Eur. Phys. J. B (2012) 85: 195
https://doi.org/10.1140/epjb/e2012-30112-5

Regular Article

Time-reversal characteristics of quantum normal diffusion: time-continuous models

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: 8 February 2012
Received in final form: 19 April 2012
Published online: 18 June 2012

Abstract

In quantum map systems exhibiting normal diffusion, time-reversal characteristics converge to a universal scaling behavior which implies a prototype of irreversible quantum process [H.S. Yamada, K.S. Ikeda, Eur. Phys. J. B 85, 41 (2012)]. In the present paper, we extend the investigation of time-reversal characteristic to time-continuous quantum systems which show normal diffusion. Typical four representative models are examined, which is either deterministic or stochastic, and either has or not has the classical counterpart. Extensive numerical examinations demonstrate that three of the four models have the time-reversal characteristics obeying the same universal limit as the quantum map systems. The only nontrivial counterexample is the critical Harper model, whose time-reversal characteristics significantly deviates from the universal curve. In the critical Harper model modulated by a weak noise that does not change the original diffusion constant, time-reversal characteristic recovers the universal behavior.