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Displaying similar documents to “Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation”

On the Ginzburg-Landau and related equations

Yu N. Ovchinnikov, Israel Michael Sigal (1997-1998)

Séminaire Équations aux dérivées partielles

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We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture...

Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations

Jakob Yngvason (2008-2009)

Séminaire Équations aux dérivées partielles

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One of the most interesting phenomena exhibited by ultracold quantum gases is the appearance of vortices when the gas is put in rotation. The talk will bring a survey of some recent progress in understanding this phenomenon starting from the many-body ground state of a Bose gas with short range interactions. Mathematically this amounts to describing solutions of a linear Schrödinger equation with a very large number of variables in terms of a nonlinear equation with few variables and...