Quench dynamics of the interacting Bose gas in one dimension

TL;DR

This paper derives an exact solution for the time evolution of an interacting 1D Bose gas after a quench, revealing universal long-term behaviors depending on the interaction type, with implications for understanding quantum dynamics.

Contribution

It provides an exact analytical expression for the dynamics of the 1D Bose gas post-quench using the Yudson representation, highlighting universal asymptotic behaviors.

Findings

Repulsive interactions lead to a strongly repulsive gas asymptote.

Attractive interactions result in dominance by the maximal bound state.

The long-time behavior is independent of initial conditions.

Abstract

We obtain an exact expression for the time evolution of the interacting Bose gas following a quench from a generic initial state using the Yudson representation for integrable systems. We study the time evolution of the density and noise correlation for a small number of bosons and their asymptotic behavior for any number. We show that for any value of the coupling, as long as it is repulsive, the system asymptotes towards a strongly repulsive gas, while for any value of an attractive coupling the long time behavior is dominated by the maximal bound state. This occurs independently of the initial state and can be viewed as an emerging "dynamic universality".