Coarse Grained Liouville Dynamics of piecewise linear discontinuous maps

TL;DR

This paper investigates the spectral properties of classical and quantum coarse-grained propagators for a piecewise linear discontinuous map, exploring quantum-classical correspondence and spectrum evolution as resolution increases.

Contribution

It introduces a detailed analysis of the spectrum of coarse-grained propagators for a specific discontinuous map, highlighting quantum-classical relationships and spectral evolution.

Findings

Spectrum analysis reveals differences between classical and quantum cases.

Quantum-classical correspondence varies with resolution.

Results compared to mixed systems show unique spectral features.

Abstract

We compute the spectrum of the classical and quantum mechanical coarse-grained propagators for a piecewise linear discontinuous map. We analyze the quantum - classical correspondence and the evolution of the spectrum with increasing resolution. Our results are compared to the ones obtained for a mixed system.