Entanglement entropy production in the Dynamical Casimir Effect.

Abstract

In this work, we investigate the production of entanglement entropy in the dynamical Casimir effect at parametric resonance. Symplectic techniques for the description of the time evolution of Gaussian states in bosonic systems allow us to relate the asymptotic production of entanglement entropy to the classical Lyapunov exponents. We consider the case where one boundary is static, and the other is oscillating sinusoidally. We find trough numerical computations that in 1+1 dimensions the Lyapunov exponents are zero and the entropy production is sublinear. In the 2+1 dimensions case, the Lyapunov exponents are nonzero, leading to a linear production of entropy.