Time-reversal Characteristics of Quantum Normal Diffusion

TL;DR

This study investigates how quantum systems with normal diffusion behave under time-reversal, revealing universal scaling laws and fundamental units of perturbation that deepen understanding of quantum irreversibility.

Contribution

It introduces the concept of the time-reversal characteristic and demonstrates universal scaling behavior across various quantum diffusive systems.

Findings

Existence of a fundamental quantum unit of perturbation.

Universal scaling behavior in time-reversal dynamics.

Insights into the nature of quantum irreversibility.

Abstract

This paper concerns with the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties are quantified by the time-reversal test; the system evolved in the forward direction for a certain period is time-reversed for the same period after applying a small perturbation at the reversal time, and the separation between the time-reversed perturbed and unperturbed states is measured as a function of perturbation strength, which characterizes sensitivity of the time reversed system to the perturbation and is called the time-reversal characteristic. Time-reversal characteristics are investigated for various quantum systems, namely, classically chaotic quantum systems and disordered systems including various stochastic diffusion systems. When the system is normally diffusive, there exists a fundamental quantum unit of perturbation, and all the models exhibit a universal scaling behavior in the time-reversal dynamics as well as in the time-reversal characteristics, which leads us to a basic understanding on the nature of quantum irreversibility.