Simulational Study on Dimensionality Dependence of Heat Conduction

Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-one-dimensional system of the size of Lₓ× Ly× Lz(Lz Lₓ,Ly) is simulated. Heat baths are put in both end: one has higher temperature than the other. In the crystal case, the interaction potential V has fourth-order non-linear term in addition to the harmonic term, and Nose-Hoover method is used for the heat baths. In the fluid case, stochastic boundary condition is charged, which works as the heat baths. Fourier-type heat conduction is reproduced both in crystal and fluid models in three-dimensional system, but it is not observed in lower dimensional system. Autocorrelation function of heat flux is also observed and long-time tails of the form of ~ t-d/2, where d denotes the dimensionality of the system, are confirmed.