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Leggett, Anthony J. Lobo, Carlos Antonio Souza E. 2012-06-04T16:31:37Z 2012-06-04T16:31:37Z 10000-01-01 2001 This thesis is comprised of four separate parts: in the first we calculate the second and third virial coefficients of 3He and 4He at low temperatures with an empirical interatomic potential by Janzen and Aziz and using the Path Integral Monte Carlo (PIMC) technique. We show that, for the calculation of the second coefficient, the method is successful whereas for the third the particular implementation that we chose (free particle sampling) is not sufficient to produce reliable results at low temperatures. In the second part we consider the Josephson Effect between two spatially separated Bose-Einstein condensates of atoms each of which can be in two hyperfine states. We derive simple equations of motion for this system closely analogous to the Bloch equations. We also map the dynamics of the system onto those of a classical particle in a well. We find novel density and spin modes of oscillation and new stable equilibrium points of the motion. Finally we analyze the oscillation modes in the spin-1 (F = 1) case. In the third part of the thesis we propose a powerful method to study the time evolution of Bose condensed gases perturbed from an initial thermal equilibrium, based on the Wigner representation of the N-body density operator. We show how to generate an ensemble of random classical fields sampling the initial Wigner distribution in the number conserving Bogoliubov approximation. The fields are then evolved with the time dependent Gross-Pitaevskii equation. We illustrate the method with the damping of a collective excitation of a one dimensional Bose gas. The fourth part deals with inhomogeneous superconductivity in the presence of magnetic fields that couple only to the spin and not to the orbital motion. They induce a splitting of the Fermi surfaces of up and down spins. We start by considering a one dimensional system and explicitly write down the wavefunction that pairs states with unequal energies due to the splitting. Next we consider an extension to three dimensions and work out explicitly certain aspects of the crossover from one to two dimensions. We then discuss the relationship of this state with those of Fulde, Ferrell, Larkin and Ovchinnikov. Finally, we consider an extension to the case of a paired state which has a gap with a spherically symmetric spatial dependence. Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T16:31:37Z No. of bitstreams: 1 2001_souzaelobo.pdf: 4461848 bytes, checksum: dd37d65cdccd5ee5e96ba48e7ad9c960 (MD5) Made available in DSpace on 2012-06-04T16:31:37Z (GMT). No. of bitstreams: 1 2001_souzaelobo.pdf: 4461848 bytes, checksum: dd37d65cdccd5ee5e96ba48e7ad9c960 (MD5) Previous issue date: 2001 Restriction data tranferred 2014-07-01T11:11:21-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T16:31:37Z Item is restricted indefinitely. thesis U of I Only 4555039 http://hdl.handle.net/2142/31325 en ©2001 Carlos António Souza e Lobo quantum degenerate particles Bose-Einstein condensation Topics in the theory of quantum degenerate gases Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.