Hidden thermal structure in Fock space

TL;DR

This paper reveals a hidden thermal structure in Fock space caused by exchange interactions, which helps explain how quantum statistical mechanics emerges from individual eigenstates of many-body systems.

Contribution

It analytically demonstrates the impact of exchange interactions on Fock space structure and links it to the emergence of thermal distributions in quantum systems.

Findings

Hidden thermal structure in Fock space related to exchange interactions.

New mechanisms for quantum statistical mechanics emergence in Fermi gases.

Connection between Fock space structure and mathematical limit shapes.

Abstract

The emergence of quantum statistical mechanics from individual pure states of closed many-body systems is currently under intensive investigations. While most efforts have been put on the impacts of the direct interaction (i.e., the usual mutual interaction) between particles, here we study systematically and analytically the impacts of the exchange interaction, that arises from the particle indistinguishability. We show that this interaction leads an overwhelming number of Fock states to exhibit a structure, that can be resolved only by observables adjusted according to system's dynamical properties and from which thermal distributions emerge. This hidden thermal structure in Fock space is found to be related to the so-called limit shape of random geometric objects in mathematics. The structure enables us to uncover, for both ideal and nonideal Fermi gases, new mechanisms for the emergence of quantum statistical mechanics from individual eigenstates.