Heat transfer and entanglement -- non-equilibrium correlation spectra of two quantum oscillators

TL;DR

This paper analyzes the non-equilibrium quantum correlations and entanglement spectra of two coupled oscillators interacting with separate heat baths, providing exact analytical results and challenging previous assumptions about heat flow.

Contribution

It offers an exact spectral representation for the covariance matrix of two oscillators in non-equilibrium, without using the rotating-wave approximation, and explores entanglement measures in this context.

Findings

Fluctuation-dissipation theorem holds at global equilibrium.

Anomalous heat transport from cold to hot bath is not observed.

Spectral measures of entanglement are proposed based on zero-point fluctuations.

Abstract

The non-equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation-dissipation theorem is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero-point fluctuations. No rotating-wave approximation is applied, and anomalous heat transport from cold to hot bath, as reported in earlier work, is demonstrated not to occur.