All ETDs from UAB

Advisory Committee Chair

Christian Hainzl

Advisory Committee Members

Kenneth B Howell

Ryoichi Kawai

Junfang Li

Tavan Trent

Document Type

Dissertation

Date of Award

2010

Degree Name by School

Doctor of Philosophy (PhD) College of Arts and Sciences

Abstract

We present a rigorous analysis of the Bardeen-Cooper-Schrieer (BCS) functional for asymmetric fermionic systems with general pair interaction potentials. We relate the existence of a non-trivial solution to the non-linear BCS gap equation to the spectrum of certain linear operators. In addition, we derive upper and lower bounds on the asymptotic behavior of the critical temperature and energy gap (at zero temperature) for the BCS gap equation, describing asymmetric fermions interacting via a two-body interaction potential \lambdaV , in the small coupling limit. Our results hold for all values of the chemical potential.

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