Universal Characteristics of Time-irreversibility in Quantum Normal Diffusion(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Abstract

Time-irreversibility of apparently irreversible phenomena observed in quantum systems with a very small number of degrees of freedom is studied quantitatively by a time-reversal test: the system evolved in the forward-time direction is time-reversed after applying a small perturbation at the reversal time and the separation between the time-reversed perturbed and the time-reversed unperturbed states is measured as a function of perturbation strength. If the system exhibits a normal diffusion, the time-reversal characteristics has a universal threshold of perturbation strength above which a complete loss of memory is realized. A remarkable fact is that, for almost all the model systems we examined, including discrete-time/continuous-time systems and deterministic/stochastic systems, the time reversal characteristics as well as the time-reversal dynamics itself converge asymptotically to universal behaviors independent of the details of the systems, which implies the prototype of quantum irreversibility. Only the diffusive behavior of the critical states in Harper equation deviates significantly from the universal behavior.