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On the Gross–Pitaevskii equation for trapped dipolar quantum gases

Rémi Carles1, Peter A Markowich2 and Christof Sparber2

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Recommended by C P Dettmann

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 Schrödinger equation.


PACS

03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow

05.30.Jp Boson systems

37.10.De Atom cooling methods

03.65.Ge Solutions of wave equations: bound states

MSC

82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

Subjects

Atomic and molecular physics

Quantum gases, liquids and solids

Quantum information and quantum mechanics

Statistical physics and nonlinear systems

Dates

Issue 11 (November 2008)

Received 5 May 2008, in final form 19 August 2008

Published 29 September 2008



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