Abstract
The emergence of quantum statistical mechanics from individual pure states of closed many-body systems is under intensive investigation. While most effort has been put on the impact of the direct interaction (i.e., the usual mutual interaction), here we study systematically and analytically the impact 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 the 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, a striking mechanism for the emergence of quantum statistical mechanics from individual eigenstates.
- Received 2 August 2018
DOI:https://doi.org/10.1103/PhysRevE.98.060103
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