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

DOI10.1007/JHEP03(2018)025zbMATH Open1388.81431arXiv1709.00427WikidataQ130137889 ScholiaQ130137889MaRDI QIDQ1750877

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Publication date: 23 May 2018

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Abstract: The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate $h_{mathrmKS}$ 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 $S_A$ of a Gaussian state grows linearly for large times in unstable systems, with a rate $Lambd{a}_{A}leq{h}_{KS}$ 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 $Lambd{a}_A$ appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.

Full work available at URL: https://arxiv.org/abs/1709.00427

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