On the Gross-Pitaevskii equation for trapped dipolar quantum gases
R\'emi Carles (I3M), Peter Markowich (DAMTP), Christof Sparber (DAMTP)
TL;DR
This paper investigates the mathematical properties of the Gross-Pitaevskii equation for trapped dipolar quantum gases, focusing on existence, uniqueness, blow-up phenomena, and dimension reduction techniques.
Contribution
It provides new insights into the well-posedness and dimensional analysis of the nonlinear nonlocal Schrödinger equation modeling dipolar Bose-Einstein condensates.
Findings
Proved existence and uniqueness of solutions.
Analyzed conditions for solution blow-up.
Explored dimension-reduction methods.
Abstract
We study the time-dependent Gross-Pitaevskii equation describing Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension-reduction for this nonlinear and nonlocal Schrodinger equation.
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