Hidden thermal structure in Fock space
arXiv:1808.00784 · doi:10.1103/PhysRevE.98.060103
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.
arXiv comment6 pages, 3 figures
References in corpus (18)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Canonical Typicality
- Eigenstate Thermalization Hypothesis
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
- Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
- Random free fermions: An analytical example of eigenstate thermalization
- Chaos and Thermalization in a Dynamical Model of Two Interacting Particles
- Eigenstate Gibbs Ensemble in Integrable Quantum Systems
- Temperature of a single chaotic eigenstate
Cited by in corpus (5)
- Generalized Wigner-von Neumann entropy and its typicality
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- Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems
- Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
- Breakdown of quantum-classical correspondence and dynamical generation of entanglement