Dynamic virial theorem at nonequilibrium and applications

TL;DR

This paper introduces the dynamic virial theorem as a universal relation governing nonequilibrium dynamics in many-body quantum systems, linking quantum correlations, energy growth, and thermodynamics, with experimental relevance to ultracold atoms.

Contribution

It presents the dynamic virial theorem as a new fundamental relation applicable to nonequilibrium quantum dynamics, connecting Tan's contact to observable phenomena and thermodynamic properties.

Findings

Dynamic virial theorem universally characterizes nonequilibrium quantum dynamics.

Quantum correlations are governed by Tan's contact during evolution.

Provides experimentally testable relations for ultracold atom experiments.

Abstract

We show that a variety of nonequilibrium dynamics of interacting many-body systems are universally characterized by an elegant relation, which we call the dynamic virial theorem. The out-of-equilibrium dynamics of quantum correlations is entirely governed by Tan\textquoteright s contact. It gives rise to a series of observable consequences and is closely related to experiments with ultracold atoms. Especially, we show that the dynamic virial theorem provides an experimentally accessible verification of maximum energy growth theorem [Qi et al., Phys. Rev. Lett. 126, 240401 (2021)], which is encoded in the evolution of the atomic cloud size during expansion. In addition, the dynamic virial theorem leads to a simple thermodynamic relation of strongly interacting quantum gases in the framework of two-fluid hydrodynamic theory, which holds in a wide range of temperature. This thermodynamic relation is a kind of the out-of-equilibrium analog of Tan's pressure relation at equilibrium. Our results provide fundamental understanding of generic behaviors of interacting many-body systems at nonequilibrium, and are readily examined in experiments with ultracold atoms.