Quantum Tunneling In Real Superlattices And Some Nonlinear Excitations In BEC

This thesis is divided into two main parts. In part I, some topics on coherent dynamics and tunneling phenomenon of Bloch electron in actual superlattice have been investigated. Based on theoretical results of Tight-Bind-Two-Band (TBTB) model and with the help of powerful numerical simulation, the effects of some kind of actual imperfect factors on coherent dynamics and tun- neling phenomenon of Bloch electron in actual superlattice have been investigated, which has two motivation: (1)the validity of theoretical results in actual superlattice; (2)investigation of new physics phenomenon which can not be analytically investigated in actual superlattice. At first, by using Finite-Element-Method (FEM), the eigen- function and eigenenergy of the actual superlattice driven by uni- form static electric field have been discussed. Furthermore, the evolution of Bloch electron in actual superlattice driven by both uniform static electric field and laser electric field has been in- vestigated. The tunneling and hopping between quasibands are the center of the first part of this thesis. The numerical results show that under the resonant conditions which were derived from the theoretical TBTB model, Rabi oscillation can still subsist in the multiband superlattice, and the resonant condition is changed from single frequency into a four times Rabi frequency wide, in other words, the orderly Rabi oscillation with some extent of am- plitude can turn up if Wac ?WresanceI < 2WRabi. Second, dynamical behavior of coupled chains in the mag- netic and electric fields has been investigated by applying the method of single band to the coupling chains. The results ex- hibit that the static electric field makes the energy spectrum of the coupled chains to turn out the structure of Wannier-Stark ladder. In the general case, the energy spectrum of the sys- tem is that of two interspaced Wannier-Stark ladders. The in- terplay of a uniform electric field and a uniform magnetic field brings about tunneling between quasibands of the coupled chains which can destroy the dynamical localization of the system. In strong field regime, the condition of destruction tunneling be- tween quasibands is the roots of Jo(4Vsin(y/2)/eE) = 0, whereas in weak field regime, the conditions of destruction tunneling be- tween quasibands are complex. However, in weak field regime, the electron oscillation between upper and lower chains becomes slowly when Jo(4VsinQy/2)/eE) 0, otherwise the electron os- cillates more quickly than that in the vicinity of the roots of Jo(4Vsin(-y/2)/eE) 0. Third, current response in coupling chains under a dc-ac electric field and a uniform magnetic field is investigated. For a special case of extremely low coupling between chains, simple and physically explicit analytical current expressions are derived, from which the field dependence of some physical properties can be clearly seen. Under some condition, the current of the cou- pled chains can be smeared. In other words, current response in coupling chains can be controlled by adjusting external fields and parameters of the coupled chains. In part II, nonlinear excitations and interfere striation of the Bose-Einstein condensation have been discussed. As is well known, the behaviour of BECs in the vicinity of critical temper- ature can be described by nonlinear Schringer equations (or Gross-Pitaevski equations). In chapter five, the analytical...