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

TL;DR

This paper investigates how bright matter-wave solitons respond to weak external potentials, reviewing their localization in disordered media and analyzing their linear response to various external influences.

Contribution

It provides a detailed calculation of the linear response of mean-field solitons to arbitrary weak external potentials, extending understanding beyond previous perturbative approaches.

Findings

Solitons can undergo Anderson localization in disordered potentials.

The linear response framework applies to arbitrary weak external potentials.

The study offers insights into soliton behavior in lattice and disordered environments.

Abstract

Two aspects of bright matter-wave solitons in weak external potentials are discussed. First, we briefly review recent results on the Anderson localization of an entire soliton in disordered potentials [Sacha et al. PRL 103, 210402 (2009)], as a paradigmatic showcase of genuine quantum dynamics beyond simple perturbation theory. Second, we calculate the linear response of the mean-field soliton shape to a weak, but otherwise arbitrary external potential, with a detailed application to lattice potentials.