Many-body chaos at weak coupling

TL;DR

This paper calculates the chaos growth rate in large N quantum systems with weak coupling using a matrix Phi^4 theory, providing a numerical approach that simplifies to a classical problem.

Contribution

It introduces a numerical method to compute the chaos exponent in weakly coupled matrix theories by diagonalizing a ladder kernel.

Findings

Calculated the chaos exponent $mbda_L$ at leading order.

Reduced the problem to a classical computation.

Provided numerical results for weakly coupled systems.

Abstract

The strength of chaos in large $N$ quantum systems can be quantified using $\lambda_L$, the rate of growth of certain out-of-time-order four point functions. We calculate $\lambda_L$ to leading order in a weakly coupled matrix $\Phi^4$ theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.