How can we derive Fourier's Law from quantum mechanics? Exact master equation analysis

Abstract

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting an exchange effect. The pure exchange model directly leads to energy diffusion in a weakly coupled spin-1/2 chain.

References in corpus (8)

• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Time-convolutionless master equation for mesoscopic electron-phonon systems
• Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential
• Fourier's Law from Closure Equations
• Microscopic Quantum Mechanical Foundation of Fourier's Law
• Transition from diffusive to ballistic dynamics for a class of finite quantum models
• From Pure Schroedingerian to Statistical Dynamics
• Application of the Hilbert Space Average Method on Heat Conduction Models

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• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Nonlinear quantum heat transfer in hybrid structures: Sufficient conditions for thermal rectification
• Fourier's Law: insight from a simple derivation
• Heat flux operator, current conservation and the formal Fourier's law
• Density dynamics from current auto-correlations at finite time- and length-scales
• Reconstructing Fourier's law from disorder in quantum wires
• From thermal rectifiers to thermoelectric devices
• Ising chain: Thermal conductivity and first-principle validation of Fourier law
• Fundamental aspects of steady state heat to work conversion
• Emergence of Fourier's law of heat transport in quantum electron systems
• Projection operator approach to transport in complex single-particle quantum systems
• Entanglement versus Bell nonlocality of quantum nonequilibrium steady states
• Diffusive lossless energy and coherence transfer by noisy coupling
• First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model
• Transient unidirectional energy flow and diode-like phenomenon induced by non-Markovian environments
• Phonon Gravity, Non-equilibrium QFT, and the Tolman Thermal Equivalence Principle
• Quantum master equation approach to heat transport in dielectrics and semiconductors
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection