Eur. Phys. J. B (2012) 85: 41
https://doi.org/10.1140/epjb/e2011-20811-8

Regular Article

Time-reversal characteristics of quantum normal diffusion

¹ Yamada Physics Research Laboratory, Aoyama 5-7-14-205, 950-2002 Niigata, Japan
² Department of Physics, Ritsumeikan University Noji-higashi 1-1-1, 525 Kusatsu, Japan

^a e-mail: hyamada@uranus.dti.ne.jp

Received: 4 October 2011
Received in final form: 29 November 2011
Published online: 23 January 2012

Abstract

This paper concerns 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 system. 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 of the nature of quantum irreversibility.