Heat flux operator, current conservation and the formal Fourier's law

Abstract

By revisiting previous definitions of the heat current operator, we show that one can define a heat current operator that satisfies the continuity equation for a general Hamiltonian in one dimension. This expression is useful for studying electronic, phononic and photonic energy flow in linear systems and in hybrid structures. The definition allows us to deduce the necessary conditions that result in current conservation for general-statistics systems. The discrete form of the Fourier's Law of heat conduction naturally emerges in the present definition.

References in corpus (15)

• Thermal Logic Gates: Computation with phonons
• Single-mode heat conduction by photons
• Modeling heat transport through completely positive maps
• Decoherence induced by interacting quantum spin baths
• Heat Transistor: Demonstration of Gate-Controlled Electron Refrigeration
• Single mode heat rectifier: Controlling energy flow between electronic conductors
• Local effective dynamics of quantum systems: A generalized approach to work and heat
• Normal metal - superconductor tunnel junction as a Brownian refrigerator
• Transport in open spin chains: A Monte Carlo wave-function approach
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential
• Limited validity of the Kubo formula for thermal conduction in modular quantum systems
• Heat conduction in simple networks: The effect of inter-chain coupling
• Fourier's Law from Closure Equations
• Microscopic Quantum Mechanical Foundation of Fourier's Law

Cited by in corpus (11)

• Sufficient conditions for thermal rectification in hybrid quantum structures
• Stochastic pumping of heat: Approaching the Carnot efficiency
• Reconstructing Fourier's law from disorder in quantum wires
• Environment-assisted quantum transport and mobility edges
• Geometric energy transport and refrigeration with driven quantum dots
• Exact steady state of the open XX-spin chain: entanglement and transport properties
• Nonequilibrium Quantum Thermodynamics in Non-Markovian Adiabatic Speedup
• Dynamics and quantumness of excitation energy transfer through a complex quantum network
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Energy densities in quantum mechanics
• Local heat current flow in ballistic phonon transport of graphene nanoribbons