Quantum Rayleigh problem and thermocoherent Onsager relations

Abstract

The role of quantum coherence and correlations in heat flow and equilibration is investigated by exploring the Rayleigh's dynamical problem to equilibration in the quantum regime and following Onsager's approach to thermoelectricity. Specifically, we consider a qubit bombarded by two-qubit projectiles from a side. For arbitrary collision times and initial states, we develop the master equation for sequential and collective collisions. By deriving the Fokker-Planck equation out of the master equation, we identify the quantum version of the Rayleigh's heat conduction equation. We find that quantum discord and entanglement shared between the projectiles can contribute to genuine heat flow only when they are associated with so-called heat-exchange coherences. Analogous to Onsager's use of Rayleigh's principle of least dissipation of energy, we use the entropy production rate to identify the coherence current. Both coherence and heat flows can be written in the form of quantum Onsager relations, from which we predict coherent Peltier and coherent Seebeck effects. The effects can be optimized by the collision times and collectivity. Finally, we discuss some of the possible experimental realizations and technological applications of the thermocoherent phenomena in different platforms.

12 pages, 8 figures. Some sections were moved to the Appendix

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• A brief journey through collision models for multipartite open quantum dynamics
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Heat as a witness of quantum properties
• Classical and Quantum Orbital Correlations in the Molecular Electronic States
• Boosting Biomolecular Switch Efficiency With Quantum Coherence
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Quantum Onsager relations
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Anomalous flow in correlated quantum systems: No-go result and multiple-charge scenario