Fluctuations in the Fourier coefficient of the current in periodically driven systems

Oren Raz (Weizmann Institute, Rehovot)

Sep 27. 2022, 11:45 — 12:30

Probability current fluctuations play an important role in nonequilibrium statistical mechanics. Most of the studies on current fluctuations were devoted to the fluctuations of the time-averaged probability current, the zero-frequency Fourier component of the time-dependent current. However, in many practical applications the fluctuations at other frequencies are of equal importance. We study the statistics of all the probability current’s Fourier component in periodically driven stochastic systems. First, I will discuss possible methods to calculate the current statistics, valid even when the current’s Fourier frequency is incommensurate with the driving frequency, breaking the time periodicity of the system. Somewhat surprisingly, we find that the cumulant generating function (CGF), that encodes all the statistics of the current, is composed of a continuous background at any frequency accompanied by either positive or negative discontinuities at current’s frequencies commensurate with the driving frequency. We show that cumulants of increasing orders display discontinuities at an increasing number of locations but with decreasing amplitudes that depend on the rational frequency ratio.

Further Information
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Large Deviations, Extremes and Anomalous Transport in Non-equilibrium Systems (Thematic Programme)
Christoph Dellago (U Vienna)
Satya Majumdar (U Paris Sud, Orsay)
David Mukamel (Weizmann Institute, Rehovot)
Harald Posch (U Vienna)
Gregory Schehr (U Paris Sud, Orsay)