Lieb's soliton-like excitations in harmonic trap

TL;DR

This paper investigates Lieb's soliton-like excitations in a one-dimensional Bose gas within harmonic traps, calculating their properties across different density regimes using Bethe-ansatz equations.

Contribution

It provides a detailed analysis of the effective mass and oscillation frequency of Lieb's excitations in trapped Bose gases, bridging high and low density regimes.

Findings

Oscillation frequency varies from h/\u221a2 to h with density change.

Effective mass of solitons depends on velocity near the speed of sound.

Quantitative predictions for excitation dynamics in harmonic traps.

Abstract

We study the solitonic Lieb II branch of excitations in one-dimensional Bose-gas in homogeneous and trapped geometry. Using Bethe-ansatz Lieb's equations we calculate the "effective number of atoms" and the "effective mass" of the excitation. The equations of motion of the excitation are defined by the ratio of these quantities. The frequency of oscillations of the excitation in a harmonic trap is calculated. It changes continuously from its "soliton-like" value \omega_h/\sqrt{2} in the high density mean field regime to \omega_h in the low density Tonks-Girardeau regime with \omega_h the frequency of the harmonic trapping. Particular attention is paid to the effective mass of a soliton with velocity near the speed of sound.