This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/31325
Description
Title
Topics in the theory of quantum degenerate gases
Author(s)
Lobo, Carlos Antonio Souza E.
Issue Date
2001
Doctoral Committee Chair(s)
Leggett, Anthony J.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
quantum degenerate particles
Bose-Einstein condensation
Language
en
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 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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
