10 research outputs found
Functional determinants for general Sturm-Liouville problems
Simple and analytically tractable expressions for functional determinants are
known to exist for many cases of interest. We extend the range of situations
for which these hold to cover systems of self-adjoint operators of the
Sturm-Liouville type with arbitrary linear boundary conditions. The results
hold whether or not the operators have negative eigenvalues. The physically
important case of functional determinants of operators with a zero mode, but
where that mode has been extracted, is studied in detail for the same range of
situations as when no zero mode exists. The method of proof uses the properties
of generalised zeta-functions. The general form of the final results are the
same for the entire range of problems considered.Comment: 28 pages, LaTe
Multiply-connected Bose-Einstein condensed alkali gases: Current-carrying states and their decay
The ability to support metastable current-carrying states in
multiply-connected settings is one of the prime signatures of superfluidity.
Such states are investigated theoretically for the case of trapped Bose
condensed alkali gases, particularly with regard to the rate at which they
decay via thermal fluctuations. The lifetimes of metastable currents can be
either longer or shorter than experimental time-scales. A scheme for the
experimental detection of metastable states is sketched.Comment: 4 pages, including 1 figure (REVTEX
Regularization of functional determinants using boundary perturbations
The formalism which has been developed to give general expressions for the
determinants of differential operators is extended to the physically
interesting situation where these operators have a zero mode which has been
extracted. In the approach adopted here, this mode is removed by a novel
regularisation procedure, which allows remarkably simple expressions for these
determinants to be derived