Scaling laws in the quantum to classical transition in chaotic systems

TL;DR

This paper investigates how quantum chaos systems transition to classical behavior under environmental noise, revealing different scaling laws depending on the measurement method and highlighting limitations of the Renyi entropy in detecting quantum coherences.

Contribution

It compares two different scaling laws for quantum-classical transition and discusses their implications, also highlighting the limitations of Renyi entropy in detecting certain quantum coherences.

Findings

Renyi entropy transition scales with 7_{ m eff}^2/D

Different scaling laws apply depending on the measurement method

Renyi entropy cannot detect all quantum coherences

Abstract

We study the quantum to classical transition in a chaotic system surrounded by a diffusive environment. The emergence of classicality is monitored by the Renyi entropy, a measure of the entanglement of a system with its environment. We show that the Renyi entropy has a transition from quantum to classical behavior that scales with $\hbar^2_{\rm eff}/D$, where $\hbar_{\rm eff}$ is the effective Planck constant and $D$ is the strength of the noise. However, it was recently shown that a different scaling law controls the quantum to classical transition when it is measured comparing the corresponding phase space distributions. We discuss here the meaning of both scalings in the precise definition of a frontier between the classical and quantum behavior. We also show that there are quantum coherences that the Renyi entropy is unable to detect which questions its use in the studies of decoherence.