Pong, Yue Hin = 超低溫費米氣體中的對關聯粒子 / 龐宇軒. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 77-81). / Text in English, abstracts in English and Chinese. / Pong, Yue Hin = Chao di wen fei mi qi ti zhong de dui guan lian li zi / Pang Yuxuan. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review on BCS theory --- p.4 / Chapter 2.1 --- BCS in uniform gas --- p.4 / Chapter 2.2 --- Hartree Fock Bogoliubov equations --- p.7 / Chapter 2.3 --- Regularization techniques --- p.13 / Chapter 2.4 --- Homogeneous solution to HFB --- p.15 / Chapter 3 --- HFB Computation --- p.17 / Chapter 3.1 --- Example: 1D infinite well --- p.18 / Chapter 3.2 --- Example: 1D SHO --- p.22 / Chapter 3.3 --- Example: Spherical harmonic oscillator --- p.23 / Chapter 3.4 --- Conclusion --- p.26 / Chapter 4 --- Natural Orbits --- p.28 / Chapter 4.1 --- Two-point correlation functions --- p.29 / Chapter 4.2 --- Connection with the BCS --- p.32 / Chapter 4.3 --- Natural orbits in a spherical harmonic potential --- p.33 / Chapter 4.4 --- Remarks --- p.38 / Chapter 5 --- Bosonic characters of atomic Cooper pairs across resonance --- p.43 / Chapter 5.1 --- Resonance in Fermi gas --- p.44 / Chapter 5.2 --- Bosonic tests --- p.50 / Chapter 5.3 --- Choosing a Cooper pair wave function --- p.52 / Chapter 5.3.1 --- Cooper pair I --- p.52 / Chapter 5.3.2 --- Cooper pair II --- p.55 / Chapter 5.4 --- Results in a uniform gas --- p.55 / Chapter 5.5 --- Remark --- p.61 / Chapter 6 --- Time dependent BCS: A numerical study --- p.63 / Chapter 6.1 --- Time evolution in uniform BCS --- p.64 / Chapter 6.2 --- Perturbation to interaction strength --- p.66 / Chapter 6.2.1 --- Sudden decrease in the interaction strength --- p.66 / Chapter 6.2.2 --- Sinusoidal variation of interaction strength --- p.68 / Chapter 6.2.3 --- A decaying energy gap --- p.69 / Chapter 6.3 --- Perturbation to particle numbers --- p.71 / Chapter 6.4 --- Remarks --- p.74 / Chapter 7 --- Summary and Outlook --- p.75 / Chapter 7.1 --- Outlook --- p.75 / Bibliography --- p.77 / Chapter A --- Analytic solutions to homogeneous BCS --- p.82 / Chapter B --- Local Density Approximation (LDA) --- p.84 / Chapter B.1 --- One dimensional LDA --- p.85 / Chapter C --- Finding the regularized Green's Function --- p.87 / Chapter D --- Variational approach to finding natural orbits --- p.90 / Chapter D.1 --- Variation with respect to natural orbits --- p.90 / Chapter D.2 --- Variation with respect to the occupation amplitude --- p.93

Thesis (Ph. D.)--University of Washington, 2008. / Vita. Includes bibliographical references (p. 82-91).

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A dissertation submitted in fulfillment of the requirements for the degree of Master of Science in Physics at the University of the Witwatersrand. November 7th, 2016 / The spin-1=2 Kondo model describes an antiferromagnetic exchange interaction between an impurity spin and the spin-density of a Fermi gas. Although the thermodynamics of this system have been resolved, there are still some unanswered questions regarding its spatial features. The spatial region of correlation between the impurity spin and the spin-density of the Fermi gas is referred to as the Kondo screening cloud. For the case of anisotropic couplings, the cloud consists of four distinct components. In this dissertation we use the bosonization technique to derive both an exact numeric and an approximate analytic expression for the forward scattering longitudinal cloud at the Toulouse point. The expressions are then extended to incorporate the effects of a time-independent external magnetic field. The non-magnetic case displays universal scaling behavior, while the addition of an external magnetic field only slightly spoils the scaling in the vicinity of the crossover length (B) K , but remarkably not deep inside or outside the cloud. / MT2017

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Immersion energies for an impurity in a homogeneous electron gas with a uniform positive background charge density have been calculated numerically using density functional theory. The numerical aspects of this problem are very demanding and have not been properly discussed in previous work. The numerical problems are related to approximations of infinity and continuity, and they have been corrected using physics based on the Friedel sum rule and Friedel oscillations. The numerical precision is tested extensively. Immersion energies are obtained for non-spin-polarized systems, and are compared with published data. Numerical results, such as phase shifts, density of states, dielectric constants, and compressibilities, are obtained and compared with analytical theories. Immersion energies for excited systems are obtained by varying the number of electrons in the bound states of an impurity. The model is extended to spin-polarized systems and is tested in detail for a carbon impurity. The spin-coupling with an external magnetic field is considered mainly for a hydrogen impurity. These new results show very interesting behavior at low densities. / Graduation date: 2005

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