Emergence of correlations in the process of thermalization of interacting bosons

TL;DR

This paper investigates how correlations develop during thermalization in a finite system of interacting bosons, revealing quadratic and algebraic growth patterns in correlations and OTOC, contrasting with exponential predictions.

Contribution

It provides analytical and numerical evidence that correlations and OTOC grow algebraically or quadratically, challenging the common exponential growth assumptions in thermalization studies.

Findings

Correlations between occupation numbers increase quadratically before saturation.

Out-of-time-order correlator (OTOC) increases algebraically, not exponentially.

Results are experimentally testable and relevant to black hole scrambling.

Abstract

We address the question of the relevance of thermalization to the increase of correlations in the quench dynamics of an isolated system with a finite number of interacting bosons. Specifically, we study how, in the process of thermalization, the correlations between occupation numbers increase in time resulting in the emergence of the Bose-Einstein distribution. We show, both analytically and numerically, that before saturation the two-point correlation function increases quadratically in time. This time dependence is at variance with the exponential increase of the number of principal components of the wave function, recently discovered and explained in Ref.\cite{BIS18}. We also demonstrate that the out-of-time-order correlator (OTOC) increases algebraically in time but not exponentially as predicted in many publications. Our results, that can be confirmed experimentally in traps with interacting bosons, may be also relevant to the problem of black hole scrambling.