Trends in resonance energy shifts and decay rates for Bose condensates in a harmonic trap - art. no. 013613

This is a study of quasidiscrete Bogoliubov quasiparticles in a spherically symmetric harmonic trap. We first evaluate analytically the aymptotic ener gy shifts of the high-energy modes and find them to have 1/rootn dependence on the number of radial nodes n, consistent with earlier semiclassical dis cussions. To address the question of the widths or decay rates gamma, we at tempt to clarify previous discussions by deriving an implicit equation for gamma from an assumption of exponential decay. Numerically, we study the tr ends in the behavior of the widths as a function of temperature, energy, pa rticle number, and scattering lengths. In particular, we find that the widt h due to Landau decay rises rapidly at low n and then declines, while the B eliaev decay rate rises slowly with n. As temperature -->0, Beliaev decay r eaches a constant (greater than 0 for n>0), while the Landau decay rate goe s to zero. The decay rate gamma is approximately linear in the s-wave scatt ering length.