Stationary state after a quench to the Lieb-Liniger from rotating BECs

TL;DR

This paper investigates the long-time stationary states of a bosonic system on a ring after a sudden interaction quench, focusing on initial states of rotating and counter-propagating BECs, with analytical and numerical results on their rapidity distributions.

Contribution

It provides analytical solutions for the stationary state rapidity distribution after a quench from a rotating BEC and numerical results for counter-propagating BECs, highlighting differences based on quench size.

Findings

Analytical rapidity distribution for rotating BEC initial state.

Numerical rapidity distribution for counter-propagating BECs.

Differences in stationary states for large versus small quenches.

Abstract

We study long-time dynamics of a bosonic system after suddenly switching on repulsive delta-like interactions. As initial states, we consider two experimentally relevant configurations: a rotating BEC and two counter-propagating BECs with opposite momentum, both on a ring. In the first case, the rapidity distribution function for the stationary state is derived analytically and it is given by the distribution obtained for the same quench starting from a BEC, shifted by the momentum of each boson. In the second case, the rapidity distribution function is obtained numerically for generic values of repulsive interaction and initial momentum. The significant differences for the case of large versus small quenches are discussed.