64 research outputs found
Bose-Einstein condensation of atomic gases in a harmonic oscillator confining potential trap
We present a model which predicts the temperature of Bose-Einstein
condensation in atomic alkali gases and find excellent agreement with recent
experimental observations. A system of bosons confined by a harmonic oscillator
potential is not characterized by a critical temperature in the same way as an
identical system which is not confined. We discuss the problem of Bose-Einstein
condensation in an isotropic harmonic oscillator potential analytically and
numerically for a range of parameters of relevance to the study of low
temperature gases of alkali metals.Comment: 11 pages latex with two postscript figure
The Hahn Quantum Variational Calculus
We introduce the Hahn quantum variational calculus. Necessary and sufficient
optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange
problems, are studied. We also show the validity of Leitmann's direct method
for the Hahn quantum variational calculus, and give explicit solutions to some
concrete problems. To illustrate the results, we provide several examples and
discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted:
18/June/2010; for publication in Journal of Optimization Theory and
Application
Casimir Energies for Spherically Symmetric Cavities
A general calculation of Casimir energies --in an arbitrary number of
dimensions-- for massless quantized fields in spherically symmetric cavities is
carried out. All the most common situations, including scalar and spinor
fields, the electromagnetic field, and various boundary conditions are treated
with care. The final results are given as analytical (closed) expressions in
terms of Barnes zeta functions. A direct, straightforward numerical evaluation
of the formulas is then performed, which yields highly accurate numbers of, in
principle, arbitrarily good precision.Comment: 18 pages, LaTeX, sub. Ann. Phy
p-form spectra and Casimir energies on spherical tesselations
Casimir energies on space-times having the fundamental domains of
semi-regular spherical tesselations of the three-sphere as their spatial
sections are computed for scalar and Maxwell fields. The spectral theory of
p-forms on the fundamental domains is also developed and degeneracy generating
functions computed. Absolute and relative boundary conditions are encountered
naturally. Some aspects of the heat-kernel expansion are explored. The
expansion is shown to terminate with the constant term which is computed to be
1/2 on all tesselations for a coexact 1-form and shown to be so by topological
arguments. Some practical points concerning generalised Bernoulli numbers are
given.Comment: 43 pages. v.ii. Puzzle eliminated, references added and typos
corrected. v.iii. topological arguments included, references adde
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