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2019-06-12 | A no-go result for the quantum damped harmonic oscillator | In this letter we show that it is not possible to set up a canonical
quantization for the damped harmonic oscillator using the Bateman lagrangian.
In particular, we prove that no square integrable vacuum exists for the {\em
natural} ladder operators of the system, and that the only vacua can be found
as distributions. This implies that the procedure proposed by some authors is
only formally correct, and requires a much deeper analysis to be made rigorous. | 1906.05121v2 |
2019-06-26 | Mismatched Estimation of Polynomially Damped Signals | In this work, we consider the problem of estimating the parameters of
polynomially damped sinusoidal signals, commonly encountered in, for instance,
spectroscopy. Generally, finding the parameter values of such signals
constitutes a high-dimensional problem, often further complicated by not
knowing the number of signal components or their specific signal structures. In
order to alleviate the computational burden, we herein propose a mismatched
estimation procedure using simplified, approximate signal models. Despite the
approximation, we show that such a procedure is expected to yield predictable
results, allowing for statistically and computationally efficient estimates of
the signal parameters. | 1906.11113v1 |
2019-06-27 | Temperature-Dependent Lifetimes of Low-Frequency Adsorbate Modes from Non-Equilibrium Molecular Dynamics Simulations | We present calculations on the damping of a low-frequency adsorbate mode on a
metal surface, namely the frustrated translation of Na on Cu(100). For the
first time, vibrational lifetimes of excited adlayers are extracted from
non-equilibrium molecular dynamics calculations accounting for both the
phononic and the electronic dissipation channels. The relative contributions of
the two damping mechanisms, which we show to be additive, are found to disagree
with textbook predictions. A simple model based on separable harmonic and
anharmonic contributions is able to semi-quantitatively reproduce the
temperature dependence of the computed lifetimes. | 1906.11776v1 |
2019-07-10 | Formal expansions in stochastic model for wave turbulence 1: kinetic limit | We consider the damped/driver (modified) cubic NLS equation on a large torus
with a properly scaled forcing and dissipation, and decompose its solutions to
formal series in the amplitude. We study the second order truncation of this
series and prove that when the amplitude goes to zero and the torus' size goes
to infinity the energy spectrum of the truncated solutions becomes close to a
solution of the damped/driven wave kinetic equation. Next we discuss higher
order truncations of the series. | 1907.04531v4 |
2019-07-22 | Thresholds for low regularity solutions to wave equations with structural damping | We study the asymptotic behavior of solutions to wave equations with a
structural damping term \[ u_{tt}-\Delta u+\Delta^2 u_t=0, \qquad
u(0,x)=u_0(x), \,\,\, u_t(0,x)=u_1(x), \] in the whole space. New thresholds
are reported in this paper that indicate which of the diffusion wave property
and the non-diffusive structure dominates in low regularity cases. We develop
to that end the previous author's research in 2019 where they have proposed a
threshold that expresses whether the parabolic-like property or the wave-like
property strongly appears in the solution to some regularity-loss type
dissipative wave equation. | 1907.09299v1 |
2019-08-03 | Lindblad dynamics of the damped and forced quantum harmonic oscillator | The quantum dynamics of a damped and forced harmonic oscillator is
investigated in terms of a Lindblad master equation. Elementary algebraic
techniques are employed allowing for example to analyze the long time behavior,
i.e. the quantum limit cycle. The time evolution of various expectation values
is obtained in closed form as well as the entropy and the Husimi phase space
distribution. We also discuss the related description in terms of a
non-Hermitian Hamiltonian. | 1908.01187v2 |
2019-08-07 | Decay estimates for the linear damped wave equation on the Heisenberg group | This paper is devoted to the derivation of $L^2$ - $L^2$ decay estimates for
the solution of the homogeneous linear damped wave equation on the Heisenberg
group $\mathbf{H}_n$, for its time derivative and for its horizontal gradient.
Moreover, we consider the improvement of these estimates when further
$L^1(\mathbf{H}_n)$ regularity is required for the Cauchy data. Our approach
will rely strongly on the group Fourier transform of $\mathbf{H}_n$ and on the
properties of the Hermite functions that form a maximal orthonormal system for
$L^2(\mathbb{R}^n)$ of eigenfunctions of the harmonic oscillator. | 1908.02657v1 |
2019-08-08 | Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity | In this paper, we consider the Cauchy problem for the semilinear damped wave
equation on the Heisenberg group with power nonlinearity. We prove that the
critical exponent is the Fujita exponent $p_{\mathrm{Fuj}}(\mathscr{Q}) = 1+2 /
\mathscr{Q}$, where $\mathscr{Q}$ is the homogeneous dimension of the
Heisenberg group. On the one hand, we will prove the global existence of small
data solutions for $p >p_{\mathrm{Fuj}}(\mathscr{Q})$ in an exponential
weighted energy space. On the other hand, a blow-up result for $1 < p \leq
p_{\mathrm{Fuj}}(\mathscr{Q})$ under certain integral sign assumptions for the
Cauchy data by using the test function method. | 1908.02989v1 |
2019-09-01 | Invariant measures for stochastic damped 2D Euler equations | We study the two-dimensional Euler equations, damped by a linear term and
driven by an additive noise. The existence of weak solutions has already been
studied; pathwise uniqueness is known for solutions that have vorticity in
$L^\infty$. In this paper, we prove the Markov property and then the existence
of an invariant measure in the space $L^\infty$ by means of a
Krylov-Bogoliubov's type method, working with the weak$\star$ and the bounded
weak$\star$ topologies in $L^\infty$. | 1909.00424v2 |
2019-09-03 | A blow-up result for semi-linear structurally damped $σ$-evolution equations | We would like to prove a blow-up result for semi-linear structurally damped
$\sigma$-evolution equations, where $\sigma \ge 1$ and $\delta\in [0,\sigma)$
are assumed to be any fractional numbers. To deal with the fractional Laplacian
operators $(-\Delta)^\sigma$ and $(-\Delta)^\delta$ as well-known non-local
operators, in general, it seems difficult to apply the standard test function
method directly. For this reason, in this paper we shall construct new test
functions to overcome this difficulty. | 1909.01181v1 |
2019-09-09 | Action Functional for a Particle with Damping | In this brief report we discuss the action functional of a particle with
damping, showing that it can be obtained from the dissipative equation of
motion through a modification which makes the new dissipative equation
invariant for time reversal symmetry. This action functional is exactly the
effective action of Caldeira-Leggett model but, in our approach, it is derived
without the assumption that the particle is weakly coupled to a bath of
infinite harmonic oscillators. | 1909.03694v2 |
2019-09-11 | Equilibrium radiation in a plasma medium with spatial and frequency dispersion | Examination of equilibrium radiation in plasma media shows that the spectral
energy distribution of such radiation is different from the Planck equilibrium
radiation. Using the approach of quantum electrodynamics the general relation
for the spectral energy density of equilibrium radiation in a system of charged
particles is found. The obtained result takes into account the influence of
plasma on equilibrium radiation through the explicit transverse dielectric
permittivity which takes into account spatial and frequency dispersion, as well
as the finite collisional damping. For the limiting case of an infinitesimal
damping the result coincides with the known expression. | 1909.08056v1 |
2019-10-14 | Blow-up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain | In this paper, we consider the initial boundary value problem in an exterior
domain for semilinear strongly damped wave equations with power nonlinear term
of the derivative-type $|u_t|^q$ or the mixed-type $|u|^p+|u_t|^q$, where
$p,q>1$. On one hand, employing the Banach fixed-point theorem we prove local
(in time) existence of mild solutions. On the other hand, under some conditions
for initial data and the exponents of power nonlinear terms, the blow-up
results are derived by applying the test function method. | 1910.05981v1 |
2019-11-03 | Linear Inviscid Damping in Sobolev and Gevrey Spaces | In a recent article Jia established linear inviscid damping in Gevrey
regularity for compactly supported Gevrey regular shear flows in a finite
channel, which is of great interest in view of existing nonlinear results. In
this article we provide an alternative very short proof of stability in Gevrey
regularity as a consequence of stability in high Sobolev regularity. Here, we
consider both the setting of a finite channel with compactly supported
perturbations and of an infinite channel without this restriction. Furthermore,
we consider the setting where perturbations vanish only of finite order. | 1911.00880v1 |
2019-11-03 | A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain | We study two-dimensional semilinear strongly damped wave equation with mixed
nonlinearity $|u|^p+|u_t|^q$ in an exterior domain, where $p,q>1$. Assuming the
smallness of initial data in exponentially weighted spaces and some conditions
on powers of nonlinearity, we prove global (in time) existence of small data
energy solution with suitable higher regularity by using a weighted energy
method. | 1911.00899v1 |
2019-11-05 | Critical exponent for a weakly coupled system of semi-linear $σ$-evolution equations with frictional damping | We are interested in studying the Cauchy problem for a weakly coupled system
of semi-linear $\sigma$-evolution equations with frictional damping. The main
purpose of this paper is two-fold. We would like to not only prove the global
(in time) existence of small data energy solutions but also indicate the
blow-up result for Sobolev solutions when $\sigma$ is assumed to be any
fractional number. | 1911.01946v1 |
2019-11-11 | Existence and nonexistence of global solutions for a structurally damped wave system with power nonlinearities | Our interest itself of this paper is strongly inspired from an open problem
in the paper [1] published by D'Abbicco. In this article, we would like to
study the Cauchy problem for a weakly coupled system of semi-linear
structurally damped wave equations. Main goal is to find the threshold, which
classifies the global (in time) existence of small data solutions or the
nonexistence of global solutions under the growth condition of the
nonlinearities. | 1911.04412v1 |
2019-11-15 | Some $L^1$-$L^1$ estimates for solutions to visco-elastic damped $σ$-evolution models | This note is to conclude $L^1-L^1$ estimates for solutions to the following
Cauchy problem for visco-elastic damped $\sigma$-evolution models:
\begin{equation} \begin{cases} u_{tt}+ (-\Delta)^\sigma u+ (-\Delta)^\sigma u_t
= 0, &\quad x\in \mathbb{R}^n,\, t \ge 0, \\ u(0,x)= u_0(x),\quad
u_t(0,x)=u_1(x), &\quad x\in \mathbb{R}^n, \label{pt1.1} \end{cases}
\end{equation} where $\sigma> 1$, in all space dimensions $n\ge 1$. | 1911.06563v1 |
2019-11-22 | Long-time asymptotics for a coupled thermoelastic plate-membrane system | In this paper we consider a transmission problem for a system of a
thermoelastic plate with (or without) rotational inertia term coupled with a
membrane with different variants of damping for the plate and/or the membrane.
We prove well-posedness of the problem and higher regularity of the solution
and study the asymptotic behaviour of the solution, depending on the damping
and on the presence of the rotational term. | 1911.10161v1 |
2019-11-28 | Tikhonov regularization of a second order dynamical system with Hessian driven damping | We investigate the asymptotic properties of the trajectories generated by a
second-order dynamical system with Hessian driven damping and a Tikhonov
regularization term in connection with the minimization of a smooth convex
function in Hilbert spaces. We obtain fast convergence results for the function
values along the trajectories. The Tikhonov regularization term enables the
derivation of strong convergence results of the trajectory to the minimizer of
the objective function of minimum norm. | 1911.12845v2 |
2019-12-15 | Negative mobility, sliding and delocalization for stochastic networks | We consider prototype configurations for quasi-one-dimensional stochastic
networks that exhibit negative mobility, meaning that current decreases or even
reversed as the bias is increased. We then explore the implications of
disorder. In particular we ask whether lower and upper bias thresholds restrict
the possibility to witness non-zero current (sliding and anti-sliding
transitions respectively), and whether a delocalization effect manifest itself
(crossover from over-damped to under-damped relaxation). In the latter context
detailed analysis of the relaxation spectrum as a function of the bias is
provided for both on-chain and off-chain disorder. | 1912.07059v2 |
2019-12-23 | On a damped Szego equation (with an appendix in collaboration with Christian Klein) | We investigate how damping the lowest Fourier mode modifies the dynamics of
the cubic Szeg{\"o} equation. We show that there is a nonempty open subset of
initial data generating trajec-tories with high Sobolev norms tending to
infinity. In addition, we give a complete picture of this phenomenon on a
reduced phase space of dimension 6. An appendix is devoted to numerical
simulations supporting the generalisation of this picture to more general
initial data. | 1912.10933v1 |
2020-01-29 | The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems | In this paper we propose new numerical algorithms in the setting of
unconstrained optimization problems and we study the rate of convergence in the
iterates of the objective function. Furthermore, our algorithms are based upon
splitting and symplectic methods and they preserve the energy properties of the
inherent continuous dynamical system that contains a Hessian perturbation. At
the same time, we show that Nesterov gradient method is equivalent to a
Lie-Trotter splitting applied to a Hessian driven damping system. Finally, some
numerical experiments are presented in order to validate the theoretical
results. | 2001.10831v2 |
2020-02-05 | Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation | For the one-dimensional nonlinear damped Klein-Gordon equation \[
\partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad
\mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove
that any global finite energy solution either converges to $0$ or behaves
asymptotically as $t\to \infty$ as the sum of $K\geq 1$ decoupled solitary
waves. In the multi-soliton case $K\geq 2$, the solitary waves have alternate
signs and their distances are of order $\log t$. | 2002.01826v1 |
2020-02-11 | Distributional Solutions of the Damped Wave Equation | This work presents results on solutions of the one-dimensional damped wave
equation, also called telegrapher's equation, when the initial conditions are
general distributions, not only functions. We make a complete deduction of its
fundamental solutions, both for positive and negative times. To obtain them we
use only self-similarity arguments and distributional calculus, making no use
of Fourier or Laplace transforms. We next use these fundamental solutions to
prove both the existence and the uniqueness of solutions to the distributional
initial value problem. As applications we recover the semigroup property for
initial data in classical function spaces and also the probability distribution
function for a certain financial model of evolution of prices. | 2002.04249v2 |
2020-02-13 | Description of the wavevector dispersion of surface plasmon-phonon-polaritons | We reported here the results of the calculations of wavevector dispersion of
oscillations frequencies, $\omega'(k)$, and damping $\omega''(k)$ of the
surface plasmon phonon polaritons (\mbox{SPPhP}) for the heavy-doped GaN
sample. We showed that $\omega'(k)$- dependence consists of the three branches
with the specific anticrossing behavior due to the interaction of surface
plasmon polariton (SPP) with surface phonon polariton(SPhP). The strong
renormalization of the damping $\omega''(k)$ in the vicinity of the
anticrossing region was found. The obtained dispersions of the $\omega'(k)$ and
$\omega''(k)$ were applied for the analytical analysis of exact electrodynamic
simulation of the resonant behavior of the reflectivity spectrum of the n-GaN
grating. | 2002.05473v1 |
2020-03-20 | The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping | In the present paper, we prove time decay estimates of solutions in weighted
Sobolev spaces to the second order evolution equation with fractional Laplacian
and damping for data in Besov spaces. Our estimates generalize the estimates
obtained in the previous studies. The second aim of this article is to apply
these estimates to prove small data global well-posedness for the Cauchy
problem of the equation with power nonlinearities. Especially, the estimates
obtained in this paper enable us to treat more general conditions on the
nonlinearities and the spatial dimension than the results in the previous
studies. | 2003.09239v1 |
2020-03-31 | Time-Asymptotics of Physical Vacuum Free Boundaries for Compressible Inviscid Flows with Damping | In this paper, we prove the leading term of time-asymptotics of the moving
vacuum boundary for compressible inviscid flows with damping to be that for
Barenblatt self-similar solutions to the corresponding porous media equations
obtained by simplifying momentum equations via Darcy's law plus the possible
shift due to the movement of the center of mass, in the one-dimensional and
three-dimensional spherically symmetric motions, respectively. This gives a
complete description of the large time asymptotic behavior of solutions to the
corresponding vacuum free boundary problems. The results obtained in this paper
are the first ones concerning the large time asymptotics of physical vacuum
boundaries for compressible inviscid fluids, to the best of our knowledge. | 2003.14072v2 |
2020-04-13 | Landau damping for analytic and Gevrey data | In this paper, we give an elementary proof of the nonlinear Landau damping
for the Vlasov-Poisson system near Penrose stable equilibria on the torus
$\mathbb{T}^d \times \mathbb{R}^d$ that was first obtained by Mouhot and
Villani in \cite{MV} for analytic data and subsequently extended by Bedrossian,
Masmoudi, and Mouhot \cite{BMM} for Gevrey-$\gamma$ data,
$\gamma\in(\frac13,1]$. Our proof relies on simple pointwise resolvent
estimates and a standard nonlinear bootstrap analysis, using an ad-hoc family
of analytic and Gevrey-$\gamma$ norms. | 2004.05979v3 |
2020-04-16 | Strichartz estimates for mixed homogeneous surfaces in three dimensions | We obtain sharp mixed norm Strichartz estimates associated to mixed
homogeneous surfaces in $\mathbb{R}^3$. Both cases with and without a damping
factor are considered. In the case when a damping factor is considered our
results yield a wide generalization of a result of Carbery, Kenig, and Ziesler
[CKZ13]. The approach we use is to first classify all possible singularities
locally, after which one can tackle the problem by appropriately modifying the
methods from the paper of Ginibre and Velo [GV92], and by using the recently
developed methods by Ikromov and M\"uller [IM16]. | 2004.07751v1 |
2020-04-17 | Critical exponent for semi-linear structurally damped wave equation of derivative type | Main purpose of this paper is to study the following semi-linear structurally
damped wave equation with nonlinearity of derivative type: $$u_{tt}- \Delta u+
\mu(-\Delta)^{\sigma/2} u_t= |u_t|^p,\quad u(0,x)= u_0(x),\quad
u_t(0,x)=u_1(x),$$ with $\mu>0$, $n\geq1$, $\sigma \in (0,2]$ and $p>1$. In
particular, we are going to prove the non-existence of global weak solutions by
using a new test function and suitable sign assumptions on the initial data in
both the subcritical case and the critical case. | 2004.08486v2 |
2020-04-29 | Exponential decay for damped Klein-Gordon equations on asymptotically cylindrical and conic manifolds | We study the decay of the global energy for the damped Klein-Gordon equation
on non-compact manifolds with finitely many cylindrical and subconic ends up to
bounded perturbation. We prove that under the Geometric Control Condition, the
decay is exponential, and that under the weaker Network Control Condition, the
decay is logarithmic, by developing the global Carleman estimate with multiple
weights. | 2004.13894v2 |
2020-05-06 | Zero-dimensional models for gravitational and scalar QED decoherence | We investigate the dynamics of two quantum mechanical oscillator system-bath
toy models obtained by truncating to zero spatial dimensions linearized gravity
coupled to a massive scalar field and scalar QED. The scalar-gravity toy model
maps onto the phase damped oscillator, while the scalar QED toy model
approximately maps onto an oscillator system subject to two-photon damping. The
toy models provide potentially useful insights into solving for open system
quantum dynamics relevant to the full scalar QED and weak gravitational field
systems, in particular operational probes of the decoherence for initial scalar
field system superposition states. | 2005.02554v2 |
2020-05-16 | On the asymptotic stability of wave equations coupled by velocities of anti-symmetric type | In this paper, we study the asymptotic stability of two wave equations
coupled by velocities of anti-symmetric type via only one damping. We adopt the
frequency domain method to prove that the system with smooth initial data is
logarithmically stable, provided that the coupling domain and the damping
domain intersect each other. Moreover, we show, by an example, that this
geometric assumption of the intersection is necessary for 1-D case. | 2005.07977v2 |
2020-05-27 | On the blow-up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups | In this note, we prove a blow-up result for the semilinear damped wave
equation in a compact Lie group with power nonlinearity $|u|^p$ for any $p>1$,
under suitable integral sign assumptions for the initial data, by using an
iteration argument. A byproduct of this method is the upper bound estimate for
the lifespan of a local in time solution. As a preliminary result, a local (in
time) existence result is proved in the energy space via Fourier analysis on
compact Lie groups. | 2005.13479v2 |
2020-06-13 | On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations | We study the time-harmonic Galbrun equation describing the propagation of
sound in the presence of a steady background flow. With additional rotational
and gravitational terms these equations are also fundamental in helio- and
asteroseismology as a model for stellar oscillations. For a simple damping
model we prove well-posedness of these equations, i.e. uniqueness, existence,
and stability of solutions under mild conditions on the parameters (essentially
subsonic flows). The main tool of our analysis is a generalized Helmholtz
decomposition. | 2006.07658v1 |
2020-06-22 | Prediction of short time qubit readout via measurement of the next quantum jump of a coupled damped driven harmonic oscillator | The dynamics of the next quantum jump for a qubit [two level system] coupled
to a readout resonator [damped driven harmonic oscillator] is calculated. A
quantum mechanical treatment of readout resonator reveals non exponential short
time behavior which could facilitate detection of the state of the qubit faster
than the resonator lifetime. | 2006.11950v1 |
2020-07-08 | The interplay of critical regularity of nonlinearities in a weakly coupled system of semi-linear damped wave equations | We would like to study a weakly coupled system of semi-linear classical
damped wave equations with moduli of continuity in nonlinearities whose powers
belong to the critical curve in the $p-q$ plane. The main goal of this paper is
to find out the sharp conditions of these moduli of continuity which classify
between global (in time) existence of small data solutions and finite time
blow-up of solutions. | 2007.04157v1 |
2020-07-09 | Semi-uniform stability of operator semigroups and energy decay of damped waves | Only in the last fifteen years or so has the notion of semi-uniform
stability, which lies between exponential stability and strong stability,
become part of the asymptotic theory of $C_0$-semigroups. It now lies at the
very heart of modern semigroup theory. After briefly reviewing the notions of
exponential and strong stability, we present an overview of some of the best
known (and often optimal) abstract results on semi-uniform stability. We go on
to indicate briefly how these results can be applied to obtain (sometimes
optimal) rates of energy decay for certain damped second-order Cauchy problems. | 2007.04711v1 |
2020-07-10 | Quasi-periodic travelling waves for a class of damped beams on rectangular tori | This article concerns a class of beam equations with damping on rectangular
tori. When the generators satisfy certain relationship, by excluding some value
of two model parameters, we prove that such models admit small amplitude
quasi-periodic travelling wave solutions with two frequencies, which are
continuations of two rotating wave solutions with one frequency. This result
holds not only for an isotropic torus, but also for an anisotropic torus. The
proof is mainly based on a Lyapunov--Schmidt reduction together with the
implicit function theorem. | 2007.05154v1 |
2020-07-24 | A Framework to Control Inter-Area Oscillations with Local Measurement | Inter-area oscillations in power system limit of power transfer capability
though tie-lines. For stable operation, wide-area power system stabilizers are
deployed to provide sufficient damping. However, as the feedback is through a
communication network, it brings challenges such as additional communication
layer and cybersecurity issues. To address this, a framework for synthesizing
remote signal from local measurement as feedback in the wide-area power system
stabilizer is proposed. The remote signal is synthesized using different
variants of observers in a case study of two-area benchmark system. The
proposed framework can improve the damping of inter-area oscillations for
static output feedback controller. The presented framework should help to
design attack-resilient controller design in smart grid. | 2007.12426v1 |
2020-08-17 | Dynamics of spatially indistinguishable particles and entanglement protection | We provide a general framework which allows one to obtain the dynamics of $N$
noninteracting spatially indistinguishable particles locally coupled to
separated environments. The approach is universal, being valid for both bosons
and fermions and for any type of system-environment interaction. It is then
applied to study the dynamics of two identical qubits under paradigmatic
Markovian noises, such as phase damping, depolarizing and amplitude damping. We
find that spatial indistinguishability of identical qubits is a controllable
intrinsic property of the system which protects quantum entanglement against
detrimental noise. | 2008.07471v1 |
2020-09-02 | Discriminating qubit amplitude damping channels | We address the issue of the discrimination between two-qubit amplitude
damping channels by exploring several strategies. For the single-shot, we show
that the excited state does not always give the optimal input, and that side
entanglement assistance has limited benefit. On the contrary, feedback
assistance from the environment is more beneficial. For the two-shot, we prove
the in-utility of entangled inputs. Then focusing on individual (local)
measurements, we find the optimal adaptive strategy. | 2009.01000v3 |
2020-09-03 | Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation | This article is concerned with the asymptotic behavior of the two-dimensional
inviscid Boussinesq equations with a damping term in the velocity equation.
Precisely, we provide the time-decay rates of the smooth solutions to that
system. The key ingredient is a careful analysis of the Green kernel of the
linearized problem in Fourier space, combined with bilinear estimates and
interpolation inequalities for handling the nonlinearity. | 2009.01578v2 |
2020-08-05 | The perturbational stability of the Schr$\ddot{o}$dinger equation | By using the Wigner transform, it is shown that the nonlinear
Schr$\ddot{\textmd{o}}$dinger equation can be described, in phase space, by a
kinetic theory similar to the Vlasov equation which is used for describing a
classical collisionless plasma. In this paper we mainly show Landau damping in
the quantum sense, namely,quantum Landau damping exists for the Wigner-Poisson
system. At the same time, we also prove the existence and the stability of the
nonlinear Schr$\ddot{\textmd{o}}$dinger equation under the quantum stability
assumption. | 2009.09855v1 |
2020-10-12 | Long time behavior of solutions for a damped Benjamin-Ono equation | We consider the Benjamin-Ono equation on the torus with an additional damping
term on the smallest Fourier modes (cos and sin). We first prove global
well-posedness of this equation in $L^2_{r,0}(\mathbb{T})$. Then, we describe
the weak limit points of the trajectories in $L^2_{r,0}(\mathbb{T})$ when time
goes to infinity, and show that these weak limit points are strong limit
points. Finally, we prove the boundedness of higher-order Sobolev norms for
this equation. Our key tool is the Birkhoff map for the Benjamin-Ono equation,
that we use as an adapted nonlinear Fourier transform. | 2010.05520v1 |
2020-10-18 | Classical limit of quantum mechanics for damped driven oscillatory systems: Quantum-classical correspondence | The investigation of quantum-classical correspondence may lead to gain a
deeper understanding of the classical limit of quantum theory. We develop a
quantum formalism on the basis of a linear-invariant theorem, which gives an
exact quantum-classical correspondence for damped oscillatory systems that are
perturbed by an arbitrary force. Within our formalism, the quantum trajectory
and expectation values of quantum observables are precisely coincide with their
classical counterparts in the case where we remove the global quantum constant
h from their quantum results. In particular, we illustrate the correspondence
of the quantum energy with the classical one in detail. | 2010.08971v1 |
2020-10-21 | Initial boundary value problem for a strongly damped wave equation with a general nonlinearity | In this paper, a strongly damped semilinear wave equation with a general
nonlinearity is considered. With the help of a newly constructed auxiliary
functional and the concavity argument, a general finite time blow-up criterion
is established for this problem. Furthermore, the lifespan of the weak solution
is estimated from both above and below. This partially extends some results
obtained in recent literatures and sheds some light on the similar effect of
power type nonlinearity and logarithmic nonlinearity on finite time blow-up of
solutions to such problems. | 2010.10696v1 |
2020-10-21 | MRI Image Recovery using Damped Denoising Vector AMP | Motivated by image recovery in magnetic resonance imaging (MRI), we propose a
new approach to solving linear inverse problems based on iteratively calling a
deep neural-network, sometimes referred to as plug-and-play recovery. Our
approach is based on the vector approximate message passing (VAMP) algorithm,
which is known for mean-squared error (MSE)-optimal recovery under certain
conditions. The forward operator in MRI, however, does not satisfy these
conditions, and thus we design new damping and initialization schemes to help
VAMP. The resulting DD-VAMP++ algorithm is shown to outperform existing
algorithms in convergence speed and accuracy when recovering images from the
fastMRI database for the practical case of Cartesian sampling. | 2010.11321v1 |
2020-11-05 | Mathematical modelling of an unstable bent flow using the selective frequency damping method | The selective frequency damping method was applied to a bent flow. The method
was used in an adaptive formulation. The most dangerous frequency was
determined by solving an eigenvalue problem. It was found that one of the
patterns, steady-state or pulsating, may exist at some relatively high Reynolds
numbers. The periodic flow occurs due to the instability of the steady-state
flow. This numerical method is easy to use but requires a great deal of time
for calculations. | 2011.02646v1 |
2020-11-04 | The "Dark disk" model in the light of DAMPE experiment | There are a lot of models considering the Dark Matter (DM) to be the origin
of cosmic ray (CR) positron excess. However, they face an obstacle in the form
of gamma-rays. Simple DM models tend to overproduce gamma-rays, leading to
contradiction with isotropic gamma-ray background (IGRB). The <<dark disk>>
model has been proposed to alleviate this contradiction. This work considers
results of DAMPE experiment in the framework of the disk model. It is obtained
that such a framework allows improving data fit considerably. | 2011.04425v2 |
2020-12-15 | On the stability of Bresse system with one discontinuous local internal Kelvin-Voigt damping on the axial force | In this paper, we investigate the stabilization of a linear Bresse system
with one discontinuous local internal viscoelastic damping of Kelvin-Voigt type
acting on the axial force, under fully Dirichlet boundary conditions. First,
using a general criteria of Arendt-Batty, we prove the strong stability of our
system. Finally, using a frequency domain approach combined with the multiplier
method, we prove that the energy of our system decays polynomially with
different rates. | 2012.08219v1 |
2020-12-28 | An efficient method for approximating resonance curves of weakly-damped nonlinear mechanical systems | A method is presented for tracing the locus of a specific peak in the
frequency response under variation of a parameter. It is applicable to
periodic, steady-state vibrations of harmonically forced nonlinear mechanical
systems. It operates in the frequency domain and its central idea is to assume
a constant phase lag between forcing and response. The method is validated for
a two-degree-of-freedom oscillator with cubic spring and a bladed disk with
shroud contact. The method provides superior computational efficiency, but is
limited to weakly-damped systems. Finally, the capability to reveal isolated
solution branches is highlighted. | 2012.14458v1 |
2021-01-16 | Convergence of non-autonomous attractors for subquintic weakly damped wave equation | We study the non-autonomous weakly damped wave equation with subquintic
growth condition on the nonlinearity. Our main focus is the class of
Shatah--Struwe solutions, which satisfy the Strichartz estimates and are
coincide with the class of solutions obtained by the Galerkin method. For this
class we show the existence and smoothness of pullback, uniform, and cocycle
attractors and the relations between them. We also prove that these
non-autonomous attractors converge upper-semicontinuously to the global
attractor for the limit autonomous problem if the time-dependent nonlinearity
tends to time independent function in an appropriate way. | 2101.06523v1 |
2021-01-20 | A Damped Newton Algorithm for Generated Jacobian Equations | Generated Jacobian Equations have been introduced by Trudinger [Disc. cont.
dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re
equations arising in optimal transport. In this paper, we introduce and study a
damped Newton algorithm for solving these equations in the semi-discrete
setting, meaning that one of the two measures involved in the problem is
finitely supported and the other one is absolutely continuous. We also present
a numerical application of this algorithm to the near-field parallel refractor
problem arising in non-imaging problems. | 2101.08080v1 |
2021-02-04 | Global existence results for semi-linear structurally damped wave equations with nonlinear convection | In this paper, we consider the Cauchy problem for semi-linear wave equations
with structural damping term $\nu (-\Delta)^2 u_t$, where $\nu >0$ is a
constant. As being mentioned in [8,10], the linear principal part brings both
the diffusion phenomenon and the regularity loss of solutions. This implies
that, for the nonlinear problems, the choice of solution spaces plays an
important role to obtain global solutions with sharp decay properties in time.
Our main purpose of this paper is to prove the global (in time) existence of
solutions for the small data and their decay properties for the supercritical
nonlinearities. | 2102.02445v2 |
2021-02-15 | Piezoelectric beam with magnetic effect, time-varying delay and time-varying weights | The main result of this work is to obtain the exponential decay of the
solutions of a piezoelectric beam model with magnetic effect and delay term.
The dampings are inserted into the equation of longitudinal displacement. The
terms of damping, whose weight associated with them varies over time, are of
the friction type, and one of them has delay. This work will also address the
issue of existence and uniqueness of solution for the model. | 2102.07538v1 |
2021-02-23 | Effects of ground-state correlations on damping of giant dipole resonaces in $LS$ closed shell nuclei | The effects of ground-state correlations on the damping of isovector giant
dipole resonances in $LS$ closed shell nuclei $^{16}$O and $^{40}$Ca are
studied using extended random-phase-approximation (RPA) approaches derived from
the time-dependent density-matrix theory. It is pointed out that unconventional
two-body amplitudes of one particle--three hole and three particle--one hole
types which are neglected in most extended RPA theories play an important role
in the fragmentation of isovector dipole strength. | 2102.11505v2 |
2021-03-01 | On a damped nonlinear beam equation | In this note we analyze the large time behavior of solutions to an
initial/boundary problem involving a damped nonlinear beam equation. We show
that under physically realistic conditions on the nonlinear terms in the
equation of motion the energy is a decreasing function of time and solutions
converge to a stationary solution with respect to a desirable norm. | 2103.00969v3 |
2021-03-23 | Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics | In this paper, we propose in a Hilbertian setting a second-order
time-continuous dynamic system with fast convergence guarantees to solve
structured convex minimization problems with an affine constraint. The system
is associated with the augmented Lagrangian formulation of the minimization
problem. The corresponding dynamics brings into play three general time-varying
parameters, each with specific properties, and which are respectively
associated with viscous damping, extrapolation and temporal scaling. By
appropriately adjusting these parameters, we develop a Lyapunov analysis which
provides fast convergence properties of the values and of the feasibility gap.
These results will naturally pave the way for developing corresponding
accelerated ADMM algorithms, obtained by temporal discretization. | 2103.12675v1 |
2021-03-29 | Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation | We analyze the analytic Landau damping problem for the Vlasov-HMF equation,
by fixing the asymptotic behavior of the solution. We use a new method for this
"scattering problem", closer to the one used for the Cauchy problem. In this
way we are able to compare the two results, emphasizing the different influence
of the plasma echoes in the two approaches. In particular, we prove a
non-perturbative result for the scattering problem. | 2103.15932v2 |
2021-04-06 | Realising Einstein's mirror: Optomechanical damping with a thermal photon gas | In 1909 Einstein described the thermalization of a mirror within a blackbody
cavity by collisions with thermal photons. While the time to thermalize the
motion of even a microscale or nanoscale object is so long that it is not
feasible, we show that it is using the high intensity light from an amplified
thermal light source with a well-defined chemical potential. We predict damping
of the center-of mass motion due to this effect on times scales of seconds for
small optomechanical systems, such as levitated nanoparticles, allowing
experimental observation. | 2104.02708v2 |
2021-04-12 | The pressureless damped Euler-Riesz equations | In this paper, we analyze the pressureless damped Euler-Riesz equations posed
in either $\mathbb{R}^d$ or $\mathbb{T}^d$. We construct the global-in-time
existence and uniqueness of classical solutions for the system around a
constant background state. We also establish large-time behaviors of classical
solutions showing the solutions towards the equilibrium as time goes to
infinity. For the whole space case, we first show the algebraic decay rate of
solutions under additional assumptions on the initial data compared to the
existence theory. We then refine the argument to have the exponential decay
rate of convergence even in the whole space. In the case of the periodic
domain, without any further regularity assumptions on the initial data, we
provide the exponential convergence of solutions. | 2104.05153v1 |
2021-04-12 | Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation | In this paper we consider the inverse problem of identifying the initial data
in a fractionally damped wave equation from time trace measurements on a
surface, as relevant in photoacoustic or thermoacoustic tomography. We derive
and analyze a time stepping method for the numerical solution of the
corresponding forward problem. Moreover, to efficiently obtain reconstructions
by minimizing a Tikhonov regularization functional (or alternatively, by
computing the MAP estimator in a Bayesian approach), we develop an adjoint
based scheme for gradient computation. Numerical reconstructions in two space
dimensions illustrate the performance of the devised methods. | 2104.05577v1 |
2021-04-15 | Explaining Neptune's Eccentricity | Early migration damped Neptune's eccentricity. Here, we assume that the
damped value was much smaller than the value observed today, and show that the
closest flyby of $\sim 0.1 \; \mathrm{M_{\odot}}$ star over $\sim 4.5
\mathrm{\; Gyr}$ in the field, at a distance of $\sim 10^3 \mathrm{\; AU}$
would explain the value of Neptune's eccentricity observed today. | 2104.07672v3 |
2021-04-17 | Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds | In this work, we investigate the problem of finite time blow up as well as
the upper bound estimates of lifespan for solutions to small-amplitude
semilinear wave equations with time dependent damping and potential, and mixed
nonlinearities $c_1 |u_t|^p+c_2 |u|^q$, posed on asymptotically Euclidean
manifolds, which is related to both the Strauss conjecture and the Glassey
conjecture. | 2104.08497v2 |
2021-06-02 | Convergent dynamics of optimal nonlinear damping control | Following Demidovich's concept and definition of convergent systems, we
analyze the optimal nonlinear damping control, recently proposed [1] for the
second-order systems. Targeting the problem of output regulation,
correspondingly tracking of $\mathcal{C}^1$-trajectories, it is shown that all
solutions of the control system are globally uniformly asymptotically stable.
The existence of the unique limit solution in the origin of the control error
and its time derivative coordinates are shown in the sense of Demidovich's
convergent dynamics. Explanative numerical examples are also provided along
with analysis. | 2106.00962v1 |
2021-06-26 | Role of Dissipation on the Stability of a Parametrically Driven Quantum Harmonic Oscillator | We study the dissipative dynamics of a single quantum harmonic oscillator
subjected to a parametric driving with in an effective Hamiltonian approach.
Using Liouville von Neumann approach, we show that the time evolution of a
parametrically driven dissipative quantum oscillator has a strong connection
with the classical damped Mathieu equation. Based on the numerical analysis of
the Monodromy matrix, we demonstrate that the dynamical instability generated
by the parametric driving are reduced by the effect of dissipation. Further, we
obtain a closed relationship between the localization of the Wigner function
and the stability of the damped Mathieu equation. | 2106.14018v1 |
2021-07-29 | Global existence for damped $σ$-evolution equations with nonlocal nonlinearity | In this research, we would like to study the global (in time) existence of
small data solutions to the following damped $\sigma$-evolution equations with
nonlocal (in space) nonlinearity: \begin{equation*}
\partial_{t}^{2}u+(-\Delta)^{\sigma}u+\partial_{t}u+(-\Delta)^{\sigma}\partial_{t}u=I_{\alpha}(|u|^{p}),
\ \ t>0, \ \ x\in \mathbb{R}^{n}, \end{equation*} where $\sigma\geq1$, $p>1$
and $I_{\alpha}$ is the Riesz potential of power nonlinearity $|u|^{p}$ for any
$\alpha\in (0,n)$. More precisely, by using the $(L^{m}\cap L^{2})-L^{2}$ and
$L^{2}-L^{2}$ linear estimates, where $m\in[1,2]$, we show the new influence of
the parameter $\alpha$ on the admissible ranges of the exponent $p$. | 2107.13924v1 |
2021-08-17 | Estimate of the attractive velocity of attractors for some dynamical systems | In this paper, we first prove an abstract theorem on the existence of
polynomial attractors and the concrete estimate of their attractive velocity
for infinite-dimensional dynamical systems, then apply this theorem to a class
of wave equations with nonlocal weak damping and anti-damping in case that the
nonlinear term~$f$~is of subcritical growth. | 2108.07410v4 |
2021-08-27 | Distributed Mirror Descent Algorithm with Bregman Damping for Nonsmooth Constrained Optimization | To solve distributed optimization efficiently with various constraints and
nonsmooth functions, we propose a distributed mirror descent algorithm with
embedded Bregman damping, as a generalization of conventional distributed
projection-based algorithms. In fact, our continuous-time algorithm well
inherits good capabilities of mirror descent approaches to rapidly compute
explicit solutions to the problems with some specific constraint structures.
Moreover, we rigorously prove the convergence of our algorithm, along with the
boundedness of the trajectory and the accuracy of the solution. | 2108.12136v1 |
2021-08-27 | Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation | We study the non relativistic and ultra relativistic limits in the
two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time
white noise on the torus. In order to take the limits, it is crucial to clarify
the parameter dependence in the estimates of solution. In this paper we present
two methods to confirm this parameter dependence. One is the classical, simple
energy method. Another is the method via Strichartz estimates. | 2108.12183v4 |
2021-09-08 | The isothermal limit for the compressible Euler equations with damping | We consider the isothermal Euler system with damping. We rigorously show the
convergence of Barenblatt solutions towards a limit Gaussian profile in the
isothermal limit $\gamma$ $\rightarrow$ 1, and we explicitly compute the
propagation and the behavior of Gaussian initial data. We then show the weak L
1 convergence of the density as well as the asymptotic behavior of its first
and second moments. Contents 1. Introduction 1 2. Assumptions and main results
3 3. The limit $\gamma$ $\rightarrow$ 1 of Barenblatt's solutions 6 4. Gaussian
solutions 9 5. Evolution of certain quantities 10 6. Convergence 15 7.
Conclusion 17 References 17 | 2109.03590v1 |
2021-11-01 | Strong solution of modified 3D-Navier-stockes equations | In this paper we study the incompressible Navier-Stokes equations with
logarithme damping {\alpha} log(e + |u|2)|u|2u, where we used new methods, new
tools and Fourier analysis | 2111.00859v2 |
2021-11-02 | Blow-up of solutions to semilinear wave equations with a time-dependent strong damping | The paper investigates a class of a semilinear wave equation with
time-dependent damping term ($-\frac{1}{{(1+t)}^{\beta}}\Delta u_t$) and a
nonlinearity $|u|^p$. We will show the influence of the the parameter $\beta$
in the blow-up results under some hypothesis on the initial data and the
exponent $p$ by using the test function method. We also study the local
existence in time of mild solution in the energy space $H^1(\mathbb{R}^n)\times
L^2(\mathbb{R}^n)$. | 2111.01433v1 |
2021-11-02 | Around plane waves solutions of the Schr{ö}dinger-Langevin equation | We consider the logarithmic Schr{\"o}dinger equations with damping, also
called Schr{\"o}dinger-Langevin equation. On a periodic domain, this equation
possesses plane wave solutions that are explicit. We prove that these solutions
are asymptotically stable in Sobolev regularity. In the case without damping,
we prove that for almost all value of the nonlinear parameter, these solutions
are stable in high Sobolev regularity for arbitrary long times when the
solution is close to a plane wave. We also show and discuss numerical
experiments illustrating our results. | 2111.01487v1 |
2021-11-12 | GCGE: A Package for Solving Large Scale Eigenvalue Problems by Parallel Block Damping Inverse Power Method | We propose an eigensolver and the corresponding package, GCGE, for solving
large scale eigenvalue problems. This method is the combination of damping
idea, subspace projection method and inverse power method with dynamic shifts.
To reduce the dimensions of projection subspaces, a moving mechanism is
developed when the number of desired eigenpairs is large. The numerical
methods, implementing techniques and the structure of the package are
presented. Plenty of numerical results are provided to demonstrate the
efficiency, stability and scalability of the concerned eigensolver and the
package GCGE for computing many eigenpairs of large symmetric matrices arising
from applications. | 2111.06552v1 |
2021-11-25 | Continuity and topological structural stability for nonautonomous random attractors | In this work, we study continuity and topological structural stability of
attractors for nonautonomous random differential equations obtained by small
bounded random perturbations of autonomous semilinear problems. First, we study
existence and permanence of unstable sets of hyperbolic solutions. Then, we use
this to establish lower semicontinuity of nonautonomous random attractors and
to show that the gradient structure persists under nonautonomous random
perturbations. Finally, we apply the abstract results in a stochastic
differential equation and in a damped wave equation with a perturbation on the
damping. | 2111.13006v1 |
2021-12-20 | Dense Coding Capacity in Correlated Noisy Channels with Weak Measurement | Capacity of dense coding via correlated noisy channel is greater than that in
uncorrelated noisy channel. It is shown that weak measurement and reversal
measurement can make further effort to improve quantum dense coding capacity in
correlated amplitude damping channel, but this effort is very small in
correlated phase damping channel and correlated depolarizing channel. | 2112.10346v1 |
2021-12-22 | Low-frequency squeezing spectrum of a laser drivenpolar quantum emitter | It was shown by a study of the incoherent part of the low-frequency resonance
fluorescence spectrum of the polar quantum emitter driven by semiclassical
external laser field and damped by non-squeezed vacuum reservoir that the
emitted fluorescence field is squeezed to some degree nevertheless. As was also
found, a higher degree of squeezing could, in principle, be achieved by damping
the emitter by squeezed vacuum reservoir. | 2112.11809v1 |
2022-01-13 | Cavity optomechanics in a fiber cavity: the role of stimulated Brillouin scattering | We study the role of stimulated Brillouin scattering in a fiber cavity by
numerical simulations and a simple theoretical model and find good agreement
between experiment, simulation and theory. We also investigate an
optomechanical system based on a fiber cavity in the presence on the nonlinear
Brillouin scattering. Using simulation and theory, we show that this hybrid
optomechanical system increases optomechanical damping for low mechanical
resonance frequencies in the unresolved sideband regime. Furthermore, optimal
damping occurs for blue detuning in stark contrast to standard optomechanics.
We investigate whether this hybrid optomechanical system is capable cooling a
mechanical oscillator to the quantum ground state. | 2201.04987v1 |
2022-01-20 | Vacuum and singularity formation for compressible Euler equations with time-dependent damping | In this paper, vacuum and singularity formation are considered for
compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$,
by constructing some new control functions ingeniously, we obtain the lower
bounds estimates on density for arbitrary classical solutions. Basing on these
lower estimates, we succeed in proving the singular formation theorem for all
$\lambda$, which was open in [1] for some cases.Moreover, the singularity
formation of the compressible Euler equations when $\gamma=3$ is investigated,
too. | 2201.07957v1 |
2022-03-19 | The Equilibrium Temperature of Planets on Eccentric Orbits: Time Scales and Averages | From estimates of the near-surface heat capacity of planets it is shown that
the thermal time scale is larger than the orbital period in the presence of a
global ocean that is well-mixed to a depth of 100 m, or of an atmosphere with a
pressure of several tens of bars. As a consequence, the temperature
fluctuations of such planets on eccentric orbits are damped. The average
temperature should be calculated by taking the temporal mean of the irradiation
over an orbit, which increases with $1/\sqrt{1-e^2}$. This conclusion is
independent of the orbital distance and valid for Sun-like stars; the damping
is even stronger for low-mass main sequence hosts. | 2203.11723v1 |
2022-03-31 | Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings | This paper is concerned with the long-time dynamical behavior of a
piezoelectric system with magnetic effect, which has nonlinear damping terms
and external forces with a parameter. At first, we use the nonlinear semigroup
theory to prove the well-posedness of solutions. Then, we investigate the
properties of global attractors and the existence of exponential attractors.
Finally, the upper semicontinuity of global attractors has been investigated. | 2203.16736v1 |
2022-04-04 | Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions | In this paper, we investigate the exponential ergodicity in a
Wasserstein-type distance for a damping Hamiltonian dynamics with
state-dependent and non-local collisions, which indeed is a special case of
piecewise deterministic Markov processes while is very popular in numerous
modelling situations including stochastic algorithms. The approach adopted in
this work is based on a combination of the refined basic coupling and the
refined reflection coupling for non-local operators. In a certain sense, the
main result developed in the present paper is a continuation of the counterpart
in \cite{BW2022} on exponential ergodicity of stochastic Hamiltonian systems
with L\'evy noises and a complement of \cite{BA} upon exponential ergodicity
for Andersen dynamics with constant jump rate functions. | 2204.01372v1 |
2022-04-08 | Effect of Tamm surface states on hot electron generation and Landau damping in nanostructures metal-semiconductor | The hot electron generation in plasmonic nanoparticles is the key to
efficient plasmonic photocatalysis. In the paper, we study theoretically for
the first time the effect of Tamm states (TSs) at the interface
metal-semiconductor on hot electron generation and Landau damping (LD) in metal
nanoparticles. TSs can lead to resonant hot electron generation and to the LD
rate enhanced by several times. The resonant hot electron generation is
reinforced by the transition absorption due to the jump of the permittivity at
the metal-semiconductor interface. | 2204.04021v1 |
2022-04-11 | Certified Reduced Basis Method for the Damped Wave Equations on Networks | In this paper we present a reduced basis method which yields
structure-preservation and a tight a posteriori error bound for the simulation
of the damped wave equations on networks. The error bound is based on the
exponential decay of the energy inside the system and therefore allows for
sharp bounds without the need of regularization parameters. The fast
convergence of the reduced solution to the truth solution as well as the
tightness of the error bound are verified numerically using an academic network
as example. | 2204.05010v1 |
2022-04-27 | Spectrum of the wave equation with Dirac damping on a non-compact star graph | We consider the wave equation on non-compact star graphs, subject to a
distributional damping defined through a Robin-type vertex condition with
complex coupling. It is shown that the non-self-adjoint generator of the
evolution problem admits an abrupt change in its spectral properties for a
special coupling related to the number of graph edges. As an application, we
show that the evolution problem is highly unstable for the critical couplings.
The relationship with the Dirac equation in non-relativistic quantum mechanics
is also mentioned. | 2204.12747v1 |
2022-04-27 | Dependence on the thermodynamic state of self-diffusion of pseudo hard-spheres | Self-diffusion, $D$, in a system of particles that interact with a pseudo
hard sphere potential is analyzed. Coupling with a solvent is represented by a
Langevin thermostat, characterized by the damping time $t_d$. The hypotheses
that $D=D_0 \varphi$ is proposed, where $D_0$ is the small concentration
diffusivity and $\varphi$ is a thermodynamic function that represents the
effects of interactions as concentration is increased. Molecular dynamics
simulations show that different values of the noise intensity modify $D_0$ but
do not modify $\varphi$. This result is consistent with the assumption that
$\varphi$ is a thermodynamic function, since the thermodynamic state is not
modified by the presence of damping and noise. | 2204.12969v1 |
2022-04-29 | Plasmon damping rates in Coulomb-coupled two-dimensional layers in a heterostructure | The Coulomb excitations of charge density oscillation are calculated for a
double-layer heterostructure. Specifically, we consider two-dimensional (2D)
layers of silicene and graphene on a substrate. From the obtained surface
response function, we calculated the plasmon dispersion relations which
demonstrate the way in which the Coulomb coupling renormalizes the plasmon
frequencies. Additionally, we present a novel result for the damping rates of
the plasmons in this Coulomb coupled heterostructure and compare these results
as the separation between layers is varied. | 2205.00053v1 |
2022-05-08 | A regularity criterion for a 3D tropical climate model with damping | In this paper we deal with the 3D tropical climate model with damping terms
in the equation of the barotropic mode $u$ and in the equation of the first
baroclinic mode $v$ of the velocity, and we establish a regularity criterion
for this system thanks to which the local smooth solution $(u, v, \theta)$ can
actually be extended globally in time. | 2205.03841v3 |
2022-06-04 | Radiation backreaction in axion electrodynamics | Energy-momentum conservation of classical axion-electrodynamics is carefully
analyzed in the Hamiltonian formulation of the theory. The term responsible for
the energy transfer between the electromagnetic and the axion sectors is
identified. As a special application the axion-to-light Primakoff-process in
the background of a static magnetic field is worked out and the radiative
self-damping of the axion oscillations is characterized quantitatively. The
damping time turns out comparable to the age of the Universe in the preferred
axion mass range. | 2206.02052v1 |
2022-06-07 | Strong attractors for weakly damped quintic wave equation in bounded domains | In this paper, we study the longtime dynamics for the weakly damped wave
equation with quintic non-linearity in a bounded smooth domain of
$\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded
domains, we establish the existence of a strong global attractor in the phase
space $H^2(\Omega)\cap H^1_0(\Omega)\times H^1_0(\Omega)$. Moreover, the finite
fractal dimension of the attractor is also shown with the help of the
quasi-stable estimation. | 2206.03158v1 |
2022-06-07 | Long-time dynamics of the wave equation with nonlocal weak damping and sup-cubic nonlinearity in 3-D domains | In this paper, we study the long-time dynamics for the wave equation with
nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of
$\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded
domains, we first prove the global well-posedness of the Shatah-Struwe
solutions. Then we establish the existence of the global attractor for the
Shatah-Struwe solution semigroup by the method of contractive function.
Finally, we verify the existence of a polynomial attractor for this semigroup. | 2206.03163v1 |
2022-06-17 | On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers | This paper presents a stable finite element approximation for the acoustic
wave equation on second-order form, with perfectly matched layers (PML) at the
boundaries. Energy estimates are derived for varying PML damping for both the
discrete and the continuous case. Moreover, a priori error estimates are
derived for constant PML damping. Most of the analysis is performed in Laplace
space. Numerical experiments in physical space validate the theoretical
results. | 2206.08507v1 |
2022-06-20 | Harmonic Oscillators of Mathematical Biology: Many Faces of a Predator-Prey Model | We show that a number of models in virus dynamics, epidemiology and plant
biology can be presented as ``damped" versions of the Lotka-Volterra
predator-prey model, by analogy to the damped harmonic oscillator. The analogy
deepens with the use of Lyapunov functions, which allow us to characterize
their dynamics and even make some estimates. | 2206.09561v1 |
2022-06-21 | Phase-covariant mixtures of non-unital qubit maps | We analyze convex combinations of non-unital qubit maps that are
phase-covariant. In particular, we consider the behavior of maps that combine
amplitude damping, inverse amplitude damping, and pure dephasing. We show that
mixing non-unital channels can result in restoring the unitality, whereas
mixing commutative maps can lead to non-commutativity. For the convex
combinations of Markovian semigroups, we prove that classical uncertainties
cannot break quantum Markovianity. Moreover, contrary to the Pauli channel
case, the semigroup can be recovered only by mixing two other semigroups. | 2206.10742v1 |
2022-07-01 | Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings | In this paper, we investigate the stabilization of a one-dimensional Lorenz
piezoelectric (Stretching system) with partial viscous dampings. First, by
using Lorenz gauge conditions, we reformulate our system to achieve the
existence and uniqueness of the solution. Next, by using General criteria of
Arendt-Batty, we prove the strong stability in different cases. Finally, we
prove that it is sufficient to control the stretching of the center-line of the
beam in x-direction to achieve the exponential stability. Numerical results are
also presented to validate our theoretical result. | 2207.00488v1 |
2022-07-06 | Quantum Decomposition Algorithm For Master Equations of Stochastic Processes: The Damped Spin Case | We introduce a quantum decomposition algorithm (QDA) that decomposes the
problem $\frac{\partial \rho}{\partial t}=\mathcal{L}\rho=\lambda \rho$ into a
summation of eigenvalues times phase-space variables. One interesting feature
of QDA stems from its ability to simulate damped spin systems by means of pure
quantum harmonic oscillators adjusted with the eigenvalues of the original
eigenvalue problem. We test the proposed algorithm in the case of undriven
qubit with spontaneous emission and dephasing. | 2207.02755v3 |
2022-07-25 | Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport | In this paper we describe a fast algorithm for generating periodic RVEs of
polycrystalline materials. In particular, we use the damped Newton method from
semi-discrete optimal transport theory to generate 3D periodic Laguerre
tessellations (or power diagrams) with cells of given volumes. Complex,
polydisperse RVEs with up to 100,000 grains of prescribed volumes can be
created in a few minutes on a standard laptop. The damped Newton method relies
on the Hessian of the objective function, which we derive by extending recent
results in semi-discrete optimal transport theory to the periodic setting. | 2207.12036v1 |
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