Relation between irreversibility and entanglement in classically chaotic quantum kicked rotors

¹ Department of Physics, College of Science and Engineering, Ritsumeikan University - Noji-higashi 1-1-1, Kusatsu 525-8577, Japan
² Yamada Physics Research Laboratory - Aoyama 5-7-14-205, Niigata 950-2002, Japan
³ College of Science and Engineering, Ritsumeikan University - Noji-higashi 1-1-1, Kusatsu 525-8577, Japan

^(a) fumihiro-matsui@xnea.net
^(b) hyamada@uranus.dti.ne.jp
^(c) ahoo@ike-dyn.ritsumei.ac.jp

Received: 19 March 2016
Accepted: 1 July 2016

Abstract

The relation between the degree of entanglement and time scale of time-irreversible behavior is investigated for classically chaotic quantum coupled kicked rotors by comparing the entanglement entropy (EE) and the lifetime of correspondence with classical decay of correlation, which was recently introduced. Both increase on average drastically with a strong correlation when the strength of coupling between the kicked rotors exceeds a certain threshold. The EE shows an anomalously large fluctuation resembling a critical fluctuation around the threshold value of coupling strength where the entanglement sharply increases toward full entanglement. In this regime it can be shown that, although the correlation is hidden, EE and the lifetime of individual eigenfunctions also have a positive correlation that can be seen via another measure.