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

Abstract

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|.

23 pages, no figures

References in corpus (5)

• Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
• Rigorous Derivation of the Gross-Pitaevskii Equation
• Observation of Strong Quantum Depletion in a Gaseous Bose-Einstein Condensate
• Elementary excitations in trapped Bose gases beyond mean field approximation
• The Mathematics of the Bose Gas and its Condensation

Cited by in corpus (2)

• Second-order corrections to mean field evolution for weakly interacting Bosons. I
• Pair excitations and the mean field approximation of interacting Bosons, I