Dynamics Of Finite Temperature Quantum Spin-Bose Model

The main content of this paper is the Davydov-Ansatze trial wave function method to study the dynamics of the finite temperature quantum spin-Bose model.The research method is mainly based on theoretical analysis and numerical calculation.Numerical analysis is performed using matlab software.In the first chapter,we introduce the open quantum system.The open quantum system mainly describes the quantum mechanical system in which the quantum system interacts with the environment or the bath,and describes the dynamic processes of the different initial states of the system-environment to help us better understand the evolution of dynamics.In the second chapter,we briefly introduce Markov and non-Markov processes.First,it is explained that the conditional probability of the Markov attribute is only related to the current state of the system,and it is independent and unrelated to its past history or future state.Then,it is stated that a non-Markov process is a random process without Markov properties,and the next state of a non-Markov system is determined by all its previous states,which rapidly increases the memory required for the evolution of the computing system.In the third chapter,we introduce two different numerical methods for solving the quantum dissipation model,namely the quasi-adiabatic propagation path integration(QUAPI)method based on the time-dependent evolution of the density matrix and the trial wave function method(MCTDH method and Davydov-Ansatze method).First,we explored the QUAPI method,which is a powerful path integration scheme based on improved propagators that are accurate for large time steps.In addition,we briefly introduce the implementation process of the QUAPI method.Subsequently,we introduce the MCTDH wave function propagation method and the Davydov-Ansatze trial wave function method,respectively.In the fourth chapter,we mainly introduce the quantum Rabi model in the dissipative environment.The quantum Rabi model is the simplest description of a two-state system in a dissipative two-level system,where atoms are considered quantified,and fields are treated as classical rotating fields.After the analytical solution of the quantum Rabi model proposed by Braak,people have found various methods to construct the analytical solution of the eigenspectrum of the quantum Rabi model.This chapter gives a brief overview of the common models of the quantum Rabi model,and briefly introduces the application direction of the model.Finally,the dynamic evolution of quantum Rabi model from zero temperature to finite temperature is introduced.In the fifth chapter,the quantum spin-Bose model is introduced.We briefly introduce the Hamiltonian and continuous discretization methods of the spin-Bose model.Then,the Davydov-Ansatze trial wave function is introduced to study its dynamic behavior from zero temperature to finite temperature.Next,the dynamic evolution of population of the system under various adjustable parameters(coupling strength of spectral density ?,electronic coupling constant ?,etc.)is summarized and compared with the results of the QUAPI method.It is found that the method of testing the wave function has a good agreement with QUAPI in the low-temperature ohmic or sub-ohmic environment.Finally,the commonly used dynamic research devices are briefly introduced.In the sixth chapter,the numerical methods introduced in the article and the Davydov-Ansatze trial wave function method are summarized,as well as the prospects for subsequent research.