Behavior of correlation functions in the dynamics of the Multiparticle Quantum Arnol'd Cat

TL;DR

This paper investigates the dynamics of the multi-particle quantum Arnol'd cat system by analyzing correlation functions to understand quantum-classical correspondence and decoherence effects.

Contribution

It introduces a study of correlation functions in the quantum Arnol'd cat, extending previous work to include autocorrelation and out-of-time correlators for this system.

Findings

Correlation functions reveal quantum-classical correspondence behavior.

Decoherence effects influence the decay of correlation functions.

Out-of-time correlators provide insights into quantum chaos.

Abstract

The multi-particle Arnol'd cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renown map that bears its name. It is obtained following the Joos-Zeh prescription for decoherence, by adding a number of scattering particles in the configuration space of the cat. Quantization follows swiftly, if the Hamiltonian approach, rather than the semiclassical, is adopted. I have studied this system in a series of previous works, focusing on the problem of quantum-classical correspondence. In this paper I test the dynamics of this system by two related yet different indicators: the time autocorrelation function of the canonical position and the out of time correlator of position and momentum.