Lifetime of the arrow of time inherent in chaotic eigenstates: case of coupled kicked rotors

Abstract

A linear oscillator very weakly coupled with the object quantum system is proposed as a detector measuring the lifetime of irreversibility exhibited by the system, and classically chaotic coupled kicked rotors are examined as ideal examples. The lifetime increases drastically in close correlation with the enhancement of entanglement entropy(EE) between the kicked rotors. In the transition regime to the full entanglement, the EE of individual eigenstates fluctuates anomalously, and the lifetime also fluctuates in correlation with the EE. In the fully entangled regime the fluctuation disappear, but the lifetime is not yet unique but increases in proportion to the number of superposed eigenstates and is proportional to the square of Hilbert space dimension in the full superposition.

Slow heating in a quantum coupled kicked rotors system

“…As stated above, even a partly chaotic phase space is enough to have Arnold diffusion, and this fact translates in a diffusive long-term dynamics, possibly after a transient [36,5,37,38,7]. In the quantum case the behavior is different and dynamical localization can persist for a finite number of rotors [39,40,41,42,43]. Nevertheless, it disappears in the thermodynamic limit, when the number of rotors tends to infinity [39] (although it can persist in the thermodynamic limit in other systems [44,45]).…”

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

“…Specifically, we study the dynamics of many quantum kicked rotors non-linearly coupled through the kicking. Until now only the case of two rotors [80][81][82][83][84][85] and the interacting linear case [140] has been considered in literature and a clear picture of the effect of quantum mechanics on the dynamics of the general nonlinear case is missing. Our goal is to to consider the case of a generic number N of coupled rotors, considering also the thermodynamic limit N → ∞.…”