Kink propagation through disordered media

Abstract

Using a collective-coordinate approach, we study kink propagation along nonlinear systems with local, randomly distributed inhomogeneities. We develop a general method to compute dynamical variable statistics which can be generalized to a number of soli ton-bearing systems, and we apply it to the sine-Gordon equation as an example. PACS number(s): 03.40. Kf, 42.25.Bs, 71.55.Jv

Localization of solitons: linear response of the mean-field ground state to weak external potentials

“…While soliton deformation in external potentials is certainly not a new topic and has been considered in a rather large number of different contexts (see e.g. [8] and references therein), to our knowledge this useful expression of the linearresponse kernel is new. This solution determines also the compressibility introduced in Sec.…”

“…But what about the emission of radiation due to scattering by impurities, as discussed at length by Gredeskul and Kivshar [8] and others? It is important to realize that we specifically focus on smooth, spatially correlated potentials that are expected to provoke considerably less excitation than isolated, δ-like impurities.…”

“…Mathematically rigorous theorems assure that in 1D, the logarithmically averaged eigenfunctions decay for large distances q from their origin like [6,8] lim…”

“…A well-known paradigm of genuine quantum dynamics is disorder-induced Anderson localization [6,7], which has been studied for solitons in different settings some time ago [8], and also been observed rather recently with ultracold, noninteracting matter waves [9,10,11,12] (see also [13]). Motivated by these experimental advances, we have investigated the quantum dynamics of matter-wave solitons in spatially correlated disorder potentials [1].…”

Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations

“…The propagation of solitons in disordered media has been studied intensively in recent years [26,31].…”