Heat Conduction In One-dimensional Lattice

To understand the macroscopic phenomenological laws of irreversible thermodynamics in terms of deterministic dynamics is one of the long-standing tasks of non-equilibrium statistical physics. To understand the macroscopic phenomenological laws of irreversible thermodynamics in terms of deterministic dynamics is one of the long-standing tasks of non-equilibrium statistical physics. Since the 1980s, with the vast progress of modern computer technology, computational physics has been rapidly developed and turns out to be a most important branch of Physics. Now,using the method of molecular dynamics to investigate the dynamic behaviors of many-particle systems consisting of up to thousands of particles become practicable. Studying behaviors of heat conduction in one-dimensional (1D) systems by means of equilibrium and non-equilibrium molecular dynamics is a prominent problem that has constantly receives lots of attention for long period of time. According to the Fourier's law of heat conduction, the heat flux that transferred along the system is proportional to the temperature gradient of the systems, at a rate determined by the thermal conductivity of the material. Systems of reduced dimensions are always of peculiar propertied. Theoretical studies in the last years have already revealed that the Fourier law does not hold in most of one-dimensional systems, where the thermal conductivity diverges with the system size asκ∝N ~α(0 <α≤1). This phenomenon is now known as the anomalous heat conduction in 1D system. In the paper, we put forward a dimerized lattice model with the consideration of the Peierls instability that occurs in many realistic materials and investigate its behaviors of heat conduction. In addition, we investigate heat conduction in the 1D systems with damping. Our study will contribute to the reaching an accomplishment of the theory on the 1D heat conduction, and will provide new ides for the realistic application and laboratorial measure of the 1D systems, especially for the design and the manufacture of some new thermal device in future.The thesis consists of four chapters. In chapter one, we introduce some basic knowledge of transport theory associate with heat conduction, some classic models and the definitions of temperature and heat flux in the system. In chapter two, we introduce the behaviors of heat conduction in 1D integrabel systems, 1D non-integrable ones with momentum-conserving and 1D non-integrable ones with...