Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

TL;DR

This paper derives exact results for the evolution of a one-dimensional Bose gas in a time-periodic harmonic trap, distinguishing between stable and unstable dynamical regimes, with implications for understanding quantum many-body dynamics.

Contribution

It provides the first exact large-N analysis of the stroboscopic dynamics of a 1D Bose gas under periodic harmonic confinement, classifying stability regimes.

Findings

Exact expressions for energy and density evolution in stable and unstable regimes

Identification of monodromy classes governing the system's dynamics

Large particle number limit results for quantum dynamical behavior

Abstract

We study the unitary dynamics of a one-dimensional gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency $\omega(t)$. Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.