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Title:  Topics in the Theory of Quantum Degenerate Gases 
Author(s):  Lobo, Carlos Antonio Souza E. 
Doctoral Committee Chair(s):  Leggett, Anthony J. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Physics, Atomic 
Abstract:  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 BoseEinstein 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 spin1 ( 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 Nbody 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 GrossPitaevskii 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. 
Issue Date:  2001 
Type:  Text 
Language:  English 
Description:  151 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2001. 
URI:  http://hdl.handle.net/2142/80478 
Other Identifier(s):  (MiAaPQ)AAI3030456 
Date Available in IDEALS:  20150925 
Date Deposited:  2001 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois