A $\frac 13$ power-law universality class out of stochastic driving in interacting systems

TL;DR

This paper uncovers a universal algebraic decay in the dynamics of many-body systems with stochastic interactions, characterized by an exponent of 1/3, independent of system specifics and driven by a self-consistent diffusive process.

Contribution

It introduces a new universality class of dynamical decay with a fixed exponent arising from stochastic driving in interacting systems.

Findings

Order parameter decays as t^{-1/3} universally

Decay exponent is independent of system details

Relevance to experiments in cavity QED systems

Abstract

In this paper, we study the mean-field dynamics of a general class of many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter $m(t)\sim t^{-\chi}$ with an exponent $\chi=\frac 13$ that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion coefficient which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.