Hyperbolic Flows and the Question of Quantum Chaos

TL;DR

This paper explores the quantum analogs of classical hyperbolic flows, examining their implications for understanding quantum chaos within the operator algebraic framework of quantum theory.

Contribution

It provides an updated account of quantum hyperbolic flows and discusses their relevance to the question of quantum chaos, building on previous formulations.

Findings

Quantum hyperbolic flows are characterized within operator algebraic setting.

The paper clarifies the connection between classical chaos and quantum chaos.

Implications for the understanding of quantum chaos are discussed.

Abstract

Hyperbolic flows, as formulated by Anosov, are the prototypes of chaotic evolutions in classical dynamical systems. Here we provide a concise updated account of their quantum counterparts originally formulated by Emch, Narnhofer, Thirring and Sewell within the operator algebraic setting of quantum theory: and we discuss their bearing on the question of quantum chaos.