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- W3106225844 abstract "The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate $h_{mathrm{KS}}$ 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 $Lambda_A leq h_{KS}$ 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 $Lambda_A$ appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state." @default.
- W3106225844 created "2020-11-23" @default.
- W3106225844 creator A5001856526 @default.
- W3106225844 creator A5044784923 @default.
- W3106225844 creator A5077663153 @default.
- W3106225844 date "2018-03-01" @default.
- W3106225844 modified "2023-10-16" @default.
- W3106225844 title "Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate" @default.
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