Model Study On Heat Conduction In One-Dimensional System And The Related Dynamical Properties

The phenomena of heat transport is ubiquitous in our daily life. Understand-ing the macroscopic phenomena in terms of microscopic dynamics is not only one of the fundamental tasks of nonequilibrium statistics,but also a demand motivated by rapid progress in devices miniaturization. Starting from "bil-liard gas channel",we study heat conduction and corresponding dynamical properties in quasi-one-dimensional systems.In Chapter 2 we briefly review previous works relevant to our studies, from one-dimensional lattice to billiard gas channel to carbon nanotubes. We also discuss Molecular Dynamical approaches to the issue of heat conduction.In Chapter 3 we deal with the problem of heat conduction in a quasi-one-dimensional gas model with various degrees of chaos.To this aim we construct a channel of the combination of hyperbolic and straight boundaries. Our calculations indicate that chaos affects the mass transport of heat carriers, thus the heat transport.Numerical results suggest that the divergent exponent a of heat conduction and diffusion exponentβare related byα= 2-2/β. We explore the temperature profiles numerically and analytically, which show that the temperature jump is primarily attributed to superdiffusion for both nonchaotic and chaotic cases. Our intensive calculations extend the results of prior studies and one can conclude that strong chaos leads to the normal diffusion of heat carriers, thus,the normal heat conduction.In Chapter 4 we perform extensive simulations on the heat conductance for homogeneous systems and heterogenous systems with the single heterojunc-tion.Our simulations show a broad range of 77 where local thermal equilibrium is realized even in systems with heterojunction. In particular, we model the contact conductance at the interface between two systems and calculate the contact conductance. A remarkable discontinuity of temperature profile has been observed in the case of imperfect contact.Our study extends the billiard gas channel from homogeneous system to heterogenous one, and demonstrates the establishment of local thermal equilibrium with a wide range of parameter.In Chapter 5 we introduce for the first time an quantized rotational de-gree of freedom besides two translational ones in billiard gas channel to study the heat transport.Our results reveal three distinct temperature regimes. In particular,the intermediate regime is characterized by heat conductivity with a temperature exponentγmuch greater than 1/2 that is generally found in systems with point-like particles.A dynamical investigation indicates the occurrence of non-equipartition behavior in this regime. Moreover, the cor-responding Poincare sections also show remarkably characteristic patterns, completely different from the cases of point-like particles. We expect that our model provides a strategy to study the effects of the quantized degree of freedom on heat transport.