Lieb-Liniger gas in a constant force potential

TL;DR

This paper derives exact solutions for the Lieb-Liniger gas in a linear potential using Fermi-Bose mapping, analyzing ground state properties and quantum dynamics in a wedge-like trap.

Contribution

It introduces Lieb-Liniger-Airy wave functions and applies Fermi-Bose mapping to study the gas in a linear potential, extending previous models to include constant force effects.

Findings

Exact stationary solutions for Lieb-Liniger in linear potential

Ground state properties in strongly interacting regime

Quantum dynamics via N-dimensional Fourier transform

Abstract

We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions). The ground state properties of the gas in the wedge-like trapping potential are calculated in the strongly interacting regime by using Girardeau's Fermi-Bose mapping and the pseudopotential approach in the $1/c$-approximation ($c$ denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an $N$-dimensional Fourier transform as in the case of free expansion.