The Study Of Open Quantum System Based On The Variation Principle

Open quantum system is a quantum system that interacts with external environments.For an isolated quantum system,the evolution of the system is unitary.Open quantum systems will not be unitary.In recent years,due to the interest in fundamental problems and the applications of quantum theory in quantum computing,scientiests have studied the dynamic evolution of open quantum systems driven by external.Due to the complexity of evolution laws of open quantum systems,many methods are often used to study such systems.In this thesis,we will use the numerically rigorous dynamical variational methods to simulate the dynamics of open quantum systems by time dependent driven.In the first chapter,we will introduce the research background of this thesis.We give a preliminary introduction to the models used in this thesis and how they relate to practical problems.At the same time,we give a brief review of the main numerical simulation methods for the open quantum systems.In Chapter 2,we introduce the Dirac-Frenkel principle and the time dependent variational principle.On the basis of these principles,we derive the calculation method used in this thesis.Based on the Dirac-Frankel principle,we derive the multilayer multiconfiguration time dependent Hartree method based on Fock states.From the time dependent variational principle,we derive the multiple D₂Ansatz method based on coherent states.In the third and fourth chapters of this thesis,we study the dynamic evolution of the Landau-Zener model and the Landau-Zener-Stückelberg-Majorana model,respectively,using the dynamic evolution equations derived in the second chapter.In chapters 3,the Landau-Zener model is investigated.The external driving of this model varies linearly with time.Using the exact numerical method based on the D₂trial states,we study the dynamics of the Landau-Zener model interacting with the zero temperature photon bath under various initial states.The multiple D₂Ansatz can deal with the dynamics of the spin and the photon bath uniformly.With the advantage of the variational method,we propose a technique to analysis the dynamics of the photon bath in detail.Using the information obtained from the photon bath,we show the energy levels involved in the Landau-Zener transformation and find out the path of the system to transform between these levels.In particular,we use the Schr?dinger-cat state,which plays an important role in quantum computation,as the initial state,and studied the influences of the initial state of the Schr?dinger cat states with different parameters on the Landau-Zener transition probability.We find how the transition probability depends on the initial condition parameters.In chapter 4,we study the Landau-Zener-Stückelberg-Majorana model.The external driving satisfies a periodic sine function.Using the technique proposed in Chapter 3,the dynamic evolution under different driving amplitudes is studied.Compared with the linear driving,the dynamics of the periodic driving is more complicated.We analyze the evolution of the photon bath under various driving amplitudes.With the information obtained from the technique,the dynamical behavior of the model is understood.We also investigate the effect of the Schr?dinger cat states with different parameters on the dynamic behavior.The fifth chapter is the conclusion and prospect.