Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes
arXiv:2407.19489 · doi:10.1103/PhysRevB.111.014306
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.
10 pages, 9 figures
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