A $\frac{1}{3}$ power-law universality class out of stochastic driving in interacting 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 $\chi =\frac{1}{3}$ 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.

6 pages,accepted by Phys. Rev. Letts

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• Universal Quench Dynamics of an Open Quantum System
• Diagnosing quantum transport from wave function snapshots
• Relaxation dynamics in the alternating XY chain following a quantum quench
• Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes