Hannover 2003 – wissenschaftliches Programm

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A: Atomphysik

A 17: Postersitzung 2

A 17.32: Poster

Donnerstag, 27. März 2003, 16:00–18:30, Poster

Levinson’s relation for a Bose-Einstein condensate — •Ivo Häring, Joachim Brand, and Jan-Michael Rost — Max-Planck-Institute for the Physics ot Complex Systems Dresden

The Hartree-Fock-Bogoliubov equations [1] reduce for a spherically symmetric potential to two coupled radial equations for the quasi-particle modes. For a finite potential which allows bound states as well as continuum states [2] we numerically find that the phase shift of the free quasi-particle mode counts the number of bound states for each angular momentum.

A contour integration with respect to the momentum of the free quasi-particle mode allows us to connect the phase shift with the number of bound states similarly as from the Levinson’s theorem in the multi-channel scattering problem [3].

[1] A. Griffin Phys. Rev. B 53 9341 (1996), [2] A. Wynveen et al. Phys. Rev. A 62 023602 (2000), [3] W. Glöckle Z. Physik 190 391 (1966)