33 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
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