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

TL;DR

This paper investigates the dynamics of entropy, information, and entanglement in time-dependent quantum systems, providing exact results and exploring phenomena like quantum quenches, decoherence, and invariants in various quantum models.

Contribution

It offers new exact analytical relations for entropy and Fisher information dynamics in time-dependent quantum systems, including harmonic oscillators and fermions, and links invariants to conformal symmetries.

Findings

Entropy and Fisher information dynamics are explicitly related in time-dependent harmonic oscillators.

Quantum quenches near critical points exhibit characteristic entanglement behavior.

Conformal Killing vectors lead to Ermakov-Lewis invariants in electromagnetic field models.

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 behavior of quantum quenches (in the presence of the critical points) for the case of mutually non-interacting non-relativistic fermions in a harmonic trap.