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

We study heat conduction in a 1D chain of particles with longitudinal as well as transverse motions. The particles are connected by 2D 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.