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

Area of Science:

• Quantum Thermodynamics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Understanding thermal transport in quantum systems is crucial for developing novel electronic and thermal devices.
• Previous studies have explored thermal transport but often lack a geometric mechanism for controlled local circulation.
• The interplay between geometry and quantum dynamics in thermal transport remains an active area of research.

Purpose of the Study:

• To demonstrate a geometry-based mechanism for generating steady-state internal circulation of local thermal currents.
• To investigate the robustness and ubiquity of this mechanism in different quantum systems.
• To explore the validity of the mechanism across the quantum and classical regimes.

Main Methods:

• Formulation of harmonically coupled quantum oscillators using the Redfield quantum master equation (RQME).
• Modeling of the Bose-Hubbard model (BHM) of phonons using the Lindblad quantum master equation (LQME).
• Utilizing a simple triangular multipath geometry for both systems.
• Numerical and analytical solutions were employed depending on the system's complexity.
• Verification through quantum Langevin equation calculations.

Main Results:

• Both RQME and LQME systems exhibited atypical local thermal currents flowing against the total current, driven by reservoirs at different temperatures.
• The total thermal current consistently behaved normally, indicating localized circulation.
• The geometric-based circulation was found to be ubiquitous and robust across both modeled systems.
• Results in the high-temperature limit aligned with classical predictions, confirming generality.

Conclusions:

• A geometry-based mechanism effectively generates steady-state local thermal current circulation in quantum systems.
• This phenomenon is robust and applicable to different quantum models (oscillators, phonons) and across the quantum-classical boundary.
• The findings suggest potential for novel thermal management and device applications.