Quantum Unique Ergodicity for maps on the torus

TL;DR

This paper demonstrates quantum unique ergodicity for the perturbed Kronecker map on the torus and provides an upper bound on the convergence rate, advancing understanding of quantum-classical correspondence.

Contribution

It offers the first examples of quantum unique ergodicity for perturbed Kronecker maps and quantifies the convergence rate.

Findings

Quantum unique ergodicity established for perturbed Kronecker maps

Derived an upper bound for the rate of quantum ergodicity convergence

Supports the conjecture linking classical ergodicity to quantum behavior

Abstract

When a map is classically uniquely ergodic, it is expected that its quantization will posses quantum unique ergodicity. In this paper we give examples of Quantum Unique Ergodicity for the perturbed Kronecker map, and an upper bound for the rate of convergence.