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 systems of the size L_x × L_y × L_z (L_z ≫ L_x, L_y) are simulated. Heat baths are put in both ends: one has a higher temperature than the other. In the case of the crystal, the interaction potential V has a fourth-order nonlinear term in addition to the harmonic term, and the Nosé-Hoover method is used for the heat baths. In the case of the fluid, the stochastic boundary condition is charged, which performs the function of the heat baths. Fourier-type heat conduction is reproduced in both crystal and fluid models in a three-dimensional system, but it is not observed in lower-dimensional systems. The autocorrelation function of heat flux is also observed and long-time tails of the form ∼ t^-d/2, where d denotes the dimensionality of the system, are confirmed.