Recent theoretical progress on an information geometrodynamical approach to chaos

TL;DR

This paper introduces a new information-geometric framework to analyze chaos in complex systems, applying it to quantum spin chains and extending classical chaos criteria.

Contribution

It develops a novel theoretical approach using information geometry to characterize chaos, including quantum analogues of chaos criteria and energy level statistics.

Findings

Information-geometric analogue of Zurek-Paz chaos criterion

Characterization of quantum chaos and integrability via energy level statistics

Application to quantum antiferromagnetic Ising spin chains

Abstract

In this paper, we report our latest research on a novel theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, an information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth and an information-geometric characterization of chaotic (integrable) energy level statistics of a quantum antiferromagnetic Ising spin chain in a tilted (transverse) external magnetic field are presented.