Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes

TL;DR

This paper investigates how heavy-tailed stochastic processes influence quantum systems, revealing diverse anomalous transport behaviors and ergodicity breaking in non-equilibrium quantum dynamics.

Contribution

It introduces a model of quantum transport driven by heavy-tailed waiting times, demonstrating the emergence of various anomalous diffusion regimes and ergodicity breakdown.

Findings

Identification of superdiffusive, subdiffusive, and diffusive regimes

Anomalous transport phenomena depend on heavy-tailed waiting times

Ergodicity is broken in all observed transport behaviors

Abstract

In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two hopping processes satisfy a heavy-tailed distribution. By calculating the squared width of the wavepackets, our findings demonstrate the emergence of various anomalous transport phenomena when the system remains unchanged within the heavy-tailed regime, including superdiffusive, subdiffusive, and standard diffusive motion. Only subdiffusion occurs when the system has evolved during the waiting process. All these transport behaviors are accompanied by a breakdown of ergodicity, highlighting the complex dynamics induced by the stochastic driving mechanism.