Black holes from chaos

TL;DR

This paper connects chaotic quantum systems to black hole geometry by analyzing operator growth and spectral properties, providing a new framework for understanding late-time Green's functions.

Contribution

It introduces a novel approach linking chaos to black hole physics through the universal operator growth hypothesis and a discrete scattering problem analogy.

Findings

Spectral density is meromorphic with no zeroes under smooth Lanczos coefficients.

Framework allows accurate late-time Green's function calculations in chaotic systems.

Provides examples illustrating the analytic properties of Green's functions.

Abstract

We study the emergence of black hole geometry from chaotic systems at finite temperature. The essential input is the universal operator growth hypothesis, which dictates the asymptotic behavior of the Lanczos coefficients. Under this assumption, we map the chaotic dynamics to a discrete analog of the scattering problem on a black hole background. We give a simple prescription for computing the Green's functions, and explore some of the resulting analytic properties. In particular, assuming that the Lanczos coefficients are sufficiently smooth, we present evidence that the spectral density is a meromorphic function of frequency with no zeroes. Our formalism provides a framework for accurately computing the late time behavior of Green's functions in chaotic systems, and we work out several instructive examples.