Approximate Solutions of the Nonlinear Schrödinger Equation for Ground and Excited States of Bose-Einstein Condensates.
I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths,a, and find an analytical expression for the large-N0limit of the vortex critical frequency fora> 0, by approximate solution of the time-independent nonlinear Schrödinger equation.
National Institute of Standards and Technology, Gaithersburg, MD 20899-0001.
R J
RJ
Dodd
Bose-Einstein condensation; Ginzburg-Pitaevskii-Gross energy functional; Gross-Pitaevskii equation; Thomas-Fermi functional model; mean-field theory; superfluidity; time-independent nonlinear Schrödinger equation; variational wave function; vortex formation