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2018-11-19
|
Second order linear evolution equations with general dissipation
|
The contraction semigroup $S(t)={\rm e}^{t\mathbb{A}}$ generated by the
abstract linear dissipative evolution equation $$ \ddot u + A u + f(A) \dot u=0
$$ is analyzed, where $A$ is a strictly positive selfadjoint operator and $f$
is an arbitrary nonnegative continuous function on the spectrum of $A$. A full
description of the spectrum of the infinitesimal generator $\mathbb{A}$ of
$S(t)$ is provided. Necessary and sufficient conditions for the stability, the
semiuniform stability and the exponential stability of the semigroup are found,
depending on the behavior of $f$ and the spectral properties of its zero-set.
Applications to wave, beam and plate equations with fractional damping are also
discussed.
|
1811.07667v1
|
2018-11-21
|
Electronic properties of the Dirac and Weyl systems with first- and higher-order dispersion in non-Fermi-liquid picture
|
We investigate the non-Fermi-liquid behaviors of the 2D and 3D Dirac/Weyl
systems with low-order and higher order dispersion. The self-energy correction,
symmetry, free energy, optical conductivity, density of states, and spectral
function are studied. We found that, for Dirac/Weyl systems with higher order
dispersion, the non-Fermi-liquid features remain even at finite chemical
potential, and they are distinct from the ones in Fermi-liquid picture and the
conventional non-Fermi-liquid picture. The Landau damping of the longitudinal
excitations within random-phase-approximation (RPA) for the non-Fermi-liquid
case are also discussed.
|
1811.08809v2
|
2018-11-24
|
Hot carriers generated by plasmons: where are they are generated and where do they go from there?
|
A physically transparent unified theory of optically and plasmon induced hot
carrier generation in metals is developed with all the relevant mechanisms
included. Analytical expressions that estimate the carrier generation rates,
their locations, energy and direction of motion are obtained. Among four
mechanisms considered: interband absorption, phonon and defect assisted
absorption, electron electron scattering assisted absorption, and surface
collision assisted absorption (Landau damping), it is the last one that
generates hot carriers which are most useful for practical applications in
photo detection and photo catalysis.
|
1811.09873v1
|
2018-12-01
|
Parametric Resonance in a dissipative system á la Kronig-Penney
|
The competition between parametric resonance (PR) and dissipation is studied
in the damped Kronig-Penney model, with time-dependent dissipation rate
gamma(t). In the classical case, it is shown that dissipation leaves just a
finite number of PR-bands at most, suppressing those at higher frequencies. An
analysis of the Lewis-Reisenfeld invariant I(q,p,rho) is performed, showing
that, in the PR regime, the auxiliary function rho(t) can be chosen bounded or
unbounded, depending on the initial conditions.
|
1812.00189v1
|
2018-12-05
|
Small-scale structure from charged leptophilia
|
We consider a charged leptophilic extension of the Standard Model of particle
physics as a minimal dark sector. It accomodates a WIMP paradigm at the
TeV-scale that is sufficient to solve all small-scale problems of $\Lambda$CDM
and explain the excess of highly energetic cosmic ray Standard Model electrons
and positrons presented recently by the DAMPE collaboration. The predictive
power of this model allows to test it in the near future.
|
1812.02182v1
|
2018-12-08
|
Quantum interference and exceptional points
|
Exceptional points (EPs), i.e. branch point singularities of non-Hermitian
Hamiltonians, are ubiquitous in optics. So far, the signatures of EPs have been
mostly studied assuming classical light.
In the passive parity-time ($\mathcal{PT}$) optical coupler, a fingerprint of
EPs resulting from the coalescence of two resonance modes is a qualitative
change of the photon decay law, from damped Rabi-like oscillations to
transparency, as the EP is crossed by increasing the loss rate. However, when
probed by non-classical states of light, quantum interference can hide EPs.
Here it is shown that, under excitation with polarization-entangled two-photon
states, EP phase transition is smoothed until to disappear as the effective
particle statistics is changed from bosonic to fermionic.
|
1812.03360v1
|
2018-12-10
|
Stability preserving approximations of a semilinear hyperbolic gas transport model
|
We consider the discretization of a semilinear damped wave equation arising,
for instance, in the modeling of gas transport in pipeline networks. For time
invariant boundary data, the solutions of the problem are shown to converge
exponentially fast to steady states. We further prove that this decay behavior
is inherited uniformly by a class of Galerkin approximations, including finite
element, spectral, and structure preserving model reduction methods. These
theoretical findings are illustrated by numerical tests.
|
1812.03726v1
|
2018-12-10
|
Comment on "Negative Landau damping in bilayer graphene"
|
In [Phys. Rev. Lett. vol. 119, p. 133901 (2017)] it was argued that two
parallel graphene layers in the presence of electron drift support unstable
plasmon modes. Here we show that the predicted plasmon instability is an
artifact of errors upon evaluation of graphene polarizability in the presence
if electron drift. Crucial role of broken Galilean invariance and spatial
dispersion of conductivity for suppression of plasmon instabilities is
highlighted.
|
1812.03764v1
|
2018-12-13
|
Remark on the pointwise stabilization of an elastic string equation
|
We consider an initial and boundary value problem the one dimensional wave
equation with damping concentrated at an interior point. We prove a result of a
logarithmic decay of the energy of a system with homogeneous Dirichlet boundary
conditions. The method used is based on the resolvent estimate approach which
derives from the Carleman estimate technique. Under an algebraic assumption
describing the right location of the actuator, we prove a logarithmic decay of
the energy of solution. We show that this assumption is lower than the one
given by [Tuc] and [AHT] which depends on the diophantine approximations
properties of the actuator's location.
|
1812.05922v1
|
2018-12-18
|
No unique solution to the seismological problem of standing kink MHD waves
|
The aim of this paper is to point out that the classic seismological problem
using observations and theoretical expressions for the periods and damping
times of transverse standing magnetohydrodynamic (MHD) waves in coronal loops
is better referred to as a reduced seismological problem. Reduced emphasises
the fact that only a small number of characteristic quantities of the
equilibrium profiles can be determined. Reduced also implies that there is no
unique solution to the full seismological problem. Even the reduced
seismological problem does not allow a unique solution. Bayesian inference
results support our mathematical arguments and offer insight into the
relationship between the algebraic and the probabilistic inversions.
|
1812.07266v1
|
2019-02-01
|
Contact variational integrators
|
We present geometric numerical integrators for contact flows that stem from a
discretization of Herglotz' variational principle. First we show that the
resulting discrete map is a contact transformation and that any contact map can
be derived from a variational principle. Then we discuss the backward error
analysis of our variational integrators, including the construction of a
modified Lagrangian. Throughout the paper we use the damped harmonic oscillator
as a benchmark example to compare our integrators to their symplectic
analogues.
|
1902.00436v4
|
2019-02-13
|
Build-up of Vibron-Mediated Electron Correlations in Molecular Junctions
|
We investigate on the same footing the time-dependent electronic transport
properties and vibrational dynamics of a molecular junction. We show that
fluctuations of both the molecular vibron displacement and the electronic
current across the junction undergo damped oscillations towards the
steady-state. We assign the former to the onset of electron tunneling events
assisted by vibron-emission. The time-dependent build-up of electron-hole
correlations is revealed as a departure of the charge-transfer statistics from
the generalized-binomial one after a critical time tc. The phonon-back action
on the tunneling electrons is shown to amplify and accelerate this build-up
mechanism.
|
1902.04825v1
|
2019-02-20
|
Stability boundary approximation of periodic dynamics
|
We develop here the method for obtaining approximate stability boundaries in
the space of parameters for systems with parametric excitation. The monodromy
(Floquet) matrix of linearized system is found by averaging method. For system
with 2 degrees of freedom (DOF) we derive general approximate stability
conditions. We study domains of stability with the use of fourth order
approximations of monodromy matrix on example of inverted position of a
pendulum with vertically oscillating pivot. Addition of small damping shifts
the stability boundaries upwards, thus resulting to both stabilization and
destabilization effects.
|
1902.09957v2
|
2019-03-04
|
A continuous dependence result for a dynamic debonding model in dimension one
|
In this paper we address the problem of continuous dependence on initial and
boundary data for a one-dimensional debonding model describing a thin film
peeled away from a substrate. The system underlying the process couples the
weakly damped wave equation with a Griffith's criterion which rules the
evolution of the debonded region. We show that under general convergence
assumptions on the data the corresponding solutions converge to the limit one
with respect to different natural topologies.
|
1903.01251v3
|
2019-03-09
|
On exact controllability of infinite-dimensional linear port-Hamiltonian systems
|
Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional
spatial domain with full boundary control and without internal damping are
studied. This class of systems includes models of beams and waves as well as
the transport equation and networks of nonhomogeneous transmission lines. The
main result shows that well-posed port-Hamiltonian systems, with state space
$L^2((0,1);\mathbb C^n)$ and input space $\mathbb C^n$, are exactly
controllable.
|
1903.03819v2
|
2019-03-14
|
Quantum Parametric Resonance of a dissipative oscillator: fading and persistent memory in the long-time evolution
|
The evolution of a quantum oscillator, with periodically varying frequency
and damping, is studied in the two cases of parametric resonance (PR) producing
a limited, or unlimited stretching of the wave function. The different
asymptotic behaviors of the energy distribution, show the non trivial interplay
between PR and the initial quantum state. In the first case, the oscillator's
mean energy tends asymptotically to a fully classical value, independent of the
initial state, with vanishing relative quantum fluctuations. In the second
case, the memory of the initial state persists over arbitrary long time scales,
both in the mean value and in the large quantum fluctuations of the energy.
|
1903.05874v1
|
2019-03-18
|
Theory of spin transport through antiferromagnetic insulator
|
A theoretical formulation for spin transport through an antiferromagnetic
(AF) insulator is presented in the case driven/detected by direct/inverse spin
Hall effect in two heavy metal contacts. The spin signal is shown to be
transferred by the ferromagnetic correlation function of the antiferromagnet,
which is calculated based on a magnon representation. To cover high temperature
regimes, we include an auxiliary field representing short AF correlations and a
temperature-dependent damping due to magnon scattering. The diffusion length
for spin is long close to the degeneracy of the two AF magnons, and has a
maximum as function of temperature near the N\'eel transition.
|
1903.07223v1
|
2019-03-19
|
Quantum corrections to a spin-orbit coupled Bose-Einstein Condensate
|
We study systematically the quantum corrections to a weakly interacting
Bose-Einstein condensate with spin-orbit coupling. We show that quantum
fluctuations, enhanced by the spin-orbit coupling, modify quantitatively the
mean-field properties such as the superfluid density, spin polarizability, and
sound velocity. We find that the phase boundary between the plane wave and zero
momentum phases is shifted to a smaller transverse field. We also calculate the
Beliaev and Landau damping rates and find that the Landau process dominates the
quasiparticle decay even at low temperature.
|
1903.08182v3
|
2019-03-21
|
Kinetic plasma waves carrying orbital angular momentum
|
The structure of Langmuir plasma waves carrying a finite angular orbital
momentum is revised in the paraxial optics approximation. It is shown that the
kinetic effects related to higher-order momenta of the electron distribution
function lead to coupling of Laguerre-Gaussian modes and result in modification
of the wave dispersion and damping. The theoretical analysis is compared to the
three-dimensional particle-in-cell numerical simulations for a mode with
orbital momentum l = 2. It is demonstrated that propagation of such a plasma
wave is accompanied with generation of quasi-static axial and azimuthal
magnetic fields which are consequence of the longitudinal and orbital momentum
transported with the wave.
|
1903.08955v1
|
2019-03-22
|
Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
|
The exact Kohn-Sham iteration of generalized density-functional theory in
finite dimensions witha Moreau-Yosida regularized universal Lieb functional and
an adaptive damping step is shown toconverge to the correct ground-state
density.
|
1903.09579v3
|
2019-03-28
|
Spectral function for overoccupied gluodynamics from classical lattice simulations
|
We study the spectral properties of an overoccupied gluonic system far from
equilibrium. Using classical Yang-Mills simulations and linear response theory,
we determine the statistical and spectral functions. We measure dispersion
relations and damping rates of transversally and longitudinally polarized
excitations in the gluonic plasma, and also study further structures in the
spectral function.
|
1903.11942v1
|
2019-05-03
|
Cooperative Distributed Robust Control of Modular Mobile Robots with Bounded Curvature and Velocity
|
A novel motion control system for Compliant Framed wheeled Modular Mobile
Robots (CFMMR) is studied in this paper. This type of wheeled mobile robot uses
rigid axles coupled by compliant frame modules to provide both full suspension
and enhanced steering capability without additional hardware. The proposed
control system is developed by combining a bounded curvature-based kinematic
controller and a nonlinear damping dynamic controller. In particular, multiple
forms of controller interaction are examined. A twoaxle scout CFMMR
configuration is used to evaluate the different control structures.
Experimental results verify efficient motion control of posture regulation.
|
1905.03130v1
|
2019-05-17
|
Secret objectives: promoting inquiry and tackling preconceptions in teaching laboratories
|
In its most general form, a `secret objective' is any inconsistency between
the experimental reality and the information provided to students prior to
starting work on an experiment. Students are challenged to identify the secret
objectives and then given freedom to explore and understand the experiment,
thus encouraging and facilitating genuine inquiry elements in introductory
laboratory courses. Damping of a simple pendulum is used as a concrete example
to demonstrate how secret objectives can be included. We also discuss the
implications of the secret objectives method and how this can provide a link
between the concepts of problem based learning and inquiry style labs.
|
1905.07267v1
|
2019-05-17
|
A Dynamical Systems Perspective on Nesterov Acceleration
|
We present a dynamical system framework for understanding Nesterov's
accelerated gradient method. In contrast to earlier work, our derivation does
not rely on a vanishing step size argument. We show that Nesterov acceleration
arises from discretizing an ordinary differential equation with a semi-implicit
Euler integration scheme. We analyze both the underlying differential equation
as well as the discretization to obtain insights into the phenomenon of
acceleration. The analysis suggests that a curvature-dependent damping term
lies at the heart of the phenomenon. We further establish connections between
the discretized and the continuous-time dynamics.
|
1905.07436v1
|
2019-05-19
|
Models for damped water waves
|
In this paper we derive some new weakly nonlinear asymptotic models
describing viscous waves in deep water with or without surface tension effects.
These asymptotic models take into account several different dissipative effects
and are obtained from the free boundary problems formulated in the works of
Dias, Dyachenko and Zakharov (Physics Letters A, 2008), Jiang, Ting, Perlin and
Schultz (Journal of Fluid Mechanics,1996) and Wu, Liu and Yue (Journal of Fluid
Mechanics, 2006).
|
1905.07751v2
|
2019-05-21
|
A generalized Complex Ginzburg-Landau Equation: global existence and stability results
|
We consider the complex Ginzburg-Landau equation with two pure-power
nonlinearities and a damping term. After proving a general global existence
result, we focus on the existence and stability of several periodic orbits,
namely the trivial equilibrium, bound-states and solutions independent of the
spatial variable. In particular, we construct bound-states either explicitly in
the real line or through a bifurcation argument for a double eigenvalue of the
Dirichlet-Laplace operator on bounded domains.
|
1905.08521v2
|
2019-08-13
|
An Analytical Approach to Eddy Current in Electromagnetic Damping
|
An analytical method of calculating eddy current in a metallic spinning
gyroscope in external magnetic field is presented. With reasonable assumptions,
the problem is simplified from the time-dependent one governed by Maxwell
equations to the boundary value problem of Poisson equation, which yields a
closed form expression of the eddy current. The rotation frequency as a
function of time is calculated, compared with experiment and the relative error
is found to be 8.61%.
|
1908.04713v2
|
2019-08-15
|
Saddle-Node Bifurcation and Homoclinic Persistence in AFM with Periodic Forcing
|
We study the dynamics of an Atomic Force Microscope (AFM) model, under the
Lennard-Jones force with non-linear damping, and harmonic forcing. We establish
the bifurcation diagrams for equilibria in a conservative system. Particularly,
we present conditions that guarantee the local existence of saddle-node
bifurcations. By using the Melnikov method, the region in the space parameters
where the persistence of homoclinic orbits is determined in a non-conservative
system.
|
1908.05777v1
|
2019-08-17
|
An overview of quasinormal modes in modified and extended gravity
|
As gravitational waves are now being nearly routinely measured with
interferometers, the question of using them to probe new physics becomes
increasingly legitimate. In this article, we rely on a well established
framework to investigate how the complex frequencies of quasinormal modes are
affected by different models. The tendencies are explicitly shown, for both the
pulsation and the damping rate. The goal is, at this stage, purely qualitative.
This opportunity is also taken to derive the Regge-Wheeler equation for general
static and spherically symmetric metrics.
|
1908.06311v3
|
2019-08-18
|
Uniform attractors of non-autonomous Kirchhoff wave models
|
The paper investigates the existence and upper semicontinuity of uniform
attractors of the perturbed non-autonomous Kirchhoff wave equations with strong
damping and supercritical nonlinearity: $u_{tt}-\Delta
u_{t}-(1+\epsilon\|\nabla u\|^{2})\Delta u+f(u)=g(x,t)$, where $\epsilon\in
[0,1]$ is a perturbed parameter. It shows that when the nonlinearity $f(u)$ is
of supercritical growth $p: \frac{N+2}{N-2}=p^*<p<p^{**}=\frac{N+4}{(N-4)^+}$:
(i) the related evolution process has a compact uniform attractor
$\mathcal{A}_\ls^\e $ for each $\epsilon\in [0,1]$; (ii) the family of uniform
attractor $\mathcal{A}_\ls^\e $ is upper semicontinuous on the perturbed
parameter $\epsilon$ in the sense of partially strong topology.
|
1908.06500v1
|
2019-08-25
|
An I + PI Controller Structure for Integrating Processes with Dead-Time: Application to Depth Control of an Autonomous Underwater Vehicle
|
The paper presents a feedforward plus feedback controller structure with I
and PI controllers for control of an integrating process with dead time.
Guidelines for controller gain selection based on time domain specifications of
damping factor and natural frequency are provided along with simulations
indicating the selectivity of process response. The utility of proposed
controller structure is shown by simulating the depth control of a nonlinear
autonomous underwater vehicle system by the proposed controller structure.
|
1908.09250v1
|
2019-08-27
|
Maxwell's lesser demon: a quantum engine driven by pointer measurements
|
We discuss a self-contained spin-boson model for a measurement-driven engine,
in which a demon generates work from thermal excitations of a quantum spin via
measurement and feedback control. Instead of granting it full direct access to
the spin state and to Landauer's erasure strokes for optimal performance, we
restrict this demon's action to pointer measurements, i.e. random or continuous
interrogations of a damped mechanical oscillator that assumes macroscopically
distinct positions depending on the spin state. The engine can reach
simultaneously the power and efficiency benchmarks and operate in temperature
regimes where quantum Otto engines would fail.
|
1908.10102v2
|
2019-08-29
|
Enhanced dissipation for the 2D Couette flow in critical space
|
We consider the 2D incompressible Navier-Stokes equations on
$\mathbb{T}\times \mathbf{R}$, with initial vorticity that is $\delta$ close in
$H^{log}_xL^2_{y}$ to $-1$(the vorticity of the Couette flow $(y,0)$). We prove
that if $\delta\ll \nu^{1/2}$, where $\nu$ denotes the viscosity, then the
solution of the Navier-Stokes equation approaches some shear flow which is also
close to Couette flow for time $t\gg \nu^{-1/3}$ by a mixing-enhanced
dissipation effect and then converges back to Couette flow when $t\to +\infty$.
In particular, we show the nonlinear enhanced dissipation and the inviscid
damping results in the almost critical space $H^{log}_xL^2_{y}\subset
L^2_{x,y}$.
|
1908.11035v1
|
2019-08-30
|
On equilibrium radiation and zero-point fluctuations in non-relativistic electron gas
|
Examination of equilibrium radiation in plasma media shows that the spectral
the energy distribution of such radiation is different from the Planck
equilibrium radiation. Using the previously obtained general relations for the
spectral energy density of equilibrium radiation in a system of charged
particles, we consider radiation in an electron in the limiting case of an
infinitesimal damping. It is shown that zero vacuum fluctuations which are part
of the full spectral energy distribution should be renormalized. In this case,
the renormalized zero vacuum fluctuations depend on the electron density. A
similar effect should exist in the general case of a quasineutral plasma.
|
1909.01159v1
|
2019-09-10
|
A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source
|
We consider the Neumann problem for a coupled chemotaxis-haptotaxis model of
cancer invasion with/without kinetic source in a 2D bounded and smooth domain.
For a large class of cell kinetic sources including zero source and
sub-logistic sources, we detect an explicit condition involving the chemotactic
strength, the asymptotic "damping" rate, and the initial mass of cells to
ensure uniform-in-time boundedness for the corresponding Neumann problem. Our
finding significantly improves existing 2D global existence and boundedness in
related chemotaxis-/haptotaxis systems.
|
1909.04577v1
|
2019-09-10
|
Deviations from Gaussianity in deterministic discrete time dynamical systems
|
In this paper we examine the deviations from Gaussianity for two types of
random variable converging to a normal distribution, namely sums of random
variables generated by a deterministic discrete time map and a linearly damped
variable driven by a deterministic map. We demonstrate how Edgeworth expansions
provide a universal description of the deviations from the limiting normal
distribution. We derive explicit expressions for these asymptotic expansions
and provide numerical evidence of their accuracy.
|
1909.04578v1
|
2019-09-17
|
Microwave induced tunable subharmonic steps in superconductor-ferromagnet-superconductor Josephson junction
|
We investigate the coupling between ferromagnet and superconducting phase
dynamics in superconductor-ferromagnet-superconductor Josephson junction. The
current-voltage characteristics of the junction demonstrate a pattern of
subharmonic current steps which forms a devil's staircase structure. We show
that a width of the steps becomes maximal at ferromagnetic resonance. Moreover,
we demonstrate that the structure of the steps and their widths can be tuned by
changing the frequency of the external magnetic field, ratio of Josephson to
magnetic energy, Gilbert damping and the junction size.
|
1909.08004v1
|
2019-09-19
|
Magnetization dynamics of the compensated ferrimagnet $Mn_{2}Ru_{x}Ga$
|
Here we study both static and time-resolved dynamic magnetic properties of
the compensated ferrimagnet from room temperature down to 10K, thus crossing
the magnetic compensation temperature $T_{M}$. The behaviour is analysed with a
model of a simple collinear ferrimagnet with uniaxial anisotropy and
site-specific gyromagnetic ratios. We find a maximum zero-applied-field
resonance frequency of $\sim$160GHz and a low intrinsic Gilbert damping
$\alpha$$\sim$0.02, making it a very attractive candidate for various
spintronic applications.
|
1909.09085v1
|
2019-09-20
|
$L^p$-theory for a fluid-structure interaction model
|
We consider a fluid-structure interaction model for an incompressible fluid
where the elastic response of the free boundary is given by a damped Kirchhoff
plate model. Utilizing the Newton polygon approach, we first prove maximal
regularity in $L^p$-Sobolev spaces for a linearized version. Based on this, we
show existence and uniqueness of the strong solution of the nonlinear system
for small data.
|
1909.09344v1
|
2019-11-07
|
Quantum optical levitation of a mirror
|
While the levitating mirror has seen renewed interest lately, relatively
little is known about its quantum behaviour. In this paper we present a quantum
theory of a one dimensional levitating mirror. The mirror forms a part of a
Fabry-Perot cavity where the circulating intracavity field supports the mirror
through radiation pressure alone. We find a blue and red detuned steady-state
of which only the blue detuned solution with damping on the mirror and cavity
is stable. We find strong entanglement (15-20 ebits) between the mirror output
and cavity output and squeezing in the mirror position.
|
1911.02705v2
|
2019-11-22
|
Lenard-Balescu correction to mean-field theory
|
In the mean-field regime, the evolution of a gas of $N$ interacting particles
is governed in first approximation by a Vlasov type equation with a
self-induced force field. This equation is conservative and describes return to
equilibrium only in the very weak sense of Landau damping. However, the first
correction to this approximation is given by the Lenard-Balescu operator, which
dissipates entropy on the very long timescale $O(N)$. In this paper, we show
how one can derive rigorously this correction on intermediate timescales (of
order $O(N^r)$ for $r<1$), close to equilibrium.
|
1911.10151v2
|
2019-11-28
|
Transport properties of spin superfluids: comparing easy-plane ferro- and antiferromagnets
|
We present a study on spin-superfluid transport based on an atomistic,
classical spin model. Easy-plane ferro- as well as antiferromagnets are
considered, which allows for a direct comparison of these two material classes
based on the same model assumptions. We find a spin-superfluid transport which
is robust against variations of the boundary conditions, thermal fluctuations,
and dissipation modeled via Gilbert damping. Though the spin accumulations is
smaller for antiferromagnets the range of the spin-superfluid transport turns
out to be identical for ferro- and antiferromagnets. Finally, we calculate and
explore the role of the driving frequency and especially the critical
frequency, where phase slips occur and the spin accumulation breaks down.
|
1911.12786v1
|
2020-01-03
|
Skin effect and excitation spectral of interacting non-Hermitian system
|
The non-Hermitian Su-Schrieffer-Heeger spinless Fermion model with
interacting terms is studied by exact diagonalization. The model is derived
from the spin chain with damping Dzyaloshinskii-Moriya interaction. The
presence of the interaction induce anomalous spectral function. The skin effect
is exhibited by the non-diagonal terms of the Green's function, i.e. the
spatial correlation. The interaction modifies the degeneracy between the ground
state and the first excited state of the half filled systems, as well as
between the ground state of the half and half plus one filled systems. The
energy bands of the higher excited states within the topological regime have
complicated pattern, depending on the sign and amplitude of the interaction.
|
2001.00697v1
|
2020-01-06
|
Convergence of classical optimized non-overlapping Schwarz method for Helmholtz problems in closed domains
|
In this paper we discuss the convergence of state-of-the-art optimized
Schwarz transmission conditions for Helmholtz problems defined on closed
domains (i.e. setups which do not exhibit an outgoing wave condition), as
commonly encountered when modeling cavities. In particular, the impact of
back-propagating waves on the Dirichlet-to-Neumann map is analyzed. Afterwards,
the performance of the well-established optimized 0th-order, evanescent modes
damping, optimized 2nd-order and Pad\'e-localized square-root transmission
conditions is discussed.
|
2001.01502v2
|
2020-01-06
|
Blow-up of solutions to Nakao's problem via an iteration argument
|
In this paper, we consider blow-up behavior of weak solutions to a weakly
coupled system for a semilinear damped wave equation and a semilinear wave
equation in $\mathbb{R}^n$. This problem is part of the so-called Nakao's
problem proposed by Professor Mitsuhiro Nakao (Kyushu University) for a
critical relation between the exponents $p$ and $q$. By applying an iteration
method for unbounded multipliers with a slicing procedure, we prove blow-up of
weak solutions for Nakao's problem even for small data. We improve the blow-up
result and upper bound estimates for lifespan comparing with the previous
research, especially, in higher dimensional cases.
|
2001.01533v2
|
2020-01-20
|
Classical field model for arrays of photon condensates
|
We introduce a classical phasor model for the description of multimode photon
condensates that thermalize through repeated absorptions and reemissions by dye
molecules. Thermal equilibrium is expressed through the fluctuation-dissipation
relation that connects the energy damping to spontaneous emission fluctuations.
We apply our model to a photonic Josephson junction (two coupled wells) and to
one- and two-dimensional arrays of photon condensates. In the limit of zero
pumping and cavity losses, we recover the thermal equilibrium result, but in
the weakly driven-dissipative case in the canonical regime, we find suppressed
density and phase fluctuations with respect to the ideal Bose gas.
|
2001.07137v1
|
2020-01-13
|
Obtaining the Drude Equation for Electrons in Metals Using a Fractional Variational Principle
|
A fractional variational principle was derived in order to be used with
lagrangians containing fractional derivatives of order 1/2. By forcing the
action associated to this type of lagrangian to be stationary, a modified
fractional Euler-Lagrange equation was obtained. This was shown to reproduce
the equations of motion of two basic 1-dimensional energy-dissipative systems:
a spring-mass system damped by friction, and a RLC circuit connected in series.
Finally, by using the fractional Euler-Lagrange equation, the Drude
relationship for electrons in metals was recovered when a fractional kinetic
energy was taken into consideration in the electron's associated energies.
|
2001.08531v1
|
2020-02-03
|
Undamped transverse electric mode in undoped two-dimensional tilted Dirac cone materials
|
Transverse electric (TE) modes can not propagate through the conducting
solids. This is because the continuum of particle-hole excitations of
conductors contaminates with the TE mode and dampes it out. But in solids
hosting tilted Dirac cone (TDC) that admit a description in terms of a modified
Minkowski spacetime, the new spacetime structure remedies this issue and
therefore a tilted Dirac cone material (TDM) supports the propagation of an
undamped TE mode which is sustained by density fluctuations. The resulting TE
mode propagates at fermionic velocities which strongly confines the mode to the
surface of the two-dimensional (2D) TDM.
|
2002.00561v1
|
2020-02-03
|
Observability and unique continuation of the adjoint of a linearized compressible fluid-structure model in a 2d channel
|
Our objective is to study the observability and unique continuation property
of the adjoint of a linearized compressible fluid structure interaction model
in a 2D channel. Concerning the structure we will consider a damped
Euler-Bernoulli beam located on a portion of the boundary. In the present
article we establish an observability inequality for the adjoint of the
linearized fluid structure interaction problem under consideration which in
principle is equivalent with the null controllability of the linearized system.
As a corollary of the derived observability inequality we also obtain a unique
continuation property for the adjoint problem.
|
2002.00877v1
|
2020-02-05
|
Study Zitterbewegung effect in a Quasi One-dimensional Relativistic Quantum Plasma by DHW formalization
|
Using Dirac equation together with the Wigner distribution function,the
trembling motion,known as Zitterbewegung effect,of moving electrons in
quasi-one-dimensional relativistic quantum plasma is theoretically
investigated.The relativistic Wigner matrix is used to calculate the mean
values of the position and velocity operators for a Dirac gas of electrons.It
is found that the oscillatory behavior of measurable quantities could be
associated with the Zitterbewegung effect which manifests itself as a damping
interference pattern stemming from mixing the positive and negative dispersion
modes of Dirac particles.
|
2002.01819v1
|
2020-02-28
|
Quantum Damping of Skyrmion Crystal Eigenmodes due to Spontaneous Quasiparticle Decay
|
The elementary excitations of skyrmion crystals experience both emergent
magnetic fields and anharmonic interactions brought about by the topologically
nontrivial noncollinear texture. The resulting flat bands cause strong
spontaneous quasiparticle decay, dressing the eigenmodes of skyrmion crystals
with a finite zero-temperature quantum lifetime. Sweeping the flat bands
through the spectrum by changing the magnetic field leads to an externally
controllable energy-selective magnon breakdown. In particular, we uncover that
the three fundamental modes, i.e., the anticlockwise, breathing, and clockwise
mode, exhibit distinct decay behavior, with the clockwise (anticlockwise) mode
being the least (most) stable mode out of the three.
|
2002.12676v1
|
2020-04-06
|
Spectra of Gurtin-Pipkin type of integro-differential equations and applications to waves in graded viscoelastic structures
|
In this paper, we study spectral properties and spectral enclosures for the
Gurtin-Pipkin type of integro-differential equations in several dimensions. The
analysis is based on an operator function and we consider the relation between
the studied operator function and other formulations of the spectral problem.
The theory is applied to wave equations with Boltzmann damping.
|
2004.02828v3
|
2020-04-09
|
Efficient Linear and Unconditionally Energy Stable Schemes for the Modified Phase Field Crystal Equation
|
In this paper, we construct efficient schemes based on the scalar auxiliary
variable (SAV) block-centered finite difference method for the modified phase
field crystal (MPFC) equation, which is a sixth-order nonlinear damped wave
equation. The schemes are linear, conserve mass and unconditionally dissipate a
pseudo energy. We prove rigorously second-order error estimates in both time
and space for the phase field variable in discrete norms. We also present some
numerical experiments to verify our theoretical results and demonstrate the
robustness and accuracy.
|
2004.04319v1
|
2020-04-13
|
Plasma echoes near stable Penrose data
|
In this paper we construct particular solutions to the classical
Vlasov-Poisson system near stable Penrose initial data on $\mathbb{T} \times
\mathbb{R}$ that are a combination of elementary waves with arbitrarily high
frequencies. These waves mutually interact giving birth, eventually, to an
infinite cascade of echoes of smaller and smaller amplitude. The echo solutions
do not belong to the analytic or Gevrey classes studied by Mouhot and Villani,
but do, nonetheless, exhibit damping phenomena for large times.
|
2004.05984v1
|
2020-04-14
|
Critical thresholds in 1D pressureless Euler-Poisson systems with varying background
|
The Euler Poisson equations describe important physical phenomena in many
applications such as semiconductor modeling and plasma physics. This paper is
to advance our understanding of critical threshold phenomena in such systems in
the presence of different forces. We identify critical thresholds in two damped
Euler Poisson systems, with and without alignment, both with attractive
potential and spatially varying background state. For both systems, we give
respective bounds for subcritical and supercritical regions in the space of
initial configuration, thereby proving the existence of a critical threshold
for each scenario. Key tools include comparison with auxiliary systems, phase
space analysis of the transformed system.
|
2004.06807v1
|
2020-04-17
|
Collective coordinate study of spin wave emission from dynamic domain wall
|
We study theoretically the spin wave emission from a moving domain wall in a
ferromagnet. Introducing a deformation mode describing a modulation of the wall
thickness in the collective coordinate description, we show that thickness
variation couples to the spin wave linearly and induces spin wave emission. The
dominant emitted spin wave turns out to be polarized in the out-of wall plane
($\phi$)-direction. The emission contributes to the Gilbert damping parameter
proportional to $\hbar\omega_\phi/K$, the ratio of the angular frequency
$\omega_\phi$ of $\phi$ and the easy-axis anisotropy energy $K$.
|
2004.08082v1
|
2020-04-14
|
Reinforcement Learning Approach to Vibration Compensation for Dynamic Feed Drive Systems
|
Vibration compensation is important for many domains. For the machine tool
industry it translates to higher machining precision and longer component
lifetime. Current methods for vibration damping have their shortcomings (e.g.
need for accurate dynamic models). In this paper we present a reinforcement
learning based approach to vibration compensation applied to a machine tool
axis. The work describes the problem formulation, the solution, the
implementation and experiments using industrial machine tool hardware and
control system.
|
2004.09263v1
|
2020-04-24
|
Mode Converting Alfvén Waves from Magnetic Reconnection Enhancing the Energy Source for the Aurora Borealis
|
Previous studies have concluded that the Hall magnetic field structures
generated during magnetic reconnection are carried away by kinetic Alfv\'{e}n
waves (KAW). Here we apply a kinetic simulation with an ion/electron mass ratio
closer to its natural value and find that much-reduced damping rates permit the
KAW to convert into shear Alfv\'{e}n waves (SAW). For magnetotail reconnection
these SAW provides efficient transport of wave energy, enhancing the energy
input for the Aurora Borealis by orders of magnitude above previous estimates.
|
2004.11755v1
|
2020-04-25
|
Torque-induced dispersive readout in a weakly coupled hybrid system
|
We propose a quantum state readout mechanism of a weakly coupled qubit in
dispersive regime. The hybrid system consists of ferromagnetic insulator and a
superconducting qubit in a microwave cavity. The enhancement of the measurement
sensitivity is achieved by exerting torque on the ferromagnetic insulator
magnetization, which compensates the damping of the system leading to an
exceptional point. The proposed machanism allows to measure the qubit state
either via the transmission of the cavity or the FMR signal of the magnetic
material.
|
2004.12114v1
|
2020-05-02
|
Collective excitations in biased bilayer graphene: Temperature effects
|
We have studied the temperature effect on collective excitations in biased
bilayer graphene within random-phase approximation. From the zeros of
temperature dynamical dielectric function of the system we have found one
weakly damped plasmon mode. For a given electrostatic potential bias, at low
(high) temperature T the plasmon frequency changes slightly (increases
remarkably) with T. We have also studied the effects of potential bias and
carrier density on the plasmon frequency of the system at finite temperatures.
|
2005.00736v2
|
2020-05-04
|
Blow-up and lifespan estimates for Nakao's type problem with nonlinearities of derivative type
|
In the present paper, we investigate blow-up and lifespan estimates for a
class of semilinear hyperbolic coupled system in $\mathbb{R}^n$ with
$n\geqslant 1$, which is part of the so-called Nakao's type problem weakly
coupled a semilinear damped wave equation with a semilinear wave equation with
nonlinearities of derivative type. By constructing two time-dependent
functionals and employing an iteration method for unbounded multiplier with
slicing procedure, the results of blow-up and upper bound estimates for the
lifespan of energy solutions are derived. The model seems to be hyperbolic-like
instead of parabolic-like. Particularly, the blow-up result for one dimensional
case is optimal.
|
2005.01294v2
|
2020-05-04
|
Finite time extinction for a damped nonlinear Schr{ö}dinger equation in the whole space
|
We consider a nonlinear Schr{\"o}dinger equation set in the whole space with
a single power of interaction and an external source. We first establish
existence and uniqueness of the solutions and then show, in low space
dimension, that the solutions vanish at a finite time. Under a smallness
hypothesis of the initial data and some suitable additional assumptions on the
external source, we also show that we can choose the upper bound on which time
the solutions vanish.
|
2005.01471v1
|
2020-05-05
|
Tuning Rules for a Class of Port-Hamiltonian Mechanical Systems
|
In this extended abstract, we propose a tuning approach for nonlinear
mechanical systems to modify the behavior of the closed-loop system, where we
are particularly interested in attenuating oscillations from the transient
response. Towards this end, we inject damping into the system, and we provide
two tuning methods to select the gains that are appropriate for our purposes.
Furthermore, we apply these tuning rules to a 2DoF planar manipulator and
present its simulation results.
|
2005.02319v2
|
2020-05-14
|
An SQP method for equality constrained optimization on manifolds
|
We extend the class of SQP methods for equality constrained optimization to
the setting of differentiable manifolds. The use of retractions and
stratifications allows us to pull back the involved mappings to linear spaces.
We study local quadratic convergence to minimizers. In addition we present a
composite step method for globalization based on cubic regularization of the
objective function and affine covariant damped Newton method for feasibility.
We show transition to fast local convergence of this scheme. We test our method
on equilibrium problems in finite elasticity where the stable equilibrium
position of an inextensible transversely isotropic elastic rod under dead load
is sought.
|
2005.06844v1
|
2020-05-29
|
A minimizing-movements approach to GENERIC systems
|
We present a new time discretization scheme adapted to the structure of
GENERIC systems. The scheme is variational in nature and is based on a
conditional incremental minimization. The GENERIC structure of the scheme
provides stability and convergence of the scheme. We prove that the scheme can
be rigorously implemented in the case of the damped harmonic oscillator.
Numerical evidence is collected, illustrating the performance of the method.
|
2005.14437v1
|
2020-06-01
|
A global existence result for a semilinear wave equation with lower order terms on compact Lie groups
|
In this paper, we study the semilinear wave equation with lower order terms
(damping and mass) and with power type nonlinearity $|u|^p$ on compact Lie
groups. We will prove the global in time existence of small data solutions in
the evolution energy space without requiring any lower bounds for $p>1$. In our
approach, we employ some results from Fourier analysis on compact Lie groups.
|
2006.00759v1
|
2020-06-20
|
Dynamical invariants and quantization of the one-dimensional time-dependent, damped, and driven harmonic oscillator
|
In this paper, it is proposed a quantization procedure for the
one-dimensional harmonic oscillator with time-dependent frequency,
time-dependent driven force, and time-dependent dissipative term. The method is
based on the construction of dynamical invariants previously proposed by the
authors, in which fundamental importance is given to the linear invariants of
the oscillator.
|
2006.11637v1
|
2020-06-24
|
Resonances in pulsatile channel flow with an elastic wall
|
Interactions between fluids and elastic solids are ubiquitous in application
ranging from aeronautical and civil engineering to physiological flows. Here we
study the pulsatile flow through a two-dimensional Starling resistor as a
simple model for unsteady flow in elastic vessels. We numerically solve the
equations governing the flow and the large-displacement elasticity and show
that the system responds as a forced harmonic oscillator with non-conventional
damping. We derive an analytical prediction for the amplitude of the
oscillatory wall deformation, and thus the conditions under which resonances
occur or vanish.
|
2006.13695v2
|
2020-06-22
|
A mathematical walk into the paradox of Bloch oscillations
|
We describe mathematically the apparently paradoxical phenomenon that an
electronic current in a semiconductor can flow because of collisions, and not
despite them. A transport model of charge transport in a one-dimensional
semiconductor crystal is considered, where each electron follows the periodic
hamiltonian trajectories, determined by the semiconductor band structure, and
undergoes non-elastic collisions with a phonon bath. Starting from the detailed
phase-space model, a closed system of ODEs is obtained for averaged quantities.
Such a simplified model is nevertheless capable of describing transient Bloch
oscillations, their damping and the consequent onset of a steady current flow,
which is in good agreement with the available experimental data.
|
2006.13703v1
|
2020-07-01
|
Feedback control for random, linear hyperbolic balance laws
|
We design the controls of physical systems that are faced by uncertainties.
The system dynamics are described by random hyperbolic balance laws. The
control aims to steer the system to a desired state under uncertainties. We
propose a control based on Lyapunov stability analysis of a suitable series
expansion of the random dynamics. The control damps the impact of uncertainties
exponentially fast in time. The presented approach can be applied to a large
class of physical systems and random perturbations, as e.g. Gaussian processes.
We illustrate the control effect on a stochastic viscoplastic material model.
|
2007.00526v4
|
2020-07-08
|
Computational Semi-Discrete Optimal Transport with General Storage Fees
|
We propose and analyze a modified damped Newton algorithm to solve the
semi-discrete optimal transport with storage fees. We prove global linear
convergence for a wide range of storage fee functions, the main assumption
being that each warehouse's storage costs are independent. We show that if $F$
is an arbitrary storage fee function that satisfies this independence condition
then $F$ can be perturbed into a new storage fee function so that our algorithm
converges. We also show that the optimizers are stable under these
perturbations. Furthermore, our results come with quantitative rates.
|
2007.03830v1
|
2020-07-08
|
Stabilizing entanglement in two-mode Gaussian states
|
We analyze the stabilizability of entangled two-mode Gaussian states in three
benchmark dissipative models: local damping, dissipators engineered to preserve
two-mode squeezed states, and cascaded oscillators. In the first two models, we
determine principal upper bounds on the stabilizable entanglement, while in the
last model, arbitrary amounts of entanglement can be stabilized. All three
models exhibit a tradeoff between state entanglement and purity in the
entanglement maximizing limit. Our results are derived from the
Hamiltonian-independent stabilizability conditions for Gaussian systems. Here,
we sharpen these conditions with respect to their applicability.
|
2007.04004v2
|
2020-07-16
|
Stability results of a singular local interaction elastic/viscoelastic coupled wave equations with time delay
|
The purpose of this paper is to investigate the stabilization of a
one-dimensional coupled wave equations with non smooth localized viscoelastic
damping of Kelvin-Voigt type and localized time delay. Using a general criteria
of Arendt-Batty, we show the strong stability of our system in the absence of
the compactness of the resolvent. Finally, using frequency domain approach
combining with a multiplier method, we prove a polynomial energy decay rate of
order 1/t.
|
2007.08316v1
|
2020-07-05
|
Qualitative and numerical study of the stability of a nonlinear time-delayed dispersive equation
|
This paper deals with the stability analysis of a nonlinear time-delayed
dispersive equation of order four. First, we prove the well-posedness of the
system and give some regularity results. Then, we show that the zero solution
of the system exponentially converges to zero when the time tends to infinity
provided that the time-delay is small and the damping term satisfies reasonable
conditions. Lastly, an intensive numerical study is put forward and numerical
illustrations of the stability result are provided.
|
2007.12598v1
|
2020-07-27
|
Oscillations of skyrmion clusters in Co/Pt multilayer nanodots
|
In this work we study the oscillations of the skyrmion cores in a multilayer
nanodot as a function of the number of skyrmions hosted in the system. When all
the skyrmions in the nanodot have the same core radius, and after applying a
perpendicular spin-polarized current, a relaxation process takes place towards
an equilibrium configuration that is accompanied by coherent damped
oscillations of the skyrmion cores, whose frequency depends on the number of
skyrmions present in the nanodot. Additionally, we found that the oscillation
frequency is directly related to the total energy of the system.
|
2007.13651v1
|
2021-02-01
|
Comment on "Deformed Fokker-Planck equation: inhomogeneous medium with a position-dependent mass"
|
In a recent paper by B. G. da Costa {\it et al.} [Phys. Rev. E 102,
062105(2020)], the phenomenological Langevin equation and the corresponding
Fokker-Planck equation for an inhomogeneous medium with a position-dependent
particle mass and position-dependent damping coefficient have been studied. The
aim of this comment is to present a microscopic derivation of the Langevin
equation for such a system. It is not equivalent to that in the commented
paper.
|
2102.00699v1
|
2021-02-05
|
Nonequilibrium statistical mechanics of crystals
|
The local equilibrium approach previously developed by the Authors [J.
Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken
symmetries is applied to crystalline solids. The macroscopic hydrodynamics of
crystals and their local thermodynamic and transport properties are deduced
from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo
formulas are obtained for all the transport coefficients. The eight
hydrodynamic modes and their dispersion relation are studied for general and
cubic crystals. In the same twenty crystallographic classes as those compatible
with piezoelectricity, cross effects coupling transport between linear momentum
and heat or crystalline order are shown to split the degeneracy of damping
rates for modes propagating in opposite generic directions.
|
2102.03096v1
|
2021-06-09
|
Time scaling and quantum speed limit in non-Hermitian Hamiltonians
|
We report on a time scaling technique to enhance the performances of quantum
protocols in non-Hermitian systems. The considered time scaling involves no
extra-couplings and yields a significant enhancement of the quantum fidelity
for a comparable amount of resources. We discuss the application of this
technique to quantum state transfers in 2 and 3-level open quantum systems. We
derive the quantum speed limit in a system governed by a non-Hermitian
Hamiltonian. Interestingly, we show that, with an appropriate driving, the
time-scaling technique preserves the optimality of the quantum speed with
respect to the quantum speed limit while reducing significantly the damping of
the quantum state norm.
|
2106.05155v1
|
2021-06-15
|
Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions
|
We present new approaches for solving constrained multicomponent nonlinear
Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an
artificial time and solve an extended damped second order dynamic system whose
stationary solution is the solution to the time-independent nonlinear
Schr\"odinger equation. Constraints are often considered by projection onto the
constraint set, here we include them explicitly into the dynamical system. We
show the applicability and efficiency of the methods on examples of relevance
in modern physics applications.
|
2106.08010v1
|
2021-06-22
|
Analysis of a High-Dimensional Extended B92 Protocol
|
Quantum key distribution (QKD) allows two parties to establish a shared
secret key that is secure against all-powerful adversaries. One such protocol
named B92 is quite appealing due to its simplicity but is highly sensitive to
channel noise. In this work, we investigate a high-dimensional variant of an
extended version of the B92 protocol and show that it can distill a key over
high noise channels. The protocol we consider requires that Alice send only
three high-dimensional states and Bob only perform partial measurements. We
perform an information-theoretic security analysis of our protocol and compare
its key rate to that of a high-dimensional BB84 protocol over depolarization
and amplitude damping channels.
|
2106.11460v1
|
2021-06-23
|
Universal unitary transfer of continuous-variable quantum states into a few qubits
|
We present a protocol for transferring arbitrary continuous-variable quantum
states into a few discrete-variable qubits and back. The protocol is
deterministic and utilizes only two-mode Rabi-type interactions which are
readily available in trapped-ion and superconducting circuit platforms. The
inevitable errors caused by transferring an infinite-dimensional state into a
finite-dimensional register are suppressed exponentially with the number of
qubits. Furthermore, the encoded states exhibit robustness against noise, such
as dephasing and amplitude damping, acting on the qubits. Our protocol thus
provides a powerful and flexible tool for discrete-continuous hybrid quantum
systems.
|
2106.12272v1
|
2021-06-28
|
Global well-posedness and inviscid limits of the generalized Oldroyd type models
|
We obtain the global small solutions to the generalized Oldroyd-B model
without damping on the stress tensor in $\mathbb{R}^n$. Our result give
positive answers partially to the question proposed by Elgindi and Liu (Remark
2 in Elgindi and Liu [J Differ Equ 259:1958--1966, 2015)]. The proof relies
heavily on the trick of transferring dissipation from $u$ to $\tau$, and a new
commutator estimate which may be of interest for future works. Moreover, we
prove a global result of inviscid limit of two dimensional Oldroyd type models
in the Sobolev spaces. The convergence rate is also obtained simultaneously.
|
2106.14785v1
|
2021-07-07
|
Linear stability of the Couette flow for the non-isentropic compressible fluid
|
We are concerned with the linear stability of the Couette flow for the
non-isentropic compressible Navier-Stokes equations with vanished shear
viscosity in a domain $\mathbb{T}\times \mathbb{R}$. For a general initial data
settled in Sobolev spaces, we obtain a Lyapunov type instability of the
density, the temperature, the compressible part of the velocity field, and also
obtain an inviscid damping for the incompressible part of the velocity field.
Moreover, if the initial density, the initial temperature and the
incompressible part of the initial velocity field satisfy some quality
relation, we can prove the enhanced dissipation phenomenon for the velocity
field.
|
2107.03268v1
|
2021-07-05
|
The q-Levenberg-Marquardt method for unconstrained nonlinear optimization
|
A q-Levenberg-Marquardt method is an iterative procedure that blends a
q-steepest descent and q-Gauss-Newton methods. When the current solution is far
from the correct one the algorithm acts as the q-steepest descent method.
Otherwise the algorithm acts as the q-Gauss-Newton method. A damping parameter
is used to interpolate between these two methods. The q-parameter is used to
escape from local minima and to speed up the search process near the optimal
solution.
|
2107.03304v1
|
2021-07-08
|
Fractional powers approach of operators for higher order abstract Cauchy problems
|
In this paper we explore the theory of fractional powers of non-negative (and
not necessarily self-adjoint) operators and its amazing relationship with the
Chebyshev polynomials of the second kind to obtain results of existence,
regularity and behavior asymptotic of solutions for linear abstract evolution
equations of $n$-th order in time, where $n\geqslant3$. We also prove
generalizations of classical results on structural damping for linear systems
of differential equations.
|
2107.04148v1
|
2021-07-19
|
Decoherence in the three-state quantum walk
|
Quantum walks are dynamic systems with a wide range of applications in
quantum computation and quantum simulation of analog systems, therefore it is
of common interest to understand what changes from an isolated process to one
embedded in an environment. In the present work, we analyze the decoherence in
a three-state uni-dimensional quantum walk. The approaches taken into
consideration to account for the environment effects are phase and amplitude
damping Kraus operators, unitary noise on the coin space, and broken links.
|
2107.09124v1
|
2021-07-23
|
Surface-induced reduction of the switching field in nanomagnets
|
Magnetization reversal in a many-spin nanomagnet subjected to an rf magnetic
field, on top of a DC magnetic field, is studied by numerically solving the
system of coupled (damped) Landau-Lifshitz equations. It is demonstrated that
spin-misalignment induced by surface anisotropy favors switching with a DC
magnetic field weaker than the Stoner-Wohlfarth switching field, for optimal
intensities and frequencies of the rf field.
|
2107.11407v3
|
2021-07-30
|
Fine structure of current noise spectra in nanoelectromechanical resonators
|
We study frequency dependent noise of a suspended carbon nanotube quantum dot
nanoelectromechanical resonator induced by electron-vibration coupling. By
using rigorous Keldysh diagrammatic technique, we build a formal framework to
connect the vibration properties and the electrical measurement. We find that
the noise power spectrum has a narrow resonant peak at the frequency of
vibrational modes. This fine structure feature disappears due to a coherent
cancellation effect when tuning tunneling barriers to a symmetric point. We
note that measuring the electrical current noise spectra provides an
alternative and ultra-sensitive detection method for determining the damping
and dephasing of the quantum vibration modes.
|
2107.14788v1
|
2021-11-04
|
Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics
|
We investigate the problem of reversing quantum dynamics, specifically via
optimal Petz recovery maps. We focus on typical decoherence channels, such as
dephasing, depolarizing and amplitude damping. We illustrate how well a
physically implementable recovery map simulates an inverse evolution. We extend
this idea to explore the use of recovery maps as an approximation of inverse
maps, and apply it in the context of non-Markovian dynamics. We show how this
strategy attenuates non-Markovian effects, such as the backflow of information.
|
2111.02975v2
|
2021-11-05
|
Traveling waves near Couette flow for the 2D Euler equation
|
In this paper we reveal the existence of a large family of new, nontrivial
and smooth traveling waves for the 2D Euler equation at an arbitrarily small
distance from the Couette flow in $H^s$, with $s<3/2$, at the level of the
vorticity. The speed of these waves is of order 1 with respect to this
distance. This result strongly contrasts with the setting of very high
regularity in Gevrey spaces (see arXiv:1306.5028), where the problem exhibits
an inviscid damping mechanism that leads to relaxation of perturbations back to
nearby shear flows. It also complements the fact that there not exist
nontrivial traveling waves in the $H^{\frac{3}{2}+}$ neighborhoods of Couette
flow (see arXiv:1004.5149).
|
2111.03529v1
|
2021-11-09
|
Determination of source and initial values for acoustic equations with a time-fractional attenuation
|
We consider the inverse problem of determining the initial states or the
source term of a hyperbolic equation damped by some non-local time-fractional
derivative. This framework is relevant to medical imaging such as
thermoacoustic or photoacoustic tomography. We prove a stability estimate for
each of these two problems, with the aid of a Carleman estimate specifically
designed for the governing equation.
|
2111.05240v1
|
2021-11-10
|
Energy decay for a system of Schr{ö}dinger equations in a wave guide
|
We prove exponential decay for a system of two Schr{\"o}dinger equations in a
wave guide, with coupling and damping at the boundary. This relies on the
spectral analysis of the corresponding coupled Schr{\"o}dinger operator on the
one-dimensional cross section. We show in particular that we have a spectral
gap and that the corresponding generalized eigenfunctions form a Riesz basis.
|
2111.05580v1
|
2021-11-18
|
Antiferromagnetic Resonance Revisited: Dissipative Coupling without Dissipation
|
The antiferromagnet is a closed Hermitian system, we find that its
excitations, even in the absence of dissipation, can be viewed as a
non-Hermitian system with dissipative coupling. Consequently, the
antiferromagnetic resonance spectrum does not show the typical level repulsion,
but shows the level attraction -- a characteristic behavior often observed in
non-Hermitian systems. Such behavior is because the antiferromagnetic ground
state is $\mathcal{PT}$-symmetric. This new understanding on antiferromagnetic
resonance also explains the mysterious enhancement of antiferromagnetic damping
rate. Being effectively non-Hermitian, antiferromagnetic magnons can be used
for quantum entanglement generation without introducing a third party like
external pumping.
|
2111.09682v1
|
2021-11-24
|
Photo-induced Macro/Mesoscopic Scale Ion Segregation in Mixed-Halide Perovskites: Ring Structure and Ionic Plasma Oscillations
|
Contrary to the common belief that light-induced halide ion segregation in a
mixed halide al-loy occurs within the illuminated area, we find that the Br
ions released by light diffuse away from the area, which generates a
counter-balancing Coulombic force between the anion deficit and surplus region,
together resulting in a macro/mesoscopic size anion ring surrounding the
center, showing a photoluminescence ring. Upon removing the illumination, the
displaced anions return to the illuminated area, and the restoring force leads
to a damped ultra-low-frequency oscillatory ion motion, which may be the first
observation of an ionic plasma oscillation in solids.
|
2111.12627v1
|
2021-11-25
|
Spectral analysis and stabilization of the dissipative Schrödinger operator on the tadpole graph
|
We consider the damped Schr\"odinger semigroup $e^{-it \frac{d^2}{dx^2}}$ on
the tadpole graph ${\mathcal R}$. We first give a careful spectral analysis and
an appropriate decomposition of the kernel of the resolvent. As a consequence
and by showing that the generalized eigenfunctions form a Riesz basis of some
subspace of $L^2({\mathcal R})$, we prove that the corresponding energy decay
exponentially.
|
2111.13227v1
|
2022-07-11
|
Antiferromagnetic resonance in $α$-Fe$_2$O$_3$ up to its Néel temperature
|
Hematite ($\alpha$-Fe$_2$O$_3$) is an antiferromagnetic material with a very
low spin damping and high N\'eel temperature. The temperature dependence of the
antiferromagnetic resonance in a bulk single crystal of hematite was
characterized from room temperature up to the N\'eel temperature in the
frequency range of 0.19-0.5 THz. From these data, the N\'eel temperature was
estimated as 966 K.
|
2207.05039v1
|
2022-07-12
|
Heavy-quark potential in Gribov-Zwanziger approach around deconfinement phase transition
|
The interaction potential between a pair of heavy quarks is calculated with
resummed perturbation method in Gribov-Zwanziger approach at finite
temperature. The resummed loop correction makes the potential complex. While
the real part is, as expected, screened and becomes short-ranged in hot medium,
the strength of the imaginary part increases with temperature and is comparable
with the real part, which is very different from the previous calculation in
HTL approach. This means that, both the color screening and Landau damping play
important role in the dissociation of heavy flavor hadrons in hot medium.
|
2207.05402v1
|
2022-07-20
|
Oscillating states of driven Langevin systems in large viscous regime
|
We employ an appropriate perturbative scheme in the large viscous regime to
study oscillating states in driven Langevin systems. We explicitly determine
oscillating state distribution of under-damped Brownian particle subjected to
thermal, viscous and potential drives to linear order in anharmonic
perturbation. We also evaluate various non-equilibrium observables relevant to
characterize the oscillating states. We find that the effects of viscous drive
on oscillating states are measurable even in the leading order and show that
the thermodynamic properties of the system in these states are immensely
distinct from those in equilibrium.
|
2207.09773v1
|
2022-07-26
|
Modeling compressed turbulent plasma with rapid viscosity variations
|
We propose two-equations models in order to capture the dynamics of a
turbulent plasma undergoing compression and experiencing large viscosity
variations.
The models account for possible relaminarization phases and rapid viscosity
changes through closures dependent on the turbulent Reynolds and on the
viscosity Froude numbers. These closures are determined from a data-driven
approach using eddy-damped quasi normal markovian simulations. The best model
is able to mimic the various self-similar regimes identified in
\citet{Viciconte2018} and to recover the rapid transition limits identified by
\citet{Coleman1991}.
|
2207.12680v1
|
2017-04-02
|
From Exoplanets to Quasars: Adventures in Angular Differential Imaging
|
Angular differential imaging provides a novel way of probing the high
contrast of our universe. Until now, its applications have been primarily
localized to searching for exoplanets around nearby stars. This work presents a
suite of applications of angular differential imaging from the theoretical
underpinning of data reduction, to its use characterizing substellar objects to
a new application looking for the host galaxies of damped Lyman {\alpha}
systems, which are usually lost in the glare of ultra-bright quasars along the
line of sight.
|
1704.00317v1
|
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