On Chaos in QFT

TL;DR

This paper investigates the chaotic properties of non-integrable quantum field theories by analyzing their spectral statistics and comparing them to integrable models, revealing distinct signatures consistent with random matrix theory.

Contribution

It provides a detailed spectral analysis of non-integrable QFTs using RMT tools, highlighting differences from integrable models and confirming chaos signatures.

Findings

Non-integrable QFTs exhibit GOE spectral statistics.

Integrable QFTs show Poisson spectral behavior.

Spectral properties distinguish chaotic from regular quantum systems.

Abstract

In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a truncation method. We examine the map of the corresponding energy eigenvalues to the eigenvalues of the random matrix theory (RMT) Gaussian orthogonal ensemble (GOE). This is done by computing the following properties: (a) The distribution of the adjacent spacings and their ratios (b) Higher order spacings and ratios (c) Pair correlations (d) Spectral form factors and (e) Spectral rigidity. For these properties we determine the differences between the integrable and non-integrable theories and verify that the former admits a Poisson behavior and the latter GOE (apart from the spectral rigidity).