Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
arXiv:1709.00427 · doi:10.1007/JHEP03(2018)025
Abstract
The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate 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 of a Gaussian state grows linearly for large times in unstable systems, with a rate determined by the Lyapunov exponents and the choice of the subsystem . 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 appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.
50+17 Pages, 11 figures
References in corpus (17)
- Thermalization and its mechanism for generic isolated quantum systems
- Reheating in Inflationary Cosmology: Theory and Applications
- Nonperturbative Dynamics Of Reheating After Inflation: A Review
- Circuit complexity in quantum field theory
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Thermalization of Strongly Coupled Field Theories
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Characterizing dynamics with covariant Lyapunov vectors
- An acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate
- Remarks on the entanglement entropy for disconnected regions
- "Cosmological" quasiparticle production in harmonically trapped superfluid gases
- Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
- Entanglement in a periodic quench
- Chaotic behavior in classical Yang-Mills dynamics
- Quantum entanglement due to modulated Dynamical Casimir Effect
- The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection ?
- Entropy of a subalgebra of observables and the geometric entanglement entropy
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- Linear and logarithmic entanglement production in an interacting chaotic system
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- Perturbative expansion of entanglement negativity using patterned matrix calculus
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- Measurement-induced phase transition in free bosons
- Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
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- Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
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- From orthosymplectic structure to super topological matter
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- Quantum trajectories for the variational description of closed systems: a case study with Gaussian states
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- Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum
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- Semiclassical Backreaction: A Qualitative Assessment
- Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
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- Interscale entanglement production in a quantum system simulating classical chaos
- Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States
- Entanglement entropy dynamics of non-Gaussian states in free boson systems: Random sampling approach
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