How Well a Chaotic Quantum System Can Retain Memory of Its Initial State?

TL;DR

This paper investigates how quantum systems can retain memory of their initial states despite external influences, contrasting classical irreversibility with quantum memory effects, and identifies conditions for memory preservation.

Contribution

It establishes a relationship between quantum memory retention and the complexity growth of the Wigner function, introducing a critical external influence threshold.

Findings

Quantum systems can retain initial state memory longer than classical systems.

A critical external influence strength exists below which quantum memory persists.

Memory retention is linked to the linear growth rate of Wigner function complexity.

Abstract

In classical mechanics the local exponential instability effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. We relate the latter fact to the low (at most linear) rate with which the system's Wigner function gets during evolution more and more complicated structure and establish existence of a critical strength of external influence below which such a memory still survives.