Universal long-time behavior of stochastically driven interacting quantum systems

TL;DR

This paper explores the universal long-time relaxation behavior of interacting quantum systems under stochastic driving, revealing rich dynamical universality classes despite eventual heating to infinite temperature.

Contribution

It systematically characterizes the dynamical universality classes in stochastically driven quantum systems, including effects of different perturbations and unbounded Hilbert spaces.

Findings

Universal power-law relaxation near classical critical points.

Rich dynamical behavior influenced by stochastic forces and quantum effects.

Heating dynamics studied in systems with unbounded local Hilbert spaces.

Abstract

One of the most important concepts in non-equilibrium physics is relaxation. In the vicinity of a classical critical point, the relaxation time can diverge and result in a universal power-law for the relaxation dynamics; the emerging classification of the dynamic universality class has been elucidated by Hohenberg and Halperin. In this paper, we systematically study the long-time relaxation dynamics in stochastically driven interacting quantum systems. We find that even though the stochastic forces will inevitably drive the systems into a featureless infinite temperature state, the way to approach the steady state can be highly nontrivial and exhibit rich universal dynamical behavior determined by the interplay between the stochastic driving and quantum many-body effects. We investigate the dynamical universality class by including different types of perturbations. The heating dynamics of a Hamiltonian with locally unbounded Hilbert space is also studied.