Breakdown of quantum-classical correspondence and dynamical generation of entanglement

• URL: http://arxiv.org/abs/2104.06605v1
• Date: Wed, 14 Apr 2021 03:09:24 GMT
• Title: Breakdown of quantum-classical correspondence and dynamical generation of entanglement
• Authors: Chushun Tian and Kun Yang
• Abstract summary: We study the generation of quantum entanglement induced by an ideal Fermi gas confined in a chaotic cavity. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure.
• Score: 6.167267225728292
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The {\it exchange} interaction arising from the particle indistinguishability is of central importance to physics of many-particle quantum systems. Here we study analytically the dynamical generation of quantum entanglement induced by this interaction in an isolated system, namely, an ideal Fermi gas confined in a chaotic cavity, which evolves unitarily from a non-Gaussian pure state. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure. Furthermore, for a class of initial states, such change leads to the approach to thermal equilibrium everywhere in the cavity, with the well-known Ehrenfest time in quantum chaos as the thermalization time. Specifically, the quantum expectation values of various correlation functions at different spatial scales are all determined by the Fermi-Dirac distribution. In addition, by using the reduced density matrix (RDM) and the entanglement entropy (EE) as local probes, we find that the gas inside a subsystem is at equilibrium with that outside, and its thermal entropy is the EE, even though the whole system is in a pure state. As a by-product of this work, we provide an analytical solution supporting an important conjecture on thermalization, made and numerically studied by Garrison and Grover in: Phys. Rev. X \textbf{8}, 021026 (2018), and strengthen its statement.

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