Quantum bounds and fluctuation-dissipation relations

TL;DR

This paper explores how quantum fluctuation-dissipation relations, specifically the KMS conditions, underpin bounds on correlation decay and chaos rates in quantum systems, linking these bounds to thermodynamic principles.

Contribution

It demonstrates that quantum bounds on chaos and correlation times are consequences of the KMS conditions, providing a new perspective on their physical origin.

Findings

Quantum bounds on chaos are derived from KMS conditions.

Fluctuation-dissipation relations influence correlation decay rates.

Bounds on correlations relate to thermodynamic properties.

Abstract

In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and derivation of quantum bounds on the transport coefficients or on the chaos rate. However, the physical meaning and the mechanism enforcing such bounds is still an open question. Here, we discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, we show that the quantum bound to chaos is a direct consequence of the KMS condition, as applied to a particular pair of two-time correlation and response functions. Encouraged by this, we describe how quantum fluctuation-dissipation relations act in general as a blurring of the time-dependence of correlations, which can imply bounds on their decay rates. Thinking in terms of fluctuation-dissipation opens a direct connection between bounds and other thermodynamic properties.