Davies equation without the secular approximation: Reconciling locality with quantum thermodynamics for open quadratic systems

TL;DR

This paper derives a thermodynamically consistent quantum master equation for quadratic systems that aligns with the Davies equation without using the secular approximation, enhancing the understanding of quantum thermodynamics.

Contribution

It presents a derivation of a local quantum master equation that coincides with the Davies equation without relying on the secular approximation, applicable to many-body systems.

Findings

The quasi-local Redfield equation matches the Davies equation exactly.

The derivation does not depend on the secular approximation, which fails in certain systems.

The results can be extended to slowly driven and generic quantum many-body systems.

Abstract

We derive a thermodynamically consistent quantum master equation that satisfies locality for quadratic systems coupled to independent and identical baths at each site. We show that the quasi-local Redfield equation coincides exactly with the Davies equation, which satisfies the detailed-balance condition, due to cancellation of quantum coherence generated by each bath. This derivation does not rely on the secular approximation, which fails in systems with vanishing energy-level spacings. We discuss generalizations of our result to slowly driven quadratic systems and generic quantum many-body systems. Our result paves the way to a thermodynamically consistent description of quantum many-body systems.