40 research outputs found
Role of transverse excitations in the instability of Bose-Einstein condensates moving in optical lattices
The occurrence of energetic and dynamical instabilities in a Bose-Einstein
condensate moving in a one-dimensional (1D) optical lattice is analyzed by
means of the Gross-Pitaevskii theory. Results of full 3D calculations are
compared with those of an effective 1D model, the nonpolynomial Schrodinger
equation, pointing out the role played by transverse degrees of freedom. The
instability thresholds are shown to be scarcely affected by transverse
excitations, so that they can be accurately predicted by effective 1D models.
Conversely, transverse excitations turn out to be important in characterizing
the stability diagram and the occurrence of a complex radial dynamics above the
threshold for dynamical instability. This analysis provides a realistic
framework to discuss the dissipative dynamics observed in recent experiments.Comment: 9 pages, 11 figures; typos corrected, references updated, new Figure
Zeta-Function Regularization is Uniquely Defined and Well
Hawking's zeta function regularization procedure is shown to be rigorously
and uniquely defined, thus putting and end to the spreading lore about
different difficulties associated with it. Basic misconceptions,
misunderstandings and errors which keep appearing in important scientific
journals when dealing with this beautiful regularization method ---and other
analytical procedures--- are clarified and corrected.Comment: 7 pages, LaTeX fil
Explicit Zeta Functions for Bosonic and Fermionic Fields on a Noncommutative Toroidal Spacetime
Explicit formulas for the zeta functions corresponding to
bosonic () and to fermionic () quantum fields living on a
noncommutative, partially toroidal spacetime are derived. Formulas for the most
general case of the zeta function associated to a quadratic+linear+constant
form (in {\bf Z}) are obtained. They provide the analytical continuation of the
zeta functions in question to the whole complex plane, in terms of series
of Bessel functions (of fast, exponential convergence), thus being extended
Chowla-Selberg formulas. As well known, this is the most convenient expression
that can be found for the analytical continuation of a zeta function, in
particular, the residua of the poles and their finite parts are explicitly
given there. An important novelty is the fact that simple poles show up at
, as well as in other places (simple or double, depending on the number of
compactified, noncompactified, and noncommutative dimensions of the spacetime),
where they had never appeared before. This poses a challenge to the
zeta-function regularization procedure.Comment: 15 pages, no figures, LaTeX fil
Born-Oppenheimer Approximation near Level Crossing
We consider the Born-Oppenheimer problem near conical intersection in two
dimensions. For energies close to the crossing energy we describe the wave
function near an isotropic crossing and show that it is related to generalized
hypergeometric functions 0F3. This function is to a conical intersection what
the Airy function is to a classical turning point. As an application we
calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette
The Born Oppenheimer wave function near level crossing
The standard Born Oppenheimer theory does not give an accurate description of
the wave function near points of level crossing. We give such a description
near an isotropic conic crossing, for energies close to the crossing energy.
This leads to the study of two coupled second order ordinary differential
equations whose solution is described in terms of the generalized
hypergeometric functions of the kind 0F3(;a,b,c;z). We find that, at low
angular momenta, the mixing due to crossing is surprisingly large, scaling like
\mu^(1/6), where \mu is the electron to nuclear mass ratio.Comment: 21 pages, 7 figure