Quantum Variance and Ergodicity for the baker's map

TL;DR

This paper establishes a quantum-classical correspondence for the quantised baker's map, demonstrating quantum ergodicity and decay bounds of quantum variance up to the Ehrenfest time, advancing understanding of quantum chaos.

Contribution

It proves an Egorov theorem for the quantised baker's map and derives quantum ergodicity and variance decay bounds, extending quantum chaos theory.

Findings

Quantum ergodic theorem for the baker's map

Logarithmic decay bound for quantum variance

Egorov theorem valid up to Ehrenfest time

Abstract

We prove a Egorov theorem, or quantum-classical correspondence, for the quantised baker's map, valid up to the Ehrenfest time. This yields a logarithmic upper bound for the decay of the quantum variance, and, as a corollary, a quantum ergodic theorem for this map.