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

Abstract

Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic fields, the increase of the entropy and dynamics of the Fisher information can be directly described and related. To illustrate these results, we have considered several examples for which all the relations take the elementary form. Moreover, we show that the integrals of (geodesic) motion associated with some conformal Killing vectors lead to the Ermakov–Lewis invariants for the considered electromagnetic fields. Next, we explicitly work out the dynamics of the entanglement entropy of the oscillators coupled by a continuous time-dependent parameter as well as we analyse some aspects of quantum-classical transition (in particular decoherence). Finally, we study in some detail the behaviour of quantum quenches (in the presence of the critical points) for the case of mutually non-interacting non-relativistic fermions in a harmonic trap.