Exact anomalous current fluctuations in a deterministic interacting model

TL;DR

This paper analytically investigates charge current fluctuations in a deterministic interacting particle model, revealing non-Gaussian behavior and singular cumulants, which suggest new universality classes in many-body dynamics.

Contribution

It provides an exact analytical computation of full counting statistics in a classical automaton, uncovering unconventional fluctuation properties and critical phenomena.

Findings

Charge distribution is non-Gaussian at typical fluctuation timescales.

Higher cumulants grow indefinitely with different exponents.

The scaled cumulant generating function fails to represent scaled cumulants faithfully.

Abstract

We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium state, we employ asymptotic analysis to infer the structure of charge current fluctuations for a continuous range of timescales. The solution exhibits several unorthodox features. Most prominently, on the timescale of typical fluctuations the probability distribution of the integrated charge current in a stationary ensemble without bias is distinctly non-Gaussian despite diffusive behavior of dynamical charge susceptibility. While inducing a charge imbalance is enough to recover Gaussian fluctuations, we find that higher cumulants grow indefinitely in time with different exponents, implying singular scaled cumulants. We associate this phenomenon with the lack of a regularity condition on moment generating functions and the onset of a dynamical critical point. In effect, the scaled cumulant generating function does not, irrespectively of charge bias, represent a faithful generating function of the scaled cumulants, yet the associated Legendre dual yields the correct large-deviation rate function. Our findings hint at novel types of dynamical universality classes in deterministic many-body systems.