Fourier's law: insight from a simple derivation

Area of Science:

• Quantum thermodynamics
• Condensed matter physics
• Statistical mechanics

Background:

• Fourier's law describes heat conduction in classical systems.
• Quantum systems may exhibit ballistic transport, violating Fourier's law.
• Understanding thermal transport in low-dimensional quantum systems is crucial.

Purpose of the Study:

• Investigate the onset of Fourier's law in a 1D quantum system.
• Identify the mechanism driving the transition from ballistic to diffusive heat transport.
• Explore the role of dephasing in establishing classical thermal transport laws.

Main Methods:

• Analytical investigation of a model system.
• Weakly coupled quantum systems connected to thermal baths.
• Analysis of thermal length scale and local temperature profiles.

Main Results:

• A characteristic thermal length scale governs the crossover.
• This length scale correlates with the local temperature distribution.
• Dephasing induces classical Fourier's law behavior.

Conclusions:

• The transition to Fourier's law in quantum systems is well-defined by a thermal length scale.
• Dephasing is a key factor in realizing classical heat conduction laws in quantum regimes.
• The findings offer insights into thermal transport analogous to electrical transport (Ohm's law).