Research On Quantum Thermal Transport Properties In One-dimensional Lattice System

Heat conduction in low-dimensional lattice system is as the connection between dynamics and statistics, having been studied extensively since the early 1900s. Much more attention has been paid to this problem in the past decades due to the dramatic achievement in the application of miniaturized devices which can be described by one-dimensional (1D) or 2D models. More and more numerical calculations are focused on the minimal requirements for a dynamical model whether or not Fourier's heat conduction law holds.In the thesis, the extended mean-field Ford-Kac-Mazur formalism has been proposed for the study of quantum heat transport through an one-dimensional Fermi-Pasta-Ulam (FPU) dielectric chain connected to two reservoirs. The method is more transparent and direct for linear systems to get exact results. Further it is a useful method for nonlinear systems to perform numerical simulation. The size-dependence of system heat current, heat conductivity and the local kinetic energy density have been analyzed numerically. In our study, two different reservoirs are adopted and some new phenomenons have been discovered there in the quantum version.(1) We evolved the system equation through Heisenberg equations of motion and FKM equation while the boundary particles 1 and N are coupling to the reservoirs. Further, by using Fourier transformation, we get the particular solutions of the lattice system in frequency space. At last the numerical simulation has been taken into account. We found the size dependence is not only related to the properties of the system itself, but also affected by the properties of noise reservoirs. Therefore, we can say that the effects of reservoirs, the contacts and the FPU nonlinear interactions all have played an important role in quantum thermal transport.(2) By choosing different heat reservoirs and as the whole system heat current vanishes, the local energy density of a definite size chain has been studied. We found when the even-size chain coupled to the Langevin heat bath the steady state exist in the central of the chain. Then the local energy density of dielectric atoms at the middle of nonlinear chain can be used to describe the local temperature of the chain. But when the even-size chain coupled to the Landauer noise reservoirs, in contrast with harmonic lattice system, the local temperature appears some shift in the central. Although the large fluctuations of the local temperature are sensitive to the FPU interactions near boundaries, weakly dependent on the noise reservoirs. At the end of the thesis, we found the symmetric repulsive and attractive FPU nonlinear interaction results in a good symmetric fluctuations.