Mode-coupling theory and molecular dynamics simulation for heat conduction in a chain with transverse motions

TL;DR

This paper combines mode-coupling theory and molecular dynamics simulations to analyze heat conduction in a 1D chain with transverse motions, revealing divergence of thermal conductance with system size.

Contribution

It provides a detailed comparison between full and simplified mode-coupling theories and molecular dynamics, demonstrating their agreement and explaining the size dependence of thermal conductance.

Findings

Quantitative agreement between mode-coupling theory and molecular dynamics on mode damping.

Thermal conductance diverges as N^{1/3} with system size.

Observed crossover effect leading to N^{2/5} dependence in simulations.

Abstract

We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. The problem is analyzed by mode-coupling theory and compared with molecular dynamics. We find very good, quantitative agreement for the damping of modes between a full mode-coupling theory and molecular dynamics result, and a simplified mode-coupling theory gives qualitative description of the damping. The theories predict generically that thermal conductance diverges as N^{1/3} as the size N increases for systems terminated with heat baths at the ends. The N^{2/5} dependence is also observed in molecular dynamics which we attribute to crossover effect.