The Quench Dynamics Of One-dimensional Fermi Systems

The quench dynamics is a popular but difficult research topic.Based on the experimental progress in controlling and manipulating cold atomic gases;the research on the quench dynamics of the cold atomic gases becomes hot.After quenching quantum system from an equilibrium state to another state,people expect that some interesting physical phenomena will occur.Many different models have been considered by physicists.In this thesis we research only the quench dynamics of one dimensional models due to its simplicity in numerical calculation.We research two models,the one-dimensional Fermi superfluid in an optical cavity and one dimensional disorder systems.There are seven chapters in the thesis as follows.In chapter one,we introduce the fundamental knowledge of optical cavity and the research background of the cavity opto-mechanical system.In chapter two,we introduce the theoretical and applications of the interac-tion between optical cavity and many atoms.In chapter three,we introduce the experiment setup of the one dimensional Fermi superfluid and obtain the corresponding model Hamiltonian.We put a Fermi superfluid in a ring cavity,reserve only two low energy levels of a atom by adiabatically eliminating the excited state.After introducing order parameter and some correlation operators,we apply the mean field approximation on the model Hamiltonian,and obtain a series of self-consistent dynamical equations about these correlation operators.In chapter four,by solving these dynamical equations self-consistently,we find that the cavity field and Fermi gases will evolve to a stable state when the Fermi gases don't have the superfluidity.And we investigate further the properties of the system when considering the superfluidity.We find that the superfluid have an advantage over the superradiant,the photon number will tend to zero.In chapter five,we introduce the fundamental concept of the dynamical quantum phase transitions and recent development.In chapter six,we explore a periodic dynamical quantum phase transitions which generally exist in the disorder system by analytic solution and numerical calculations.We point out the importance of our research.Conclusions and outlook are given in chapter seven.