Non-stationary heat conduction in one-dimensional chains with conserved momentum

摘要

The Letter addresses the relationship between hyperbolic equations of heatconduction and microscopic models of dielectrics. Effects of the non-stationaryheat conduction are investigated in two one-dimensional models with conservedmomentum: Fermi-Pasta-Ulam (FPU) chain and chain of rotators (CR). These modelsbelong to different universality classes with respect to stationary heatconduction. Direct numeric simulations reveal in both models a crossover fromoscillatory decay of short-wave perturbations of the temperature field tosmooth diffusive decay of the long-wave perturbations. Such behavior isinconsistent with parabolic Fourier equation of the heat conduction. Thecrossover wavelength decreases with increase of average temperature in bothmodels. For the FPU model the lowest order hyperbolic Cattaneo-Vernotteequation for the non-stationary heat conduction is not applicable, since nounique relaxation time can be determined.