Bosons in a Trap: Asymptotic Exactness of the GrossPitaevskii Ground State Energy Formula
Abstract
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in external potentials and interacting via repulsive short range forces are usually described by means of the GrossPitaevskii energy functional. In joint work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for the quantum mechanical manybody ground state problem has recently been rigorously clarified. We present a summary of this work, for both the two and threedimensional case.
 Publication:

arXiv eprints
 Pub Date:
 October 2000
 arXiv:
 arXiv:mathph/0010006
 Bibcode:
 2000math.ph..10006S
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Primary 81V70;
 Secondary 35Q55;
 46N50
 EPrint:
 For the proceedings of the International Conference on Partial Differential Equations, Clausthal, July 2428, 2000