SIAM-UW Seminar Series

Date: 11/17/05, 4:30 PM, AMATH Library

Speaker:  Brandon Bale, Applied Mathematics

Title:	Nonlocality in Bose-Einstein Condensates


Abstract:

In all applications where the nonlinear Schrodinger equation is relevant, 
it arises as a simplified model of a nonlocal description.  For a 
Bose-Einstein Condensate (BEC), a derivation of the ground state using a 
simplified mean-field description reveals a nonlocal equation that is a 
perturbation of the familiar Gross-Pitaevskii equation.  The modulational 
instability of plane wave solutions of the nonlocal Gross-Pitaevskii 
equation without external potential is examined.  The nature of the 
instabilities is characterized by the Fourier transform of the interaction 
potential and the amplitude of the plane wave solution.  If the typical 
width of the atomic interaction potential is small, a moment expansion may 
be used to obtain a local approximation.  This classical approximation is
examined and shown to lead to ill-posed models in some cases.