Dynamics Of Disordered Tavis-Cummings And Holstein-Tavis-Cummings Models

In this dissertation,the disordered dynamical properties of the Tavis-Cummings model（TC）and the Holstein-Tavis-Cummings model（HTC）are studied by using the Green function method and the Multi-D₂ansatz method based on Dirac-Frenkel time-dependent variational principle respectively.For the TC model,the influences of disorder on photon population dynamics,absorption spectrum,entanglement between qubit and cavity mode are studied by using Green function method,and the cavity detuning of the TC model are discussed.For the HTC model,the influences of disorder on photon population dynamics,absorption spec-tra and transport properties are studied by using the Multi-D₂ansatz method.Finally,the analytical method of the TC model and the numerically exact method of the HTC model together reveal various complex behaviors in quantum electro-dynamics of disordered multidimensional cavity.The basic physical images are given in this dissertation.In Chapter 1,the physical background of the TC model and the HTC model in cavity quantum electrodynamics are introduced,and the applications of Davydov Ansatz hierarchical equation of motion（HDA）theory are introduced.In Chapter 2,the Multi-D₂ansatz and Dirac-Frenkel time-dependent varia-tional principle are introduced in detail.In Chapter 3,the TC model is introduced in detail,and the analytic formula of photon population and spectrum are given by the Green function method.The effects of diagonal disorder,coupling disorder on the dynamics of the TC model,and the entanglement between qubits and cavity modes are analyzed,and the cavity detuning of the TC model are discussed.In Chapter 4,the HTC model is introduced in detail,and the spectral ex-pression based on the Multi-D₂Ansatz are given.The effects of diagonal disorder,coupling disorder on the dynamics,absorption spectra,and transport properties of the HTC model are studied.In Chapter 5,the dynamic behaviors of the two models are summarized,and the future applications of the theoretical methods in more complex physical models are discussed.In the appendix,the derivations of the Green function and the Dirac-Frenkel equation of motion are given in detail.