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

TL;DR

This paper investigates how the lifetime of irreversibility in quantum chaotic systems, specifically coupled kicked rotors, correlates with entanglement entropy and superposition, revealing a proportional relationship with Hilbert space dimension.

Contribution

It introduces a weakly coupled linear oscillator as a detector for irreversibility lifetime and analyzes its behavior in relation to entanglement in coupled kicked rotors.

Findings

Lifetime increases with entanglement entropy.

Fluctuations in lifetime correlate with EE fluctuations.

Lifetime scales with the square of Hilbert space dimension.

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.