Study On Entanglement Dyncamics In Quantum Quench

The classical statistical physics has successfully explained a large number of thermal phenomena in our life,and has become the basis of the modern physics.Statistical physics is a statistical theory based on the ergodic hypothesis in the phase space,which is based on the complexity of microdynamics of the classical systems.However,considering that the motions of microscopic particles should satisfy the quantum mechanics,how to construct statistical physics based on the unitary evolution under the Schrodinger equation has became a new research hotspot.The rapid development of the cold atom experiment technology provides a good platform for the study of the quantum non-equilibrium dynamics,especially for the quantum quench experiment which attract the attention to the thermalization of the closed quantum system.In this thesis,we systematically study the quantum quench in different many-body systems.The relation between the integrability and the thermalization,the dynamical evolutions of the different local observables are studied through the theoretical analysis and numerical simulation as well as the quantum entanglement.Based on the correlation between the entanglement and the thermalization,the physical mechanism of quantum thermalization was explored in the view point of the theory.This thesis are arranged as follows:In the first chapter,we introduce the progress of the quantum statistical physics,the main experimental and theoretical studies on the quantum thermalization as well as the related physical concepts.In the second chapter,we analyzed the quantum quench in the Dicke model,two situations that in thermodynamic limit and the finite model are calculated respectively through the analytical analysis and numerical diagonalization.Based on the post quench dynamics,we compare the relaxation dynamics with the generalized Gibbs ensemble,canonical ensemble,and the microcanonical ensemble.It is found that for the integrable Dicke model in thermodynamic limit,the generalized Gibbs ensemble is only applicable to the quench in the normal phase,while the strong excitation in the superradiant phase will lead to its failure.For the non-integrable Dicke model with finite atoms,the quench within the normal phase directly satisfies the canonical ensemble.For the quench from the normal phase to the superradiant phase,the reduced density matrix agrees with the results of the micro-canonical ensemble.We introduce the Hellinger distance of the energy level distribution to measure this agreement.The effect of equilibrium phase transition is also discussed.It is found that both the first derivative of the effective temperature and the Hellinger distance show abrupt behavior at the critical point.In the third chapter,the quantum quench in the extended Bose-Hubbard model is studied.By analyzing the local particle density,the momentum distribution and the quantum entanglement in the system,the eigenstate thermalization hypothesis is demonstrated to valid not only for the local observables,but also for the non-local entanglement.As a measurement of the thermalization degree,the fidelity of the reduced density matrix of the subsystem and the microcanonical ensemble and the Hellinger distance of the energy level distribution are calculated for the quench with different target tunneling coefficients.The correlation between the relaxation and entanglement dynamics is also obtained.It is found that the entanglement is highly correlated with the thermalization process,which is quantitatively analyzed by the Pearson correlation coefficient.This correlation analysis reveal that the quantum entanglement plays a very important role in the thermalization of the closed quantum system,provides an important theoretical foundation for exploring the physical mechanism of quantum thermalization.In the forth chapter,the summary and prospect are present.