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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