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Blow up of mechanical systems with a homogeneous energy.

Ernesto A. Lacomba, John Bryant, Luis Alberto Ibort (1991)

Publicacions Matemàtiques

By using the ideas introduced by McGehee in the study of the singularities in some problems of Celestial Mechanics, we study the singularities at the origin and at the infinity for some classical mechanical systems with homogeneous kinetic and potential energy functions. For these systems the origin and the infinity of the configuration coordinates is usually a singularity or a nullity of the Hamiltonian function and the verctor field. This work generalizes a previous one by the first and the third...

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

Jakob Yngvason (2008/2009)

Séminaire Équations aux dérivées partielles

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 analyzing the...

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