Related papers: Real Time Dynamics of Soliton Diffusion
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
We analyze theoretically the dynamics of a single colloidal particle in an externally applied electric field. The thermal motions of microions lead to an anisotropic, nonequilibrium source of noise, pro- portional to the field, in the…
This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…
We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional…
Charge transfer in homogeneous nucleotide chains is modeled on the basis of Holstein Hamiltonian. The path length of Davydov solitons in these chains is being studied. It is shown that in a dispersionless case, when the soliton velocity V…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…
Transport of charge carriers in mechanically soft semiconductors is mainly limited by their interaction with slow intermolecular phonons. Carrier motion exhibits a crossover from superdiffusive to subdiffusive, producing a distinct…
We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles are described by a Langevin equation with Rayleigh-Helmholtz…
We present a unified and nonperturbative method for calculating spectral and transport properties of Hamiltonians with simultaneous Holstein (diagonal) and Peierls (off-diagonal) electron-phonon coupling. Our approach is motivated by the…
Solitons - localized wave packets that travel without spreading - play a central role in understanding transport and properties of nonlinear systems, from optical fibers to fluid dynamics. In quantum many-body systems, however, such robust…
We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially-correlated stochastic force. A strong dissipation regime is…
A new approach to Brownian motion of atomic clusters on solid surfaces is developed. The main topic discussed is the dependence of the diffusion coefficient on the fit between the surface static potential and the internal cluster…
We explore intrinsic thermal noise in soliton microcombs, revealing thermodynamic correlations induced by nonlinearity and group-velocity dispersion. A suitable dispersion design gives rise to control over thermal-noise transduction from…
Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental…
The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the…
The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the…
We demonstrate the fundamental links existing between two different descriptions of quantum electrodynamics in inhomogeneous, lossy and dispersive dielectric media which are based either on the Huttner-Barnett formalism for polaritons [B.…
We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…
The dynamics of chaotic Hamiltonian systems such as the kicked rotor continues to guide our understanding of transport and localization processes. The localized states of the quantum kicked rotor decay due to decoherence effects if…