically investigated by taking into account the
finite-orbit-width (FOW) resonance effect to the 3rd order. The analytical
result is shown to agree well with the numerical solution. The dependence of
the damping rate on the toroidal Mach number $M$ relies on $k_r \rho_i$. For
sufficiently small $k_r \rho_i$, the damping rate monotonically decreases with
$M$. For relatively large $k_r \rho_i$, the damping rate increases with $M$
until approaching the maximum and then decreases with $M$. | 1611.05168v1 |
2017-08-20 | Radiation Damping of a Polarizable Particle | A polarizable body moving in an external electromagnetic field will slow
down. This effect is referred to as radiation damping and is analogous to
Doppler cooling in atomic physics. Using the principles of special relativity
we derive an expression for the radiation damping force and find that it solely
depends on the scattered power. The cooling of the particle's center-of-mass
motion is balanced by heating due to radiation pressure shot noise, giving rise
to an equilibrium that depends on the ratio of the field's frequency and the
particle's mass. While damping is of relativistic nature heating has it's roots
in quantum mechanics. | 1708.06628v1 |
2017-11-01 | Analysis of A Splitting Scheme for Damped Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise | In this paper, we investigate the damped stochastic nonlinear
Schr\"odinger(NLS) equation with multiplicative noise and its splitting-based
approximation. When the damped effect is large enough, we prove that the
solutions of the damped stochastic NLS equation and the splitting scheme are
exponential stable and possess some exponential integrability.
These properties lead that the strong order of the scheme is $\frac 12$ and
independent of time. Meanwhile, we analyze the regularity of the Kolmogorov
equation with respect to the equation. As a consequence, the weak order of the
scheme is shown to be twice the strong order and independent of time. | 1711.00516v2 |
2017-12-31 | Stabilization of the weakly coupled wave-plate system with one internal damping | This paper is addressed to a stabilization problem of a system coupled by a
wave and a Euler-Bernoulli plate equation. Only one equation is supposed to be
damped. Under some assumption about the damping and the coupling terms, it is
shown that sufficiently smooth solutions of the system decay logarithmically at
infinity without any geometric conditions on the effective damping domain. The
proofs of these decay results rely on the interpolation inequalities for the
coupled elliptic-parabolic systems and make use of the estimate of the
resolvent operator for the coupled system. The main tools to derive the desired
interpolation inequalities are global Carleman estimates. | 1801.00232v1 |
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