Dynamics of matter waves in Bose-Einstein condensates
Abstract:
Since their experimental realization in 1995 (leading to the Nobel Prize in Physics), there has been a great deal of theoretical interest and experimental interest in Bose-Einstein condensates. From a theoretical point of view the governing Gross-Pitaevski equations are attractive to study because they are similar to the familiar nonlinear Schrodinger equation (NLS), and yet they possess a term (the trapping potential) which destroys the integrability (but not the Hamiltonian structure) associated with the NLS. The trapping potential is experimentally tunable and can be used to change not only the spatial dimension associated with the problem, but also the inherent physical symmetries. I will present some recent mathematical results which help to better understand the dynamics associated with matter waves in BECs. The ideas are general, and the results can also be used to study, e.g., the dynamics of periodic waves to generalized KdV. The work is joint with R. Carretero, P. Kevrekidis and M. Haragus.
Applied Mathematics Seminar