Related papers: Real Time Dynamics of Soliton Diffusion
When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series…
The nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by a generalized Holstein model is presented. A combination of methodologies including the reduced density matrix formalism, the multilayer…
We investigate the dynamics of an electron coupled to dispersionless optical phonons in the Holstein model, at high temperatures. The dynamics is conventionally believed to be diffusive, as the electron is repeatedly scattered by optical…
We consider a finite region of a $d$-dimensional lattice, $d\in\mathbb{N}$, of weakly coupled harmonic oscillators. The coupling is provided by a nearest-neighbour potential (harmonic or not) of size $\varepsilon$. Each oscillator weakly…
A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to…
Optical solitons-stable waves balancing delicately between nonlinearities and dispersive effects-have advanced the field of ultrafast optics and dynamics, with contributions spanning supercontinuum generation and soliton fission, to optical…
We study the fluctuations of the phonon modes in a one-dimensional chain of anharmonic oscillators where the deterministic Hamiltonian dynamics is perturbed by random exchanges of momentum between nearest neighbor particles. There are three…
We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the…
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and…
We study the mobility of a particle coupled to a one dimensional interacting fermionic system, a Luttinger liquid. We bosonize the Luttinger liquid and find the effective interaction between the particle and the bosonic system. We show that…
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc.. The stable solitons have been captured not only…
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field…
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…
We consider the dynamics of dark matter solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the…
We statistically examine long time sequences of Brownian motion for a nonequilibrium version of the Rayleigh piston model and confirm that the third cumulant of a long-time displacement for the nonequilibrium Brownian motion linearly…
We extend our studies of thermal diffusion of non-topological solitons to anharmonic FPU-type chains with additional long-range couplings. The observed superdiffusive behavior in the case of nearest neighbor interaction (NNI) turns out to…
We present a novel one-dimensional nonlinear evolution equation governing the dynamics short-wavelength longitudinal waves in a nonrelativistic fully degenerate quantum plasma using kinetic equation for the Wigner function. The linear…
Motivated by recent experiments, we model the dynamics of bright solitons formed by cold gases in quasi-1D traps. A dynamical variational ansatz captures the far-from equilibrium excitations of these solitons. Due to a separation of scales,…
The quantum dynamics of a simplest dissipative system, a particle moving in a constant external field , is exactly studied by taking into account its interaction with a bath of Ohmic spectral density. We apply the main idea and methods…
We derive the time-evolution equation that describes the Brownian motion of labeled individual tracer particles in a simple model atomic liquid (i.e., a system of $N$ particles whose motion is governed by Newton's second law, and…