Non-Markovian dynamical effects and time evolution of entanglement entropy of a dissipative two-state system

TL;DR

This paper studies how a two-state quantum system exchanges information with its environment, revealing non-Markovian effects and a transition from coherent to incoherent dynamics as coupling strength varies.

Contribution

It uncovers non-Markovian oscillation-hump features in entropy dynamics and characterizes the coherent-incoherent crossover in a dissipative two-state system.

Findings

Entropy exhibits non-Markovian oscillations and a hump indicating memory effects.

Increasing coupling strength suppresses the hump, signaling a dynamical crossover.

Long-time entropy matches numerical renormalization group results.

Abstract

We investigate the dynamical information exchange between a two-state system and its environment which is measured by von Neumann entropy. It is found that in the underdamping regime, the entropy dynamics exhibits an extremely non-Markovian oscillation-hump feature, in which oscillations manifest quantum coherence and a hump of envelop demonstrates temporal memory of bath. It indicates that the process of entropy exchange is bidirectional. When the coupling strength increases a certain threshold, the hump along with ripple disappears, which is indicative of the coherent-incoherent dynamical crossover. The long-time limit of entropy evolution reaches the ground state value which agrees with that of numerical renormalization group.