Study Of Nonequilibrium Dynamics Of A Quantum Many Body System With Long-range Interaction

Statistical mechanics has achieved huge success since it was established.Statistical mechanics generally assumes that a system will approach thermal equilibrium after some time,we call it thermalization.For thermalization in a strong sense,we mean for any initial state,the physical observables of the system will become a roughly static value after relaxation,which is given by proper statistical ensemble,and then oscillate around it with small fluctuations.But how to connect the time reversal symmetry for microscopic dynamics with the broken time reversal symmetry for macroscopic thermalization process is still a question.Both classical and quantum systems face this question.In 1990 s,Deutsch and Srednicki proposed eigenstate thermalization hypothesis(ETH)on the basis of quantum chaos theory and random matrix theory.This is a breakthrough in the study of the thermalization of quantum systems.For a quantum system satisfying ETH with local Hamiltonian,we can prove that it will thermalize in a strong sense.Recently,people are attracted by the nonequilibrium dynamics of close quantum many body systems with nonlocal Hamiltonian,which is beyond the application of ETH.Unusual dynamics may emerge in such systems.In this thesis,we mainly study a hardcore bosonic system with long-range interaction.Such a system has been realized in the experiment with ultracold atoms in optical lattices.For finite size systems,we use the exact diagonalization method to study it.We study the energy difference distribution and test ETH of it.Then we study the dynamics of it after quantum quench.Setting different initial and final states,we found usual dynamics of the system,it will thermalize in a strong sense.And we also found unusual dynamics of the system,the physical quantity will always oscillate,and the fluctuation will increase as the size increases.For the system in thermal dynamic limit,we use self-consist mean field theory and Jordan-Wigner transformation to study it.We set different initial and final states,and also found usual and unusual dynamics.