A simple model for interactions and corrections to the Gross-Pitaevskii Equation

One of the assumptions leading to the Gross-Pitaevskii Equation (GPE) is that the interaction between atom pairs can be written effectively as a \delta -function so that the interaction range of the particles is assumed to vanish. A simple model that takes into account the extension of the inter-particle potential is introduced. The correction to the GPE predictions for the energy of a condensate confined by a harmonic trap in the Thomas-Fermi (TF) regime is estimated. Although it is found to be small, we believe that in some situations it can be measured using its dependance on the frequency of the confining trap. Due to the simplicity of the model, it may have a wide range of applications.Comment: 22 pages, 2 figure

Edge states of a three dimensional kicked rotor

Edge localization is a fascinating quantum phenomenon. In this paper, the underlying mechanism generating it is presented analytically and verified numerically for a weakly kicked three-dimensional rotor. Analogy to tight binding model in solid state physics is used. The edge states result of the edge at zero angular momentum of the three-dimensional kicked rotor.Comment: 16 pages, 3 figure