Abstract: We discuss the time-dependent Gross-Pitaevskii (GP) approximation for interacting bosons in the Thomas-Fermi (TF) regime, i.e., for a mean-field interaction potential with shrinking support and whose scattering length diverges in the large N limit (but the gas remains dilute). Under these assumptions, the many-body Schrödinger dynamics is expected to be approximated by a one-particle nonlinear Schrödinger equation: the reliability of this approximation is the problem we plan to investigate. While the mean-field or GP limits have already been studied in detail, and the approximation proven to be correct on suitable time scales, the TF limit has never been studied, in spite of its large relevance in experimental physics. We show that the question of the dynamic approximation is more subtle in the TF regime, in particular at large time scales. The results are proven by exploiting the method developed by P. Pickl.
Joint work in progress with M. Correggi, D. Mitrouskas and P. Pickl.