Quantum chaos in a weakly-coupled field theory with nonlocality

TL;DR

This paper investigates quantum chaos in weakly-coupled non-commutative field theories by calculating the Lyapunov exponent, revealing it remains comparable to the commutative case, with potential explanations involving infrared sensitivity and non-local effects.

Contribution

It provides the first calculation of the Lyapunov exponent in non-commutative field theories at large Moyal scale, highlighting the effects of non-locality on chaos.

Findings

Lyapunov exponent is similar to the commutative case in the large Moyal-scale limit.

Infrared sensitivity may influence the Lyapunov exponent.

Non-local contributions to thermodynamic quantities are sub-dominant.

Abstract

In order to study the chaotic behavior of a system with non-local interactions, we will consider weakly coupled non-commutative field theories. We compute the Lyapunov exponent of this exponential growth in the large Moyal-scale limit to leading order in the t'Hooft coupling and $1/N$. We found that in this limit, the Lyapunov exponent remains comparable in magnitude to (and somewhat smaller than) the exponent in the commutative case. This can possibly be explained by the infrared sensitivity of the Lyapunov exponent. Another possible explanation is that in examples of weakly coupled non-commutative field theories, non-local contributions to various thermodynamic quantities are sub-dominant.