Semiclassical analysis and sensitivity to initial conditions

TL;DR

This paper explores the transition from quantum to classical mechanics in hyperbolic dynamical systems, highlighting the role of invariant manifolds and comparing quantum non-determinism with classical chaos over time.

Contribution

It provides new insights into the quantum-classical transition by analyzing the influence of invariant manifolds in hyperbolic systems and their impact on long-term evolution.

Findings

Quantum non-determinism and classical chaos show overlapping behaviors over time.

Invariant manifolds play a crucial role in the quantum-classical transition.

Long-term evolution reveals similarities between quantum and classical sensitivities.

Abstract

We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be emphasized, and the long time evolution will show how the quantum non-determinism and the classical chaotic sensitivity to initial conditions can be compared, and in a certain sense overlap.