4 research outputs found
The generalized MIC-Kepler system
This paper deals with dynamical system that generalizes the MIC-Kepler
system. It is shown that the Schr\"{o}dinger equation for this generalized
MIC-Kepler system can be separated in spherical and parabolic coordinates. The
spectral problem in spherical and parabolic coordinates is solved.Comment: 8 page
On two superintegrable nonlinear oscillators in N dimensions
We consider the classical superintegrable Hamiltonian system given by
, where U
is known to be the "intrinsic" oscillator potential on the Darboux spaces of
nonconstant curvature determined by the kinetic energy term T and parametrized
by {\lambda}. We show that H is Stackel equivalent to the free Euclidean
motion, a fact that directly provides a curved Fradkin tensor of constants of
motion for H. Furthermore, we analyze in terms of {\lambda} the three different
underlying manifolds whose geodesic motion is provided by T. As a consequence,
we find that H comprises three different nonlinear physical models that, by
constructing their radial effective potentials, are shown to be two different
nonlinear oscillators and an infinite barrier potential. The quantization of
these two oscillators and its connection with spherical confinement models is
briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60
years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics,
quantization and related topics" hold in Valladolid (Spain), 14-16th july
201
Density correlations and dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates
We present a theory of the density correlations that appear in an atomic
Bose-Einstein condensate as a consequence of the dynamical Casimir emission of
pairs of Bogoliubov phonons when the atom-atom scattering length is modulated
in time. Different regimes as a function of the temporal shape of the
modulation are identified and a simple physical picture of the phenomenon is
discussed. Analytical expressions for the density correlation function are
provided for the most significant limiting cases. This theory is able to
explain some unexpected features recently observed in numerical calculations of
Hawking radiation from analog black holes