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Hidden thermal structure in Fock space

Chushun Tian, Kun Yang, Ping Fang, Hai-Jun Zhou, and Jiao Wang
Phys. Rev. E 98, 060103(R) – Published 18 December 2018
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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.

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  • Received 2 August 2018

DOI:https://doi.org/10.1103/PhysRevE.98.060103

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Chushun Tian1,*, Kun Yang2,†, Ping Fang3,1, Hai-Jun Zhou1, and Jiao Wang4

  • 1CAS Key Laboratory of Theoretical Physics and Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
  • 3Institute for Advanced Study, Tsinghua University, Beijing 100084, China
  • 4Department of Physics, Key Laboratory of Low Dimensional Condensed Matter Physics (Department of Education of Fujian Province), and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China

  • *ct@itp.ac.cn
  • kunyang@magnet.fsu.edu

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Issue

Vol. 98, Iss. 6 — December 2018

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