Geometry-based circulation of local thermal current in quantum harmonic and Bose Hubbard systems

TL;DR

This paper demonstrates a geometry-based mechanism for internal circulation of local thermal currents in quantum harmonic and Bose Hubbard systems, showing its robustness and classical-quantum consistency.

Contribution

It introduces a universal geometry-driven thermal current circulation mechanism in quantum and classical systems using master equations.

Findings

Local thermal currents can flow against the total current in a triangle geometry.

The mechanism is robust across quantum and classical regimes.

Results agree with classical predictions at high temperatures.

Abstract

A geometry-based mechanism for generating steady-state internal circulation of local thermal currents is demonstrated by harmonically coupled quantum oscillators formulated by the Redfield quantum master equation (RQME) and the Bose Hubbard model (BHM) of phonons formulated by the Lindblad quantum master equation (LQME) using the simple multi-path geometry of a triangle. Driven by two reservoirs at different temperatures, both systems can exhibit an atypical local thermal current flowing against the total current. However, the total thermal current behaves normally. While the RQME of harmonically coupled quantum oscillators allows an analytical solution, the LQME of the interacting BHM can be solved numerically. The emergence of the geometry-based circulation in both systems demonstrates the ubiquity and robustness of the mechanism. In the high-temperature limit, the results agree with the classical results, confirming the generality of the geometric-based circulation across the quantum and classical boundary. Possible experimental implications and applications are briefly discussed.