Gauge Invariance of the Thermal Conductivity in the Quantum Regime

TL;DR

This paper rigorously proves the gauge invariance of thermal conductivity in the quantum regime, validating a key assumption in linear-response theory and enabling advancements beyond traditional Boltzmann transport approaches.

Contribution

It provides a rigorous proof of gauge invariance for thermal conductivity in quantum systems, strengthening the theoretical foundation of linear-response theory.

Findings

Proves gauge invariance of thermal conductivity in quantum systems.

Validates the assumption used in Hardy's heat-flux formulation.

Enables going beyond Boltzmann transport equation in many-body systems.

Abstract

The widely used linear-response (LR) theory of thermal conduction in the quantum regime rests on the yet unproven assumption, that the thermal conductivity is invariant with respect to the gauge of the energy density of the system. This assumption manifests itself clearly in, e.g., Hardy's formulation of the heat-flux operator [Phys. Rev. 132, 168 (1963)]. In this work, we rigorously prove this assumption. Our proof, being valid for the nuclear and electronic subsystems, not only puts the state-of-the-art theory on solid grounds, but also enables going beyond the scope of the widely-used Boltzmann transport equation (BTE) within the LR framework for many-body systems.