One-dimensional Electron - Phonon Coupling System In The Base State Nonlinear Lattice Effects

The physical property of electron-phonon interaction systems is one of the fundamental problems in condensed matter theory. Its development and perfection will profit the solving of some important problems in the areas of condensed matter physics , materials physics , protein molecular dynamics as well as other related subjects. So the study of the nonlinear lattice effects in electron-phonon interaction systems has been received extensive attention of many researches in the past years. In this thesis, we study the nonlinear effects in electron-phonon interaction of one or quasi-one dimensional system with the nonlinearity of phonon (lattice). Using the variational method and coherent method we study the ground state properties of one-dimensional molecular crystal and the soliton characteristics in protein molecular chain, respectively.The thesis is made up of three chapters. In chapter one we briefly recall the history of the development of the study of nonlinear effects of electron-phonon interaction system, and review their scientific significance in other related areas. In chapter two we analytically study the nonlinear lattice effects for the ground state of electron-phonon interaction one-dimensional molecular crystal system. Based on the given linear Holstein model, and using the variational method we obtained the ground state properties of the electron-phonon interaction system with cubic and quartic lattice (phonon) terms. We obtained the relations between the ground state energy and the phonon squeezing effect and polaron squeezing effect as well as the variation of the polaron bandwidth. In chapter three we study the properties of solitons in protein molecular systems by method of quantum coherent states, and obtained the improved temperature stability of the solitons due to the cubicnonlinear phonon potential.The summary of the work and the prospects of this research area are given at the end of the thesis.