Normal heat conduction in a chain with a weak interparticle anharmonic potential

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Non-equilibrium thermodynamics

Background:

• Understanding heat transport in low-dimensional systems is crucial for nanoscale thermal management.
• Langevin heat baths are commonly used to model thermal reservoirs in physical systems.
• The interplay between interparticle interactions and thermal reservoirs affects macroscopic transport properties.

Purpose of the Study:

• To analytically investigate heat conduction in a 1D chain with a specific interparticle potential and harmonic on-site potential.
• To examine the system's behavior with thermal reservoirs at the boundaries only, by considering small coupling for interior sites.
• To determine the conditions under which Fourier's law of heat conduction is applicable in this system.

Main Methods:

• Analytical study of heat conduction.
• Perturbative analysis of heat current in the steady state.
• Investigation of a 1D system with weak interparticle potential V(x) = lambda[1-cos(x)] and harmonic on-site potential.
• Comparison of low and high temperature regimes.

Main Results:

• An expression for thermal conductivity was derived.
• The study compared heat conduction behavior in low and high temperature regimes.
• A "phase transition" was observed: Fourier's law holds only at high temperatures when interior heat baths are turned off.

Conclusions:

• Fourier's law is not universally applicable for heat conduction in this system, particularly at low temperatures or when interior thermal couplings are absent.
• The system exhibits distinct thermal transport behaviors depending on temperature and the presence of interior heat baths.
• This research provides insights into the fundamental mechanisms of heat conduction in complex 1D systems.