High Temperature Virial Expansion to Universal Quench Dynamics

TL;DR

This paper extends the high temperature virial expansion to analyze far-from-equilibrium quench dynamics in quantum gases, successfully explaining experimental observations and revealing universal features of momentum distribution and thermalization.

Contribution

It introduces a novel theoretical framework that generalizes virial expansion to non-equilibrium dynamics, providing insights into quench processes in quantum many-body systems.

Findings

Momentum distribution decreases for low k and increases for high k during quench.

Universal momentum scale k*λ matches experimental data.

Long-time steady state generally thermalizes except at very high momenta.

Abstract

High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from non-interacting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for low-momentum part with $k<k^*$, and increases for high-momentum part with $k>k^*$, where $k^*$ is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of $k^*\lambda$ that agrees perfectly with the experiment, with $\lambda$ being the thermal de Broglie wave length. We also find a jump of the half-way relaxation time across $k^*\lambda$ and the non-monotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the long-time steady state thermalizes or not, and we find that this state does thermalize except for the very high momentum tail with $k\lambda\gg 1$. Our framework can also be applied to quench dynamics in other systems.