Reflection of a Lieb-Liniger wave packet from the hard-wall potential

TL;DR

This paper develops a formalism to analyze the quantum dynamics of a Lieb-Liniger wave packet reflecting from a hard-wall potential, enabling numerical studies of interactions and momenta effects.

Contribution

It introduces a Fourier transform-based method to solve the N-particle wave function dynamics in the presence of a hard-wall potential.

Findings

Wave packet reflection depends on interaction strength and incident momentum.

The formalism accurately captures the quantum reflection process.

Numerical results illustrate the influence of system parameters.

Abstract

Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.