Universal time-fluctuations in near-critical out-of-equilibrium quantum dynamics

TL;DR

This paper investigates how time fluctuations in quantum systems near critical points can dominate over other fluctuations, revealing universal behavior characterized by critical exponents, especially in small quench experiments.

Contribution

It demonstrates that near critical points, time fluctuations can become dominant and exhibit universal distributions determined by critical exponents, confirmed through quantum Ising model calculations.

Findings

Time fluctuations can surpass equilibrium quantum fluctuations near critical points.

The distribution of observable expectation values becomes universal and depends on critical exponents.

Away from critical points, the distribution tends to Gaussian.

Abstract

Out of equilibrium quantum systems, on top of quantum fluctuations, display complex temporal patterns. Such time fluctuations are generically exponentially small in the system volume and can be therefore safely ignored in most of the cases. However, if one consider small quench experiments, time fluctuations can be greatly enhanced. We show that time fluctuations may become stronger than other forms of equilibrium quantum fluctuations if the quench is performed close to a critical point. For sufficiently relevant operators the full distribution function of dynamically evolving observable expectation values, becomes a universal function uniquely characterized by the critical exponents and the boundary conditions. At regular points of the phase diagram and for non sufficiently relevant operators the distribution becomes Gaussian. Our predictions are confirmed by an explicit calculation on the quantum Ising model.