Diffusion coefficients preserving long-time correlations: Consequences on the Einstein relation and on entanglement in a bosonic Bogoliubov system

TL;DR

This paper analytically derives diffusion coefficients for coupled harmonic oscillators with long-time correlations, revealing effects on Einstein relation and entanglement dynamics, including frequency-dependent friction and entanglement preservation.

Contribution

It introduces a method to derive diffusion coefficients accounting for persistent correlations and explores their impact on Einstein relation and entanglement in bosonic systems.

Findings

Persistent correlations renormalize oscillator frequencies and friction.

Einstein relation holds at low temperatures with effective frequency-dependent friction.

Strong coupling delays entanglement sudden death and can generate entanglement from separable states.

Abstract

We analytically derive the diffusion coefficients that drive a system of $N$ coupled harmonic oscillators to an equilibrium state exhibiting persistent correlations. It is shown that the main effect of the latter consists in a renormalization of the natural frequencies and the friction coefficients of the oscillators. We find that the Einstein relation may be satisfied at low temperatures with frequency-dependent effective friction coefficients, provided that the physical constraints are fulfilled. We also investigate the entanglement evolution in a bipartite bosonic Bogoliubov system initially prepared in a thermal squeezed state. It is found that, in contrast to what one may expect, strong coupling slows down the entanglement sudden death, and for initially separable states, entanglement generation may occur.