Dynamics of Lieb-Liniger Gases

TL;DR

This paper demonstrates that the Lieb-Liniger cusp condition remains conserved during dynamic evolution under phase imprinting, and it approximates many-body dynamics using time-dependent single-particle Schrödinger solutions, with an application to gray soliton generation.

Contribution

It introduces a method to approximate the many-body dynamics of Lieb-Liniger gases via single-particle orbitals after phase imprinting, preserving the cusp condition.

Findings

Cusp condition is dynamically conserved under phase imprinting.

Many-body dynamics can be approximated by evolving single-particle orbitals.

Gray solitons can be generated in a Lieb-Liniger gas on a ring.

Abstract

It is proved that the Lieb-Liniger (LL) cusp condition implementing the delta function interaction in one-dimensional Bose gases is dynamically conserved under phase imprinting by pulses of arbitrary spatial form and the subsequent many-body dynamics in the thermodynamic limit is expressed approximately in terms of solutions of the time-dependent single-particle Schrodinger equation for a set of time-dependent orbitals evolving from an initial LL-Fermi sea. As an illustrative application, generation of gray solitons in a LL gas on a ring by a phase-imprinting pulse is studied.