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2011-03-18 | Single File Diffusion of particles with long ranged interactions: damping and finite size effects | We study the Single File Diffusion (SFD) of a cyclic chain of particles that
cannot cross each other, in a thermal bath, with long ranged interactions, and
arbitrary damping. We present simulations that exhibit new behaviors
specifically associated to systems of small number of particles and to small
damping. In order to understand those results, we present an original analysis
based on the decomposition of the particles motion in the normal modes of the
chain. Our model explains all dynamic regimes observed in our simulations, and
provides convincing estimates of the crossover times between those regimes. | 1103.3642v1 |
2011-04-21 | Spin Damping Monopole | We present theoretical evidence that a magnetic monopole emerges in dynamic
magnetic systems in the presence of the spin-orbit interaction. The monopole
field is expressed in terms of spin damping associated with magnetization
dynamics. We demonstrate that the observation of this spin damping monopole is
accomplished electrically using Ampere's law for monopole current. Our
discovery suggests the integration of monopoles into electronics, namely,
monopolotronics. | 1104.4215v2 |
2011-08-16 | Long time dynamics for forced and weakly damped KdV on the torus | The forced and weakly damped Korteweg-de Vries (KdV) equation with periodic
boundary conditions is considered. Starting from $L^2$ and mean-zero initial
data we prove that the solution decomposes into two parts; a linear one which
decays to zero as time goes to infinity and a nonlinear one which always
belongs to a smoother space. As a corollary we prove that all solutions are
attracted by a ball in $H^s$, $s\in(0,1)$, whose radius depends only on $s$,
the $L^2$ norm of the forcing term and the damping parameter. This gives a new
proof for the existence of a smooth global attractor and provides quantitative
information on the size of the attractor set in $H^s$. | 1108.3358v1 |
2011-10-17 | Normal Mode Expansion of Damped Coupled Oscillators in 3 dimensions | In this paper, I aim to study free oscillations of a system of oscillators in
more than one dimensions in the absence of damping. The basic approach lies in
decoupling the motion in the individual perpendicular directions. Once the
equations are decoupled, the existent techniques of Normal mode expansion for
1-dimensional oscillators are used to solve for the equations of motion. I also
study the motion of a driven system of oscillators in higher dimensions in the
presence of a velocity dependent damping force. | 1110.3773v1 |
2011-10-25 | Distinguishing mesoscopic quantum superpositions from statistical mixtures in periodically shaken double wells | For Bose-Einstein condensates in double wells, N-particle Rabi-like
oscillations often seem to be damped. Far from being a decoherence effect, the
apparent damping can indicate the emergence of quantum superpositions in the
many-particle quantum dynamics. However, in an experiment it would be difficult
to distinguish the apparent damping from decoherence effects. The present paper
suggests using controlled periodic shaking to quasi-instantaneously switch the
sign of an effective Hamiltonian, thus implementing an `echo' technique which
distinguishes quantum superpositions from statistical mixtures. The scheme for
the effective time-reversal is tested by numerically solving the time-dependent
N-particle Schrodinger equation. | 1110.5444v1 |
2011-11-23 | Wave Propagation And Landau-Type Damping In Liquids | Intermolecular forces are modeled by means of a modified Lennard-Jones
potential, introducing a distance of minimum approach, and the effect of
intermolecular interactions is accounted for with a self consistent field of
the Vlasov type. A Vlasov equation is then written and used to investigate the
propagation of perturbations in a liquid. A dispersion relation is obtained and
an effect of damping, analogous to what is known in plasmas as "Landau
damping", is found to take place. | 1111.5519v3 |
2011-11-25 | Radiation Damping for Speeding-up NMR Applications | We demonstrate theoretically and numerically how to control the NMR
relaxation rate after application of the standard spin echo technique. Using
radiation damping, we return the nuclear magnetization to its equilibrium state
during a time interval that is negligible compared to the relaxation time. We
obtain an estimate for optimal radiation damping which is consistent with our
numerical simulations. | 1111.7060v1 |
2011-12-09 | Perturbed damped pendulum: finding periodic solutions | Using the damped pendulum system we introduce the averaging method to study
the periodic solutions of a dynamical system with small perturbation. We
provide sufficient conditions for the existence of periodic solutions with
small amplitude of the non--linear perturbed damped pendulum. The averaging
theory provides a useful means to study dynamical systems, accessible to Master
and PhD students. | 1112.2129v2 |
2011-12-28 | The role of damping for the driven anharmonic quantum oscillator | For the model of a linearly driven quantum anharmonic oscillator, the role of
damping is investigated. We compare the position of the stable points in phase
space obtained from a classical analysis to the result of a quantum mechanical
analysis. The solution of the full master equation shows that the stable points
behave qualitatively similar to the classical solution but with small
modifications. Both the quantum effects and additional effects of temperature
can be described by renormalizing the damping. | 1112.6119v1 |
2012-01-03 | Creating and studying ion acoustic waves in ultracold neutral plasmas | We excite ion acoustic waves in ultracold neutral plasmas by imprinting
density modulations during plasma creation. Laser-induced fluorescence is used
to observe the density and velocity perturbations created by the waves. The
effect of expansion of the plasma on the evolution of the wave amplitude is
described by treating the wave action as an adiabatic invariant. After
accounting for this effect, we determine that the waves are weakly damped, but
the damping is significantly faster than expected for Landau damping. | 1201.0786v1 |
2012-01-05 | Damped bead on a rotating circular hoop - a bifurcation zoo | The evergreen problem of a bead on a rotating hoop shows a multitude of
bifurcations when the bead moves with friction. This motion is studied for
different values of the damping coefficient and rotational speeds of the hoop.
Phase portraits and trajectories corresponding to all different modes of motion
of the bead are presented. They illustrate the rich dynamics associated with
this simple system. For some range of values of the damping coefficient and
rotational speeds of the hoop, linear stability analysis of the equilibrium
points is inadequate to classify their nature. A technique involving
transformation of coordinates and order of magnitude arguments is presented to
examine such cases. This may provide a general framework to investigate other
complex systems. | 1201.1218v1 |
2012-03-11 | Magnetic damping of a carbon nanotube NEMS resonator | A suspended, doubly clamped single wall carbon nanotube is characterized at
cryogenic temperatures. We observe specific switching effects in dc-current
spectroscopy of the embedded quantum dot. These have been identified previously
as nano-electromechanical self-excitation of the system, where positive
feedback from single electron tunneling drives mechanical motion. A magnetic
field suppresses this effect, by providing an additional damping mechanism.
This is modeled by eddy current damping, and confirmed by measuring the
resonance quality factor of the rf-driven nano-electromechanical resonator in
an increasing magnetic field. | 1203.2319v2 |
2012-04-02 | Random Symmetry Breaking and Freezing in Chaotic Networks | Parameter space of a driven damped oscillator in a double well potential
presents either a chaotic trajectory with sign oscillating amplitude or a
non-chaotic trajectory with a fixed sign amplitude. A network of such delay
coupled damped oscillators is shown to present chaotic dynamics while the
amplitude sign of each damped oscillator is randomly frozen. This phenomenon of
random broken global symmetry of the network simultaneously with random
freezing of each degree of freedom is accompanied by the existence of
exponentially many randomly frozen chaotic attractors with the ize of the
network. Results are exemplified by a network of modified Duffing oscillators
with infinite ange pseudo-inverse delayed interactions. | 1204.0528v1 |
2012-04-04 | Nonlinear Damping in Graphene Resonators | Based on a continuum mechanical model for single-layer graphene we propose
and analyze a microscopic mechanism for dissipation in nanoelectromechanical
graphene resonators. We find that coupling between flexural modes and in-plane
phonons leads to linear and nonlinear damping of out-of-plane vibrations. By
tuning external parameters such as bias and ac voltages, one can cross over
from a linear to a nonlinear-damping dominated regime. We discuss the behavior
of the effective quality factor in this context. | 1204.0911v2 |
2012-05-22 | Heavy quark damping rate in hot viscous QCD plasma | We derive an expression for the heavy quark damping rate in hot quark gluon
plasma in presence of flow. Here all the bath particles here are out of
equilibrium due to the existence of non-zero velocity gradient. The magnetic
sector shows similar infrared divergences even after hard thermal loop
corrections as one encounters in case of non-viscous plasma. We estimate the
first order correction in ($\eta/s$) for heavy quark damping rate due to the
non-zero viscosity of the QCD plasma. | 1205.4895v3 |
2012-07-24 | Quantum capacity of an amplitude-damping channel with memory | We calculate the quantum capacity of an amplitude-damping channel with time
correlated Markov noise, for two channel uses. Our results show that memory of
the channel increases it's ability to transmit quantum information
significantly. We analyze and compare our findings with earlier numerical
results on amplitude-damping channel with memory. An upper bound on the amount
of quantum information transmitted over the channel in presence of memory, for
an arbitrary number of channel uses is also presented. | 1207.5612v3 |
2012-08-21 | Protecting quantum entanglement from amplitude damping | Quantum entanglement is a critical resource for quantum information and
quantum computation. However, entanglement of a quantum system is subjected to
change due to the interaction with the environment. One typical result of the
interaction is the amplitude damping that usually results in the reduction of
the entanglement. Here we propose a protocol to protect quantum entanglement
from the amplitude damping by applying Hadamard and CNOT gates. As opposed to
some recently studied methods, the scheme presented here does not require weak
measurement in the reversal process, leading to a faster recovery of
entanglement. We propose a possible experimental implementation based on linear
optical system. | 1208.4187v2 |
2012-12-20 | How long-range interactions tune the damping in compact stars | Long-range interactions lead to non-Fermi liquid effects in dense matter. We
show that, in contrast to other material properties, their effect on the bulk
viscosity of quark matter is significant since they shift its resonant maximum
and can thereby change the viscosity by many orders of magnitude. This is of
importance for the damping of oscillations of compact stars, like in particular
unstable r-modes, and the quest to detect signatures of deconfined matter in
astrophysical observations. We find that, in contrast to neutron stars with
standard damping mechanisms, compact stars that contain ungapped quark matter
are consistent with the observed data on low mass x-ray binaries. | 1212.5242v1 |
2013-02-12 | Impact of gluon damping on heavy-quark quenching | In this conference contribution, we discuss the influence of
gluon-bremsstrahlung damping in hot, absorptive QCD matter on the heavy-quark
radiation spectra. Within our Monte-Carlo implementation for the description of
the heavy-quark in-medium propagation we demonstrate that as a consequence of
gluon damping the quenching of heavy quarks becomes significantly affected at
higher transverse momenta. | 1302.2934v1 |
2013-03-12 | On nonlinear Schrodinger type equations with nonlinear damping | We consider equations of nonlinear Schrodinger type augmented by nonlinear
damping terms. We show that nonlinear damping prevents finite time blow-up in
several situations, which we describe. We also prove that the presence of a
quadratic confinement in all spatial directions drives the solution of our
model to zero for large time. In the case without external potential we prove
that the solution may not go to zero for large time due to (non-trivial)
scattering. | 1303.3033v2 |
2013-06-15 | A formula for damping interarea oscillations with generator redispatch | We derive a new formula for the sensitivity of electromechanical oscillation
damping with respect to generator redispatch. The formula could lead to some
combination of observations, computations and heuristics to more effectively
damp interarea oscillations. | 1306.3590v2 |
2013-07-24 | Eigenvalue asymptotics for the damped wave equation on metric graphs | We consider the linear damped wave equation on finite metric graphs and
analyse its spectral properties with an emphasis on the asymptotic behaviour of
eigenvalues. In the case of equilateral graphs and standard coupling conditions
we show that there is only a finite number of high-frequency abscissas, whose
location is solely determined by the averages of the damping terms on each
edge. We further describe some of the possible behaviour when the edge lengths
are no longer necessarily equal but remain commensurate. | 1307.6377v3 |
2013-08-03 | Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping | Presented here is a study of a viscoelastic wave equation with supercritical
source and damping terms. We employ the theory of monotone operators and
nonlinear semigroups, combined with energy methods to establish the existence
of a unique local weak solution. In addition, it is shown that the solution
depends continuously on the initial data and is global provided the damping
dominates the source in an appropriate sense. | 1308.0720v2 |
2013-10-14 | Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators | The damping rates of high quality factor nanomechanical resonators are well
beyond intrinsic limits. Here, we explore the underlying microscopic loss
mechanisms by investigating the temperature-dependent damping of the
fundamental and third harmonic transverse flexural mode of a doubly clamped
silicon nitride string. It exhibits characteristic maxima reminiscent of
two-level defects typical for amorphous materials. Coupling to those defects
relaxes the momentum selection rules, allowing energy transfer from discrete
long wavelength resonator modes to the high frequency phonon environment. | 1310.3671v1 |
2013-10-25 | Quenched decoherence in qubit dynamics due to strong amplitude-damping noise | We study non-perturbatively the time evolution of a qubit subject to
amplitude-damping noise. We show that at strong coupling the qubit decoherence
can be quenched owing to large environment feedbacks, such that the qubit can
evolve coherently even in the long-time limit. As an application, we show that
for a quantum channel that consists of two independent qubits subject to
uncorrelated local amplitude-damping noises, it can maintain at strong coupling
finite entanglement and better than classical teleportation fidelity at long
times. | 1310.6843v2 |
2013-12-19 | Cyclotron dynamics of interacting bosons in artificial magnetic fields | We study theoretically quantum dynamics of interacting bosons in artificial
magnetic fields as engineered in recent ultracold atomic experiments, where
quantum cyclotron orbital motion has been observed. With exact numerical
simulations and perturbative analyses, we find that interactions induce damping
in the cyclotron motion. The damping time is found to be dependent on
interaction and tunneling strengths monotonically, while its dependence on
magnetic flux is non-monotonic. Sufficiently strong interactions would render
bosons dynamically localized inhibiting the cyclotron motion. The damping
predicted by us can be construed as an interaction-induced quantum decoherence
of the cyclotron motion. | 1312.5747v2 |
2014-03-24 | Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations | In this paper we make a subtle use of operator theory techniques and the
well-known Schauder fixed-point principle to establish the existence of
pseudo-almost automorphic solutions to some second-order damped
integro-differential equations with pseudo-almost automorphic coefficients. In
order to illustrate our main results, we will study the existence of
pseudo-almost automorphic solutions to a structurally damped plate-like
boundary value problem. | 1403.5955v1 |
2014-05-12 | A note on a strongly damped wave equation with fast growing nonlinearities | A strongly damped wave equation including the displacement depending
nonlinear damping term and nonlinear interaction function is considered. The
main aim of the note is to show that under the standard dissipativity
restrictions on the nonlinearities involved the initial boundary value problem
for the considered equation is globally well-posed in the class of sufficiently
regular solutions and the semigroup generated by the problem possesses a global
attractor in the corresponding phase space. These results are obtained for the
nonlinearities of an arbitrary polynomial growth and without the assumption
that the considered problem has a global Lyapunov function. | 1405.2707v1 |
2014-06-03 | Optimal Estimation of a Classical Force with a Damped Oscillator in the non-Markovian Bath | We solve the optimal quantum limit of probing a classical force exactly by a
damped oscillator initially prepared in the factorized squeezed state. The
memory effects of the thermal bath on the oscillator evolution are
investigated. We show that the optimal force sensitivity obtained by the
quantum estimation theory approaches to zero for the non-Markovian bath,
whereas approaches to a finite non-zero value for the Markovian bath as the
energy of the damped oscillator goes to infinity. | 1406.0658v1 |
2014-08-09 | Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions | We investigate the Westervelt equation with several versions of nonlinear
damping and lower order damping terms and Neumann as well as absorbing boundary
conditions. We prove local in time existence of weak solutions under the
assumption that the initial and boundary data are sufficiently small.
Additionally, we prove local well-posedness in the case of spatially varying
$L^{\infty}$ coefficients, a model relevant in high intensity focused
ultrasound (HIFU) applications. | 1408.2160v1 |
2014-08-11 | Characterization and suppression techniques for degree of radiation damping in inversion recovery measurements | Radiation damping (RD) has been shown to affect T1 measurement in inversion
recovery experiments. In this work, we demonstrate that the extent of RD
depends upon the T1 of the sample. RD difference spectroscopy (RADDSY) is used
to characterize the severity of RD, while gradient inversion recovery (GIR) is
used for RD suppression in T1 measurements. At 9.4 T, for the radiation damping
characteristic time (Trd) of 50 ms, these investigations show non-negligible RD
effects for T1 values greater than Trd, with severe distortions for T1 longer
than about 150 ms, showing reasonable agreement with the predicted Trd. We also
report a discrepancy between published expressions for the characteristic RD
time. | 1408.2457v2 |
2014-09-28 | Spin-electron acoustic waves: The Landau damping and ion contribution in the spectrum | Separated spin-up and spin-down quantum kinetics is derived for more detailed
research of the spin-electron acoustic waves. Kinetic theory allows to obtain
spectrum of the spin-electron acoustic waves including effects of occupation of
quantum states more accurately than quantum hydrodynamics. We apply quantum
kinetic to calculate the Landau damping of the spin-electron acoustic waves. We
have considered contribution of ions dynamics in the spin-electron acoustic
wave spectrum. We obtain contribution of ions in the Landau damping in
temperature regime of classic ions. Kinetic analysis for ion-acoustic, zero
sound, and Langmuir waves at separated spin-up and spin-down electron dynamics
is presented as well. | 1409.7885v1 |
2014-10-15 | Quasiparticle Damping of Surface Waves in Superfluid $^3$He and $^4$He | Oscillations on free surface of superfluids at the inviscid limit are damped
by quasiparticle scattering. We have studied this effect in both superfluids
$^3$He and $^4$He deep below the respective critical temperatures. Surface
oscillators offer several benefits over immersed mechanical oscillators
traditionally used for similar purposes. Damping is modeled as specular
scattering of ballistic quasiparticles from the moving free surface. The model
is in reasonable agreement with our measurements for superfluid $^4$He but
significant deviation is found for $^3$He. | 1410.4071v1 |
2014-12-22 | Long time behavior for a semilinear hyperbolic equation with asymtotically vanishing damping term and convex potential | We investigate the asymptotic behavior, as t goes to infinity, for a
semilinear hyperbolic equation with asymptotically smal dissipation and convex
potential. We prove that if the damping term behaves like K/t^\alpha for t
large enough, k>0 and 0</alpha<1 then every global solution converges weakly to
an equilibrium point. This result is a positive answer to a question left open
in the paper [A. Cabot and P. Frankel, Asymptotics for some semilinear
hyperbolic equation with non-autonomous damping. J. Differential Equations 252
(2012) 294-322.] | 1412.7008v1 |
2015-03-03 | Large Deviations for the Langevin equation with strong damping | We study large deviations in the Langevin dynamics, with damping of order
$\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient
is assumed to be state dependent. We proceed first with a change of time and
then, we use a weak convergence approach to large deviations and their
equivalent formulation in terms of the Laplace principle, to determine the good
action functional.
Some applications of these results to the exit problem from a domain and to
the wave front propagation for a suitable class of reaction diffusion equations
are considered. | 1503.01027v1 |
2015-03-14 | Stabilization of the nonlinear damped wave equation via linear weak observability | We consider the problem of energy decay rates for nonlinearly damped abstract
infinite dimensional systems. We prove sharp, simple and quasi-optimal energy
decay rates through an indirect method, namely a weak observability estimate
for the corresponding undamped system. One of the main advantage of these
results is that they allow to combine the optimal-weight convexity method of
Alabau-Boussouira and a methodology of Ammari-Tucsnak for weak stabilization by
observability. Our results extend to nonlinearly damped systems, those of
Ammari and Tucsnak. At the end, we give an appendix on the weak stabilization
of linear evolution systems. | 1503.04356v1 |
2015-06-02 | On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source | The aim of the paper is to study local Hadamard well-posedness for wave
equation with an hyperbolic dynamical boundary condition, internal and/or
boundary damping and sources for initial data in the natural energy space.
Moreover the regularity of solutions is studied. Finally a dynamical system is
generated when sources are at most linear at infinity, or they are dominated by
the damping terms. | 1506.00910v4 |
2015-06-15 | Tautochrone in the damped cycloidal pendulum | The tautochrone on a cycloid curve is usually considered without drag force.
In this work, we investigate the motion of a damped cycloidal pendulum under
presence of a drag force. Using the Lagrange formulation, and considering
linear dependence with velocity for damping force, we found the dynamics of the
system to remain tautochrone. This dictates the possibility for studying the
tautochrone experimentally, e.g. the cycloidal pendulum in water or oil. | 1506.04943v2 |
2015-07-04 | Comments on turbulence theory by Qian and by Edwards and McComb | We reexamine Liouville equation based turbulence theories proposed by Qian
{[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys.
A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov
spectrum. These theories obtained identical equation for spectral density
$q(k)$ and different results for damping coefficient. Qian proposed variational
approach and Edwards and McComb proposed maximal entropy principle to obtain
equation for the damping coefficient. We show that assumptions used in these
theories to obtain damping coefficient correspond to unphysical conditions. | 1507.01124v1 |
2015-08-24 | Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients | We study the asymptotic behavior of solutions for the semilinear damped wave
equation with variable coefficients. We prove that if the damping is effective,
and the nonlinearity and other lower order terms can be regarded as
perturbations, then the solution is approximated by the scaled Gaussian of the
corresponding linear parabolic problem. The proof is based on the scaling
variables and energy estimates. | 1508.05778v3 |
2015-10-01 | Impact of surface collisions on enhancement and quenching of the luminescence near the metal nanoparticles | The fact that surface-induced damping rate of surface plasmon polaritons
(SPPs) in metal nanoparticles increases with the decrease of particle size is
well known. We show that this rate also increases with the degree of the mode
confinement, hence damping of the higher order nonradiative SPP modes in
spherical particles is greatly enhanced relative to damping of the fundamental
(dipole) SPP mode. Since higher order modes are the ones responsible for
quenching of luminescence in the vicinity of metal surfaces, the degree of
quenching increases resulting in a substantial decrease in the amount of
attainable enhancement of the luminescence | 1510.00321v1 |
2015-10-22 | On numerical Landau damping for splitting methods applied to the Vlasov-HMF model | We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field)
equation based on splitting methods between the linear and non-linear parts. We
consider solutions starting in a small Sobolev neighborhood of a spatially
homogeneous state satisfying a linearized stability criterion (Penrose
criterion). We prove that the numerical solutions exhibit a scattering behavior
to a modified state, which implies a nonlinear Landau damping effect with
polynomial rate of damping. Moreover, we prove that the modified state is close
to the continuous one and provide error estimates with respect to the time
stepsize. | 1510.06555v1 |
2015-11-02 | Asymptotic decomposition for nonlinear damped Klein-Gordon equations | In this paper, we proved that if the solution to damped focusing Klein-Gordon
equations is global forward in time, then it will decouple into a finite number
of equilibrium points with different shifts from the origin. The core
ingredient of our proof is the existence of the "concentration-compact
attractor" which yields a finite number of profiles. Using damping effect, we
can prove all the profiles are equilibrium points. | 1511.00437v3 |
2015-11-11 | Contact Stiffness and Damping of Liquid Films in Dynamic Atomic Force Microscopy | Small-amplitude dynamic atomic force microscopy (dynamic-AFM) in a simple
nonpolar liquid was studied through molecular dynamics simulations. We find
that within linear dynamics regime, the contact stiffness and damping of the
confined film exhibit the similar solvation force oscillations, and they are
generally out-of-phase. For the solidified film with integer monolayer
thickness, further compression of the film before layering transition leads to
higher stiffness and lower damping. We find that molecular diffusion in the
solidified film was nevertheless enhanced due to the mechanical excitation of
AFM tip. | 1511.03580v1 |
2015-11-13 | Nonlinear Radiation Damping of Nuclear Spin Waves and Magnetoelastic Waves in Antiferromagnets | Parallel pumping of nuclear spin waves in antiferromagnetic CsMnF3 at liquid
helium temperatures and magnetoelastic waves in antiferromagnetic FeBO3 at
liquid nitrogen temperature in a helical resonator was studied. It was found
that the absorbed microwave power is approximately equal to the irradiated
power from the sample and that the main restriction mechanism of absortption in
both cases is defined by the nonlinear radiation damping predicted about two
decades ago. We believe that the nonlinear radiation damping is a common
feature of parallel pumping technique of all normal magnetic excitations and it
can be detected by purposeful experiments. | 1511.04396v1 |
2016-04-20 | Landau damping in finite regularity for unconfined systems with screened interactions | We prove Landau damping for the collisionless Vlasov equation with a class of
$L^1$ interaction potentials (including the physical case of screened Coulomb
interactions) on $\mathbb R^3_x \times \mathbb R^3_v$ for localized
disturbances of an infinite, homogeneous background. Unlike the confined case
$\mathbb T^3_x \times \mathbb R_v^3$, results are obtained for initial data in
Sobolev spaces (as well as Gevrey and analytic classes). For spatial
frequencies bounded away from zero, the Landau damping of the density is
similar to the confined case. The finite regularity is possible due to an
additional dispersive mechanism available on $\mathbb R_x^3$ which reduces the
strength of the plasma echo resonance. | 1604.05783v1 |
2016-04-26 | Trigonometric Splines for Oscillator Simulation | We investigate the effects of numerical damping for oscillator simulation
with spline methods. Numerical damping results in an artificial loss of energy
and leads therefore to unreliable results in the simulation of autonomous
systems, as e.g.\ oscillators. We show that the negative effects of numerical
damping can be eliminated by the use of trigonometric splines. This will be in
particular important for spline based adaptive methods. | 1604.07607v1 |
2016-09-05 | Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity | We study blow-up behavior of solutions for the Cauchy problem of the
semilinear wave equation with time-dependent damping. When the damping is
effective, and the nonlinearity is subcritical, we show the blow-up rates and
the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE
argument, and lower estimates are given by a method of scaling variables. | 1609.01035v2 |
2016-09-06 | Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping | This paper deals with diffusive limit of the p-system with damping and its
approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided
the system is endowed with an entropy-entropy flux pair, we give the
convergence rate of classical solutions of the p-system with damping towards
the smooth solutions of the porous media equation using a relative entropy
method. Adopting a semi-discrete scheme, we establish that the convergence rate
is preserved by the approximated solutions. Several numerical experiments
illustrate the relevance of this result. | 1609.01436v1 |
2016-11-08 | Emulated Inertia and Damping of Converter-Interfaced Power Source | Converter-interfaced power sources (CIPSs), like wind turbine and energy
storage, can be switched to the inertia emulation mode when the detected
frequency deviation exceeds a pre-designed threshold, i.e. dead band, to
support the frequency response of a power grid. This letter proposes an
approach to derive the emulated inertia and damping from a CIPS based on the
linearized model of the CIPS and the power grid, where the grid is represented
by an equivalent single machine. The emulated inertia and damping can be
explicitly expressed in time and turn out to be time-dependent. | 1611.02698v1 |
2017-08-27 | Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case | We study global existence of solutions to the Cauchy problem for the wave
equation with time-dependent damping and a power nonlinearity in the
overdamping case. We prove the global well-posedness for small data in the
energy space for the whole energy-subcritical case. This result implies that
small data blow-up does not occur in the overdamping case, different from the
other cases, i.e. effective or non-effective damping. | 1708.08044v2 |
2017-11-01 | Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case | The blow up problem of the semilinear scale-invariant damping wave equation
with critical Strauss type exponent is investigated. The life span is shown to
be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for
$0<\mu<\frac{n^2+n+2}{n+2}$. This result completes our previous study
\cite{Tu-Lin} on the sub-Strauss type exponent $p<p_S(n+\mu)$. Our novelty is
to construct the suitable test function from the modified Bessel function. This
approach might be also applied to the other type damping wave equations. | 1711.00223v1 |
2017-11-14 | Spin-Noise and Damping in Individual Metallic Ferromagnetic Nanoparticles | We introduce a highly sensitive and relatively simple technique to observe
magnetization motion in single Ni nanoparticles, based on charge sensing by
electron tunneling at millikelvin temperature. Sequential electron tunneling
via the nanoparticle drives nonequilibrium magnetization dynamics, which
induces an effective charge noise that we measure in real time. In the free
spin diffusion regime, where the electrons and magnetization are in detailed
balance, we observe that magnetic damping time exhibits a peak with the
magnetic field, with a record long damping time of $\simeq 10$~ms. | 1711.05142v1 |
2018-06-18 | Damped second order flow applied to image denoising | In this paper, we introduce a new image denoising model: the damped flow
(DF), which is a second order nonlinear evolution equation associated with a
class of energy functionals of image. The existence, uniqueness and
regularization property of DF are proven. For the numerical implementation,
based on the St\"{o}rmer-Verlet method, a discrete damped flow, SV-DDF, is
developed. The convergence of SV-DDF is studied as well. Several numerical
experiments, as well as a comparison with other methods, are provided to
demonstrate the feasibility and effectiveness of the SV-DDF. | 1806.06732v2 |
2018-07-10 | Cyclotron Damping along an Uniform Magnetic Field | We prove cyclotron damping for the collisionless Vlasov-Maxwell equations on
$\mathbb{T}_{x}^{3}\times\mathbb{R}_{v}^{3}$ under the assumptions that the
electric induction is zero and $(\mathcal{\mathbf{PSC}})$ holds. It is a
crucial step to solve the stability problem of the Vlasov-Maxwell equations.
Our proof is based on a new dynamical system of the plasma particles,
originating from Faraday Law of Electromagnetic induction and Lenz's Law. On
the basis of it, we use the improved Newton iteration scheme to show the
damping mechanism. | 1807.05254v3 |
2018-07-17 | On the blow-up for critical semilinear wave equations with damping in the scattering case | We consider the Cauchy problem for semilinear wave equations with variable
coefficients and time-dependent scattering damping in $\mathbf{R}^n$, where
$n\geq 2$. It is expected that the critical exponent will be Strauss' number
$p_0(n)$, which is also the one for semilinear wave equations without damping
terms. Lai and Takamura (2018) have obtained the blow-up part, together with
the upper bound of lifespan, in the sub-critical case $p<p_0(n)$. In this
paper, we extend their results to the critical case $p=p_0(n)$. The proof is
based on Wakasa and Yordanov (2018), which concerns the blow-up and upper bound
of lifespan for critical semilinear wave equations with variable coefficients. | 1807.06164v1 |
2019-06-02 | Mixed control of vibrational systems | We consider new performance measures for vibrational systems based on the
$H_2$ norm of linear time invariant systems. New measures will be used as an
optimization criterion for the optimal damping of vibrational systems. We
consider both theoretical and concrete cases in order to show how new measures
stack up against the standard measures. The quality and advantages of new
measures as well as the behaviour of optimal damping positions and
corresponding damping viscosities are illustrated in numerical experiments. | 1906.00503v1 |
2019-06-27 | Comments on the linear modified Poisson-Boltzmann equation in electrolyte solution theory | Three analytic results are proposed for a linear form of the modified
Poisson-Boltzmann equation in the theory of bulk electrolytes. Comparison is
also made with the mean spherical approximation results. The linear theories
predict a transition of the mean electrostatic potential from a
Debye-H\"{u}ckel type damped exponential to a damped oscillatory behaviour as
the electrolyte concentration increases beyond a critical value. The screening
length decreases with increasing concentration when the mean electrostatic
potential is damped oscillatory. A comparison is made with one set of recent
experimental screening results for aqueous NaCl electrolytes. | 1906.11584v1 |
2012-10-03 | Exact solutions for discrete breathers in forced-damped chain | Exact solutions for symmetric discrete breathers (DBs) are obtained in
forced-damped linear chain with on-site vibro-impact constraints. The damping
is related to inelastic impacts; the forcing may be chosen from broad class of
periodic antisymmetric functions. Global conditions for existence and stability
of the DB are established. Some unusual phenomena, like non-monotonous
dependence of the stability boundary on the forcing amplitude, are revealed
analytically for the full system and illustrated numerically for small periodic
lattices. | 1210.1085v1 |
2017-04-03 | Linear inviscid damping and vorticity depletion for shear flows | In this paper, we prove the linear damping for the 2-D Euler equations around
a class of shear flows under the assumption that the linearized operator has no
embedding eigenvalues. For the symmetric flows, we obtain the explicit decay
estimates of the velocity, which is the same as one for monotone shear flows.
We confirm a new dynamical phenomena found by Bouchet and Morita: the depletion
of the vorticity at the stationary streamlines, which could be viewed as a new
mechanism leading to the damping for the base flows with stationary
streamlines. | 1704.00428v1 |
2017-04-25 | Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity | In this paper, we study the asymptotic behavior of solutions to the wave
equation with damping depending on the space variable and growing at the
spatial infinity. We prove that the solution is approximated by that of the
corresponding heat equation as time tends to infinity. The proof is based on
semigroup estimates for the corresponding heat equation and weighted energy
estimates for the damped wave equation. To construct a suitable weight function
for the energy estimates, we study a certain elliptic problem. | 1704.07650v1 |
2017-06-05 | Mixed finite elements for global tide models with nonlinear damping | We study mixed finite element methods for the rotating shallow water
equations with linearized momentum terms but nonlinear drag. By means of an
equivalent second-order formulation, we prove long-time stability of the system
without energy accumulation. We also give rates of damping in unforced systems
and various continuous dependence results on initial conditions and forcing
terms. \emph{A priori} error estimates for the momentum and free surface
elevation are given in $L^2$ as well as for the time derivative and divergence
of the momentum. Numerical results confirm the theoretical results regarding
both energy damping and convergence rates. | 1706.01352v1 |
2017-06-13 | Uniform energy decay for wave equations with unbounded damping coefficients | We consider the Cauchy problem for wave equations with unbounded damping
coefficients in the whole space. For a general class of unbounded damping
coefficients, we derive uniform total energy decay estimates together with a
unique existence result of a weak solution. In this case we never impose strong
assumptions such as compactness of the support of the initial data. This means
that we never rely on the finite propagation speed property of the solution,
and we try to deal with an essential unbounded coefficient case. | 1706.03942v1 |
2017-06-15 | Fractional Driven Damped Oscillator | The resonances associated with a fractional damped oscillator which is driven
by an oscillatory external force are studied. It is shown that such resonances
can be manipulated by tuning up either the coefficient of the fractional
damping or the order of the corresponding fractional derivatives. | 1706.08596v1 |
2017-09-04 | A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent | We concern the blow up problem to the scale invariant damping wave equations
with sub-Strauss exponent. This problem has been studied by Lai, Takamura and
Wakasa (\cite{Lai17}) and Ikeda and Sobajima \cite{Ikedapre} recently. In
present paper, we extend the blowup exponent from $p_F(n)\leq p<p_S(n+2\mu)$ to
$1<p<p_S(n+\mu)$ without small restriction on $\mu$. Moreover, the upper bound
of lifespan is derived with uniform estimate $T(\varepsilon)\leq
C\varepsilon^{-2p(p-1)/\gamma(p,n+2\mu)}$. This result extends the blowup
result of semilinear wave equation and shows the wave-like behavior of scale
invariant damping wave equation's solution even with large $\mu>1$. | 1709.00866v2 |
2017-09-13 | Life-span of blowup solutions to semilinear wave equation with space-dependent critical damping | This paper is concerned with the blowup phenomena for initial value problem
of semilinear wave equation with critical space-dependent damping term
(DW:$V$). The main result of the present paper is to give a solution of the
problem and to provide a sharp estimate for lifespan for such a solution when
$\frac{N}{N-1}<p\leq p_S(N+V_0)$, where $p_S(N)$ is the Strauss exponent for
(DW:$0$). The main idea of the proof is due to the technique of test functions
for (DW:$0$) originated by Zhou--Han (2014, MR3169791). Moreover, we find a new
threshold value $V_0=\frac{(N-1)^2}{N+1}$ for the coefficient of critical and
singular damping $|x|^{-1}$. | 1709.04401v1 |
2018-03-14 | Damped Newton's Method on Riemannian Manifolds | A damped Newton's method to find a singularity of a vector field in
Riemannian setting is presented with global convergence study. It is ensured
that the sequence generated by the proposed method reduces to a sequence
generated by the Riemannian version of the classical Newton's method after a
finite number of iterations, consequently its convergence rate is
superlinear/quadratic. Moreover, numerical experiments illustrate that the
damped Newton's method has better performance than Newton's method in number of
iteration and computational time. | 1803.05126v2 |
2018-08-22 | Radiation Damping of a Yang-Mills Particle Revisited | The problem of a color-charged point particle interacting with a four
dimensional Yang-Mills gauge theory is revisited. The radiation damping is
obtained inspired in the Dirac's computation. The difficulties in the
non-abelian case were solved by using an ansatz for the Li\'enard-Wiechert
potentials, already used in the literature for finding solutions to the
Yang-Mills equations. Three non-trivial examples of radiation damping for the
non-abelian particle are discussed in detail. | 1808.07533v2 |
2018-08-28 | Enhancement of zonal flow damping due to resonant magnetic perturbations in the background of an equilibrium $E \times B$ sheared flow | Using a parametric interaction formalism, we show that the equilibrium
sheared rotation can enhance the zonal flow damping effect found in Ref. [M.
Leconte and P.H. Diamond, \emph{Phys. Plasmas} 19, 055903 (2012)]. This
additional damping contribution is proportional to $(L_s/L_V)^2 \times \delta
B_r^2 / B^2$, where $L_s/L_V$ is the ratio of magnetic shear length to the
scale-length of equilibrium $E \times B$ flow shear, and $\delta B_r / B$ is
the amplitude of the external magnetic perturbation normalized to the
background magnetic field. | 1808.09110v1 |
2018-08-30 | Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities | In this paper, by means of the Riesz basis approach, we study the stability
of a weakly damped system of two second order evolution equations coupled
through the velocities. If the fractional order damping becomes viscous and the
waves propagate with equal speeds, we prove exponential stability of the system
and, otherwise, we establish an optimal polynomial decay rate. Finally, we
provide some illustrative examples. | 1808.10256v1 |
2018-10-14 | Critical exponent for nonlinear damped wave equations with non-negative potential in 3D | We are studying possible interaction of damping coefficients in the
subprincipal part of the linear 3D wave equation and their impact on the
critical exponent of the corresponding nonlinear Cauchy problem with small
initial data. The main new phenomena is that certain relation between these
coefficients may cause very strong jump of the critical Strauss exponent in 3D
to the critical 5D Strauss exponent for the wave equation without damping
coefficients. | 1810.05956v1 |
2018-10-23 | Perfect absorption of water waves by linear or nonlinear critical coupling | We report on experiments of perfect absorption for surface gravity waves
impinging a wall structured by a subwavelength resonator. By tuning the
geometry of the resonator, a balance is achieved between the radiation damping
and the intrinsic viscous damping, resulting in perfect absorption by critical
coupling. Besides, it is shown that the resistance of the resonator, hence the
intrinsic damping, can be controlled by the wave amplitude, which provides a
way for perfect absorption tuned by nonlinear mechanisms. The perfect absorber
that we propose, without moving parts or added material, is simple, robust and
it presents a deeply subwavelength ratio wavelength/size $\simeq 18$. | 1810.09884v1 |
2016-08-29 | Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles | In this paper, by using classical Faedo-Galerkin approximation and
compactness method, the existence of martingale solutions for the stochastic 3D
Navier-Stokes equations with nonlinear damping is obtained. The existence and
uniqueness of strong solution are proved for $\beta > 3$ with any $\alpha>0$
and $\alpha \geq \frac12$ as $\beta = 3$. Meanwhile, a small time large
deviation principle for the stochastic 3D Navier-Stokes equation with damping
is proved for $\beta > 3$ with any $\alpha>0$ and $\alpha \geq \frac12$ as
$\beta = 3$. | 1608.07996v1 |
2018-12-16 | Damping of sound waves by bulk viscosity in reacting gases | The very long standing problem of sound waves propagation in fluids is
reexamined. In particular, from the analysis of the wave damping in reacting
gases following the work of Einsten \citep{Ein}, it is found that the damping
due to the chemical reactions occurs nonetheless the second (bulk) viscosity
introduced by Landau \& Lifshitz \citep{LL86} is zero. The simple but important
case of a recombining Hydrogen plasma is examined. | 1812.06478v1 |
2008-11-20 | An explanation for the pseudogap of high-temperature superconductors based on quantum optics | We first explain the pseudogap of high-temperature superconductivity based on
an approach of quantum optics. After introducing a damping factor for the
lifetime $\tau$ of quasiparticles, the superconducting dome is naturally
produced, and the pseudogap is the consequence of pairing with damped
coherence. We derive a new expression of Ginzburg-Landau free energy density,
in which a six-order term due to decoherence damping effect is included.
Without invoking any microscopic pairing mechanism, this approach provides a
simple universal equation of second-order phase transition, which can be
reduced to two well-known empirical scaling equations: the superconducting dome
Presland-Tallon equation, and the normal-state pseudogap crossover temperature
$T^{*}$ line. | 0811.3262v1 |
2010-04-12 | Entanglement properties of optical coherent states under amplitude damping | Through concurrence, we characterize the entanglement properties of optical
coherent-state qubits subject to an amplitude damping channel. We investigate
the distillation capabilities of known error correcting codes and obtain upper
bounds on the entanglement depending on the non-orthogonality of the coherent
states and the channel damping parameter. This work provides a first, full
quantitative analysis of these photon-loss codes which are naturally
reminiscent of the standard qubit codes against Pauli errors. | 1004.1931v2 |
2016-03-01 | Damped vacuum states of light | We consider one-dimensional propagation of quantum light in the presence of a
block of material, with a full account of dispersion and absorption. The
electromagnetic zero-point energy for some frequencies is damped (suppressed)
by the block below the free-space value, while for other frequencies it is
increased. We also calculate the regularized (Casimir) zero-point energy at
each frequency and find that it too is damped below the free-space value (zero)
for some frequencies. The total Casimir energy is positive. | 1603.00233v2 |
2017-03-14 | Landau damping in the multiscale Vlasov theory | Vlasov kinetic theory is extended by adopting an extra one particle
distribution function as an additional state variable characterizing the
micro-turbulence internal structure. The extended Vlasov equation keeps the
reversibility, the Hamiltonian structure, and the entropy conservation of the
original Vlasov equation. In the setting of the extended Vlasov theory we then
argue that the Fokker-Planck type damping in the velocity dependence of the
extra distribution function induces the Landau damping. The same type of
extension is made also in the setting of fluid mechanics. | 1703.04577v2 |
2017-03-15 | Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation | We prove local and global energy decay for the asymptotically periodic damped
wave equation on the Euclidean space. Since the behavior of high frequencies is
already mostly understood, this paper is mainly about the contribution of low
frequencies. We show in particular that the damped wave behaves like a solution
of a heat equation which depends on the H-limit of the metric and the mean
value of the absorption index. | 1703.05112v1 |
2018-09-10 | Linear inviscid damping for the $β$-plane equation | In this paper, we study the linear inviscid damping for the linearized
$\beta$-plane equation around shear flows. We develop a new method to give the
explicit decay rate of the velocity for a class of monotone shear flows. This
method is based on the space-time estimate and the vector field method in sprit
of the wave equation. For general shear flows including the Sinus flow, we also
prove the linear damping by establishing the limiting absorption principle,
which is based on the compactness method introduced by Wei-Zhang-Zhao in
\cite{WZZ2}. The main difficulty is that the Rayleigh-Kuo equation has more
singular points due to the Coriolis effects so that the compactness argument
becomes more involved and delicate. | 1809.03065v1 |
2019-09-19 | Growth rate and gain of stimulated Brillouin scattering considering nonlinear Landau damping due to particle trapping | Growth rate and gain of SBS considering the reduced Landau damping due to
particle trapping has been proposed to predict the growth and average level of
SBS reflectivity. Due to particle trapping, the reduced Landau damping has been
taken used of to calculate the gain of SBS, which will make the simulation data
of SBS average reflectivity be consistent to the Tang model better. This work
will solve the pending questions in laser-plasma interaction and have wide
applications in parametric instabilities. | 1909.11606v1 |
2020-03-04 | Existence and uniqueness of solutions to the damped Navier-Stokes equations with Navier boundary conditions for three dimensional incompressible fluid | In this article, we study the solutions of the damped Navier--Stokes equation
with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$
with smooth boundary. The existence of the solutions is global with the damped
term $\vartheta |u|^{\beta-1}u, \vartheta >0.$ The regularity and uniqueness of
solutions with Navier boundary condition is also studied. This extends the
existing results in literature. | 2003.01903v1 |
2020-04-22 | Logarithmic stabilization of an acoustic system with a damping term of Brinkman type | We study the problem of stabilization for the acoustic system with a
spatially distributed damping. Without imposing any hypotheses on the
structural properties of the damping term, we identify logarithmic decay of
solutions with growing time. Logarithmic decay rate is shown by using a
frequency domain method and combines a contradiction argument with the
multiplier technique and a new Carleman estimate to carry out a special
analysis for the resolvent. | 2004.10669v1 |
2020-08-02 | Quantum capacity analysis of multi-level amplitude damping channels | The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced
as a generalization of the standard qubit Amplitude Damping Channel to quantum
systems of finite dimension $d$. In the special case of $d=3$, by exploiting
degradability, data-processing inequalities, and channel isomorphism, we
compute the associated quantum and private classical capacities for a rather
wide class of maps, extending the set of solvable models known so far. We
proceed then to the evaluation of the entanglement assisted, quantum and
classical, capacities. | 2008.00477v3 |
2020-08-11 | An inverse spectral problem for a damped wave operator | This paper proposes a new and efficient numerical algorithm for recovering
the damping coefficient from the spectrum of a damped wave operator, which is a
classical Borg-Levinson inverse spectral problem. The algorithm is based on
inverting a sequence of trace formulas, which are deduced by a recursive
formula, bridging geometrical and spectrum information explicitly in terms of
Fredholm integral equations. Numerical examples are presented to illustrate the
efficiency of the proposed algorithm. | 2008.04523v1 |
2020-08-17 | Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I | In this paper, we are interested in the Cauchy problem for the viscoelastic
damped wave equation with memory of type I. By applying WKB analysis and
Fourier analysis, we explain the memory's influence on dissipative structures
and asymptotic profiles of solutions to the model with weighted $L^1$ initial
data. Furthermore, concerning standard energy and the solution itself, we
establish singular limit relations between the Moore-Gibson-Thompson equation
with memory and the viscoelastic damped wave equation with memory. | 2008.07151v1 |
2020-08-18 | A class of Finite difference Methods for solving inhomogeneous damped wave equations | In this paper, a class of finite difference numerical techniques is presented
to solve the second-order linear inhomogeneous damped wave equation. The
consistency, stability, and convergences of these numerical schemes are
discussed. The results obtained are compared to the exact solution, ordinary
explicit, implicit finite difference methods, and the fourth-order compact
method (FOCM). The general idea of these methods is developed by using the
C0-semigroups operator theory. We also showed that the stability region for the
explicit finite difference scheme depends on the damping coefficient. | 2008.08043v2 |
2021-05-03 | Enhanced and unenhanced dampings of Kolmogorov flow | In the present study, Kolmogorov flow represents the stationary sinusoidal
solution $(\sin y,0)$ to a two-dimensional spatially periodic Navier-Stokes
system, driven by an external force. This system admits the additional
non-stationary solution $(\sin y,0)+e^{-\nu t} (\sin y,0)$, which tends
exponentially to the Kolmogorov flow at the minimum decay rate determined by
the viscosity $\nu$. Enhanced damping or enhanced dissipation of the problem is
obtained by presenting higher decay rate for the difference between a solution
and the non-stationary basic solution. Moreover, for the understanding of the
metastability problem in an explicit manner, a variety of exact solutions are
presented to show enhanced and unenhanced dampings. | 2105.00730v2 |
2021-05-06 | On Linear Damping Around Inhomogeneous Stationary States of the Vlasov-HMF Model | We study the dynamics of perturbations around an inhomogeneous stationary
state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized
stability criterion (Penrose criterion). We consider solutions of the
linearized equation around the steady state, and prove the algebraic decay in
time of the Fourier modes of their density. We prove moreover that these
solutions exhibit a scattering behavior to a modified state, implying a linear
Landau damping effect with an algebraic rate of damping. | 2105.02484v1 |
2007-06-30 | The squeezed generalized amplitude damping channel | Squeezing of a thermal bath introduces new features absent in an open quantum
system interacting with an uncorrelated (zero squeezing) thermal bath. The
resulting dynamics, governed by a Lindblad-type evolution, extends the concept
of a generalized amplitude damping channel, which corresponds to a dissipative
interaction with a purely thermal bath. Here we present the Kraus
representation of this map, which we call the squeezed generalized amplitude
damping channel. As an application of this channel to quantum information, we
study the classical capacity of this channel. | 0707.0059v2 |
2007-07-09 | Memory in a nonlocally damped oscillator | We analyze the new equation of motion for the damped oscillator. It differs
from the standard one by a damping term which is nonlocal in time and hence it
gives rise to a system with memory. Both classical and quantum analysis is
performed. The characteristic feature of this nonlocal system is that it breaks
local composition low for the classical Hamiltonian dynamics and the
corresponding quantum propagator. | 0707.1199v2 |
2007-07-20 | Dynamics of Bloch Oscillations in Disordered Lattice Potentials | We present a detailed analysis of the dynamics of Bloch oscillations of
Bose-Einstein condensates in disordered lattice potentials. Due to the disorder
and the interparticle interactions these oscillations undergo a dephasing,
reflected in a damping of the center of mass oscillations, which should be
observable under realistic experimental conditions. The interplay between
interactions and disorder is far from trivial, ranging from an
interaction-enhanced damping due to modulational instability for strong
interactions, to an interaction-reduced damping due to a dynamical screening of
the disorder potential. | 0707.3131v1 |
2009-07-02 | Damping and decoherence of a nanomechanical resonator due to a few two level systems | We consider a quantum model of a nanomechanical flexing beam resonator
interacting with a bath comprising a few damped tunneling two level systems
(TLS's). In contrast with a resonator interacting bilinearly with an ohmic free
oscillator bath (modeling clamping loss, for example), the mechanical resonator
damping is amplitude dependent, while the decoherence of quantum superpositions
of mechanical position states depends only weakly on their spatial separation. | 0907.0431v1 |
2009-07-29 | High performance single-error-correcting quantum codes for amplitude damping | We construct families of high performance quantum amplitude damping codes.
All of our codes are nonadditive and most modestly outperform the best possible
additive codes in terms of encoded dimension. One family is built from
nonlinear error-correcting codes for classical asymmetric channels, with which
we systematically construct quantum amplitude damping codes with parameters
better than any prior construction known for any block length n > 7 except
n=2^r-1. We generalize this construction to employ classical codes over GF(3)
with which we numerically obtain better performing codes up to length 14.
Because the resulting codes are of the codeword stabilized (CWS) type, easy
encoding and decoding circuits are available. | 0907.5149v1 |
2012-02-24 | Small data global existence for the semilinear wave equation with space-time dependent damping | In this paper we consider the critical exponent problem for the semilinear
wave equation with space-time dependent damping. When the damping is effective,
it is expected that the critical exponent agrees with that of only space
dependent coefficient case. We shall prove that there exists a unique global
solution for small data if the power of nonlinearity is larger than the
expected exponent. Moreover, we do not assume that the data are compactly
supported. However, it is still open whether there exists a blow-up solution if
the power of nonlinearity is smaller than the expected exponent. | 1202.5379v1 |
2013-11-16 | Shear viscosity due to the Landau damping from quark-pion interaction | We have calculated the shear viscosity coefficient $\eta$ of the strongly
interacting matter in the relaxation time approximation, where a quasi particle
description of quarks with its dynamical mass is considered from NJL model. Due
to the thermodynamic scattering of quarks with pseudo scalar type condensate
(i.e. pion), a non zero Landau damping will be acquired by the propagating
quarks. This Landau damping may be obtained from the Landau cut contribution of
the in-medium self-energy of quark-pion loop, which is evaluated in the
framework of real-time thermal field theory. | 1311.4070v1 |
2014-01-11 | Damping in two component Bose gas | We investigate the Landau and Baliaev damping of the collective modes in a
two-component Bose gas using the mean-field approximation. We show that due to
the two body atom-atom interaction, oscillations of each component is coupled
to the thermal excitations of the other component which gives rise to creation
or destruction of the elementary excitations that can take place in the two
separate components.In addition we find that the damping is also enhanced due
to inter-component coupling. | 1401.2537v1 |
2014-04-25 | The time singular limit for a fourth-order damped wave equation for MEMS | We consider a free boundary problem modeling electrostatic
microelectromechanical systems. The model consists of a fourth-order damped
wave equation for the elastic plate displacement which is coupled to an
elliptic equation for the electrostatic potential. We first review some recent
results on existence and non-existence of steady-states as well as on local and
global well-posedness of the dynamical problem, the main focus being on the
possible touchdown behavior of the elastic plate. We then investigate the
behavior of the solutions in the time singular limit when the ratio between
inertial and damping effects tends to zero. | 1404.6342v1 |
2016-12-09 | Ornstein-Uhlenbeck Process with Fluctuating Damping | This paper studies Langevin equation with random damping due to
multiplicative noise and its solution. Two types of multiplicative noise,
namely the dichotomous noise and fractional Gaussian noise are considered.
Their solutions are obtained explicitly, with the expressions of the mean and
covariance determined explicitly. Properties of the mean and covariance of the
Ornstein-Uhlenbeck process with random damping, in particular the asymptotic
behavior, are studied. The effect of the multiplicative noise on the stability
property of the resulting processes is investigated. | 1612.03013v3 |
2016-12-20 | Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment | We consider a nonlinear Timoshenko system of partial differential equations
(PDEs) with a frictional damping term in rotation angle. The nonlinearity is
due to the arbitrary dependence on the rotation moment. A Lie symmetry group
classification of the arbitrary function of rotation moment is presented. An
optimal system of one-dimensional subalgebras of the nonlinear damped
Timoshenko system is derived for all the non-linear cases. All possible
invariant variables of the optimal systems for the three non-linear cases are
presented. The corresponding reduced systems of ordinary differential equations
(ODEs) are also provided. | 1612.06775v1 |
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