Entanglement dynamics of coupled oscillators from Gaussian states

Abstract

In this work, we explore the dynamics of entanglement of an isolated quantum system consisting of two time-dependent, coupled harmonic oscillators. Through the use of a numerical method that relies on the estimation of the system's Wigner representation by a specific Gaussian function, we investigate the time evolution of the entanglement entropy after an instant quench in the inherent parameters of the system. Besides, from the comparison of the results obtained from the analytical expression for the time-dependent von Neumann entropy with the numerically computed entropy data, the effectiveness of the numerical method is tested for a variety of angular frequency combinations. Also, we analyze how the entropy of entanglement change as a function of time.

Dynamics of entropy and information of time-dependent quantum systems: exact results

“…They can be also useful in a more general frameworks of the perturbative theory [52] (note that we can compute the explicit form of propagator for the discussed frequencies). Moreover, it would be interesting to compare the results with the numerical methods based on the so-called Gaussian state approximation (such an approach has been quite recently applied for instantaneous quenches [53]) as well as to analyse the time-dependent case of vanishing frequencies (UV divergences) in the spirit of the work [54]. Finally, note that the considerations from the last section fit perfectly into the recent studies [55] of quantum quenches of the c = 1 Matrix Model which, in turn, is related to the description of two-dimensional string theory with the time-dependent string coupling.…”