Towards the Web of Quantum Chaos Diagnostics

TL;DR

This paper explores the fundamental relationships between key quantum chaos diagnostics—OTOC, LE, and complexity—extending existing connections to infinite dimensions and proposing new applications and models to deepen understanding.

Contribution

It generalizes the links between OTOC and LE for infinite-dimensional systems, extends these to higher-order quantities, and introduces a relationship between circuit complexity and LE.

Findings

Extended the OTOC-LE connection to infinite dimensions

Proposed higher-order OTOC and LE relationships

Linked circuit complexity with LE using the inverted oscillator model

Abstract

We study the connections between three quantities that can be used as diagnostics for quantum chaos, i.e., the out-of-time-order correlator (OTOC), Loschmidt echo (LE), and complexity. We generalize the connection between OTOC and LE for infinite dimensions and extend it for higher-order OTOCs and multi-fold LEs. Novel applications of this intrinsic relation are proposed. We also propose a relationship between a specific circuit complexity and LE by using the inverted oscillator model. These relationships signal a deeper connection between these three probes of quantum chaos.