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Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

Journal of High Energy Physics volume 2018, Article number: 25 (2018) Cite this article

A preprint version of the article is available at arXiv.

Abstract

The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate hKS given by the sum of all positive Lyapunov exponents of the system. We prove a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonian. The derivation takes into account the case of time-dependent Hamiltonians with Floquet instabilities. We show that the entanglement entropy SA of a Gaussian state grows linearly for large times in unstable systems, with a rate ΛA ≤ hKS determined by the Lyapunov exponents and the choice of the subsystem A. We apply our results to the analysis of entanglement production in unstable quadratic potentials and due to periodic quantum quenches in many-body quantum systems. Our results are relevant for quantum field theory, for which we present three applications: a scalar field in a symmetry-breaking potential, parametric resonance during post-inflationary reheating and cosmological perturbations during inflation. Finally, we conjecture that the same rate ΛA appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.

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  1. Institute for Gravitation and the Cosmos & Department of Physics, The Pennsylvania State University, Davey Laboratory, University Park, Pennsylvania, U.S.A.

    Eugenio Bianchi, Lucas Hackl & Nelson Yokomizo

  2. Departamento de Física — ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, Minas Gerais, Brazil

    Nelson Yokomizo

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  1. Eugenio Bianchi
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Bianchi, E., Hackl, L. & Yokomizo, N. Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate. J. High Energ. Phys. 2018, 25 (2018). https://doi.org/10.1007/JHEP03(2018)025

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  • DOI: https://doi.org/10.1007/JHEP03(2018)025

Keywords

  • Field Theories in Lower Dimensions
  • Lattice Quantum Field Theory
  • Quantum Dissipative Systems