Entanglement entropy converges to classical entropy around periodic orbits

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the osc...

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Bibliographic Details
Published in:Annals of physics 2016-01, Vol.366 (C)
Main Authors: Asplund, Curtis T., Berenstein, David
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
Coarse graining
Entanglement entropy
Entropy production
Hilbert space factorization
Kolmogorov–Sinai entropy
Lyapunov exponent
Online Access:Get full text
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Summary:We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate the dependence of the entanglement entropy on the choice of coarse graining. Here, we find that for almost all choices the asymptotic growth rate is the same.
ISSN:0003-4916
1096-035X