Solvable model for pair excitation in trapped Boson gas at zero temperature

Details Solvable model for pair excitation in trapped Boson gas at zero temperature Solvable model for pair excitation in trapped Boson gas at zero temperature

2007-09-17

arxiv.org/abs/0709.2645v1

Physics

Mathematical Physics

23 pages, no figures

Scientific paper

10.1088/1751-8113/41/38/385002

In Bose-Einstein condensation, a macroscopically large number of particles occupy the same single-particle quantum state. Our goal is to study time-dependent aspects of particle excitations to states other than the single-particle macroscopic state in trapped dilute atomic gases. We adopt the view that atoms are excited in pairs so that their scattering from the single-particle state to vector positions x and y at time t is described by the pair-excitation function, K0(x,y,t). We solve a nonlocal equation for K0 under a slowly varying external potential by assuming that the wave function of the macroscopic state satisfies a time-independent nonlinear Schroedinger equation. For zero initial excitation (K0=0 at t=0) and sufficiently large t, we evaluate asymptotically K0 in terms of the one-variable Lommel function for any distance |x-y|.

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