The third part of this thesis is on one hole problem of asymmetric T and T -- Jz model, which we found can be turned into a single body problem and is solvable. We get the spectrum of the model and calculate as a result the mass of the hole. This model may be related to the two species fermion coexisting system which may be realized in the optical lattice. / This thesis project is mainly inspired by the newly discovered superconductor NaxCoO2 · yH 2O. It has a layered structure with an almost separated single band out of the inner band electrons. It becomes the theoretical focus because it is the first layered strongly correlated system that shows superconductivity besides the cuprate superconductors. It may help people to understand the superconductivity in the cuprate system. In this thesis we mainly focus our attention on the strongly correlated models on triangular lattice. These models are expected to provide a theoretical background for the Nax CoO2 · yH2O system. We investigate the magnetic and superconductivity properties of these models on the triangular lattice. By the mean field calculation of different magnetic orders we got a phase diagram of the triangular lattice Hubbard model for different magnetic orders in the Hubbard model in the triangular lattice. To further investigate the superconductivity pairing symmetry of the triangular lattice, we use the standard variational Monte Carlo method to find which kind of pairing symmetry is stabilized in the triangular lattice T -- J -- V model. Our finding is that the extended- f wave pairing is most stable in the lattice. / To further understand the properties of the related model in the electron interacting system in the triangular lattice, we also solve the few particle problem in the triangular lattice. For two particles with the T -- U -- J -- V model in the triangular lattice, we got the exact solutions. For four particles of the Hubbard model in the triangular lattice we got the asymptotic solutions. We discuss the existing of the bound states in these solutions and the pairing symmetry of these bound states. For system with two-hole and one down-spin away from the all up spin background we also get a solution utilizing a large U expansion. We discussed the relation of this solution with the Nagaoka states. / Fan, Rui = 三角格子上磁性與超導的研究 / 樊睿. / "September 2007." / Adviser: Lin Hai Qing. / Source: Dissertation Abstracts International, Volume: 70-03, Section: B, page: 1719. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 83-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Fan, Rui = San jiao ge zi shang ci xing yu chao dao de yan jiu / Fan Rui.

Chu Lam Long. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaf 81). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- One-dimensional Open-ended Lattice --- p.3 / Chapter 2.1 --- Propagation rules --- p.3 / Chapter 2.2 --- Propagation velocity --- p.6 / Chapter 2.3 --- Propagation direction --- p.7 / Chapter 2.4 --- Number of visits --- p.11 / Chapter 2.5 --- Lattice pattern --- p.13 / Chapter 3 --- Statistical Behaviour of One-dimensional Open-ended Lattice --- p.15 / Chapter 3.1 --- Probability function of first visit --- p.15 / Chapter 3.2 --- Long-time large-distance behaviour of first visit probability func- tion --- p.22 / Chapter 3.3 --- Total probability function --- p.24 / Chapter 4 --- Simulation Results of One-dimensional Open-ended Lattice --- p.26 / Chapter 4.1 --- Number of visits --- p.26 / Chapter 4.2 --- Average propagation velocity --- p.29 / Chapter 4.3 --- Probability function of first visit --- p.32 / Chapter 4.4 --- Total probability function --- p.35 / Chapter 5 --- One-dimensional Periodic Lattice --- p.40 / Chapter 5.1 --- Periodic Boundary Condition --- p.41 / Chapter 5.2 --- Propagation direction --- p.42 / Chapter 5.3 --- Cycle of the particle --- p.42 / Chapter 5.4 --- Lattice pattern --- p.44 / Chapter 5.4.1 --- One cycle --- p.44 / Chapter 5.4.2 --- Two cycles --- p.51 / Chapter 5.5 --- Period of the system --- p.51 / Chapter 5.5.1 --- General case --- p.51 / Chapter 5.5.2 --- Lattices of alternating spin up and spin down --- p.52 / Chapter 5.6 --- Period of the particle --- p.53 / Chapter 5.7 --- Propagation velocity --- p.56 / Chapter 6 --- Statistical Behaviour of One-dimensional Periodic Lattice --- p.57 / Chapter 6.1 --- Average propagation velocity --- p.57 / Chapter 6.2 --- Probability function --- p.58 / Chapter 7 --- Simulation Results of One-dimensional Periodic Lattice --- p.63 / Chapter 7.1 --- Trajectory of the particle --- p.63 / Chapter 7.1.1 --- General case --- p.63 / Chapter 7.1.2 --- Lattices of alternating spin up and spin down --- p.64 / Chapter 7.2 --- Average propagation velocity --- p.67 / Chapter 7.3 --- Probability function of circular lattice --- p.69 / Chapter 7.4 --- Probability function of corresponding one-dimensional lattice --- p.71 / Chapter 8 --- Conclusion --- p.75 / Chapter A --- Generating function --- p.77 / Chapter B --- Discrete and integral transform --- p.78 / Chapter C --- Normal Distribution --- p.80 / Bibliography --- p.81

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Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Daniel J. Heinzen. Vita. Includes bibliographical references.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: David, Rosen; Committee Member: Chris, Paredis; Committee Member: Seung-Kyum, Choi/

The dynamics of non-interacting, ultracold alkali atoms in the presence of counter-propagating lasers (optical lattice systems) is considered theoretically. The center of mass motion of an atom is such a system can be described by an effective Hamiltonian of a relatively simple form. Modulation of the laser fields implies a parametric variation of the effective Hamiltonian's eigenvalue spectrum, under which avoided crossings may occur. We investigate two dynamical processes arising from these near-degeneracies, which can be manipulated to coherently control atomic motion. First, we demonstrate the mechanism for the chaos-assisted, or multiple-state, tunneling observed in recent optical lattice experiments. Second, we propose a new method for the coherent acceleration of lattice atoms using the techniques of stimulated Raman adiabatic passage (STIRAP). In each case we use perturbation analysis to show the existence of a small, few level, subsystem of the full effective Schrödinger equation that determines the dynamics. / text

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.