Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
Abstract
The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate h 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 Λ A ≤ 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 Λ A appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- March 2018
- DOI:
- 10.1007/JHEP03(2018)025
- arXiv:
- arXiv:1709.00427
- Bibcode:
- 2018JHEP...03..025B
- Keywords:
-
- Field Theories in Lower Dimensions;
- Lattice Quantum Field Theory;
- Quantum Dissipative Systems;
- High Energy Physics - Theory;
- Condensed Matter - Statistical Mechanics;
- General Relativity and Quantum Cosmology;
- Quantum Physics
- E-Print:
- 50+17 Pages, 11 figures