1202.4801 (R. Cabrera-Trujillo et al.)

Scaling laws for the non-linear coupling constant of a Bose-Einstein
condensate at the threshold of delocalization    [PDF]

R. Cabrera-Trujillo, M. W. J. Bromley, B. D. Esry

We explore the localization of a quasi-one-, quasi-two-, and
three-dimensional ultra-cold gas by a finite-range defect along the
corresponding 'free'-direction/s. The time-independent non-linear Schroedinger
equation that describes a Bose-Einstein condensate was used to calculate the
maximum non-linear coupling constant, g_max, and thus the maximum number of
atoms, N_max, that the defect potential can localize. An analytical model,
based on the Thomas-Fermi approximation, is introduced for the wavefunction. We
show that g_max becomes a function of R_0 sqrt(V_0) for various one-, two-, and
three-dimensional defect shapes with depths V_0 and characteristic lengths R_0.
Our explicit calculations show surprising agreement with this crude model over
a wide range of V_0 and R_0. A scaling rule is also found for the wavefunction
for the ground state at the threshold at which the localized states approach
delocalization. The implication is that two defects with the same product R_0
sqrt(V_0) will thus be related to each other with the same g_max and will have
the same (reduced) density profile in the free-direction/s.

View original: http://arxiv.org/abs/1202.4801