Thermalization From The General Canonical Principle And Quantum Atom-heteronuclear Molecule Dark State

Recently, studies of the foundation of statistical mechanics are enjoying a renaissance.Concerning about the canonical ensemble, it was pointed out that the equal a priori probability postulate ofstatistical mechanics, which is applied to the microcanonical ensemble constituted by all pure statessatisfying the energy constraint, is not necessary. Instead, it should be replaced by the general canonicalprinciple or canonical typicality. It states that the state of a subsystem can be obtained from a single purestate rather than a mixture of microcanonical ensemble. More recently, the problem revived again becauseof the possibility of using ultracold atoms to address it experimentally. Consentrated to the generalcanonical principle, this thesis uses a numerical experiment to prove its correctness in the dynamical sense.Furthermore, comparing the density matrices themselves is used to character the state after thermalization,which may be to enlighten us to descripe the phenomenons of thermalization completely.The first chapter to fifth chapter is the first part of this thesis, in which the thermalization fromgeneral canonical principle is described. In the first chapter, the general canonical principle is proven, weuse the method which first introduced by Goldstein to prove the canonical typicality. In the second chapter,we introduce the recent experiment of thermalization, which is the fountain of studing thermalization. Thethird chapter is the explanation of why the integrable system cannot thermalize, the main theory isgeneralized Gibbs ensemble. In the forth chapter, we introduce thermalization and its mechanism forgeneric isolated quantum systems. The fifth chapter is important, we study the time evolution of a genericand finite isolated quantum many-body system starting from a pure quantum state. We find the dynamicalgeneral canonical principle is also correct, and it is better to comparing the density matrices themselvesrather than the measures of distances. Next, we investigate the influences of different lattice configurationsand different initial states. In addition, thermalization of coupled systems with different temperaturescorresponding to mixed initial states and quantum entanglement is studied.With the inspiration the atom-hemonuclear molecule dark state’s quantum exact solution of ZhaoCheng, we study the quantum atom-heteronuclear molecule dark state. this solution is fit to the ideal case ofnot considering the two-body collide and the loss of atom, but also have significant interest in physics. Onone hand, it can display rich quantum correlation, which not occur in classical solution, such as the second momentum and sub-Poisson distribution. On the other hand, we find that the initial populations imbalanceof the atoms plays a significant role in quantum conversion rate and adiabatic fidelity. In fact, for large M,this system is reduced to a linear one since the operator of one special can be replaced by a c-number,which is the soul of mean-field method. Then in the adiabatic fidelity, we see that increasing M canincrease the number of output of molecular, so it will be a significant implication in experiment.The sixth and seventh chapter is the another part of this thesis, in sixth chapter the quantum exactsolution of atom-hemonuclear molecule dark state and its quantum correlation is described. In seventhchapter, we investigate the atom-heteronuclear molecule dark state’s quantum exact solution, especially therole of initial populations imbalance of the atoms in quantum conversion rate and adiabatic fidelity.