Bose-Einstein condensation and probabilistic methods for the nonlinear Schrödinger equation

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• Kay Kirkpatrick (Paris IX Dauphine, Urbana-Champaign)
• Monday 22 November 2010, 16:00-17:00
• CMS, MR5.

If you have a question about this talk, please contact Prof. Mihalis Dafermos.

Near absolute zero, a gas of quantum particles can condense into an unusual state of matter, called Bose-Einstein condensation, that behaves like a giant quantum particle. Recently we’ve been able to make the rigorous probabilistic connection between the physics of the microscopic dynamics and the mathematics of the macroscopic model, the cubic nonlinear Schrödinger equation (NLS).

I’ll discuss new work with Sourav Chatterjee about a phase transition for invariant measures of the focusing NLS . Using techniques from probability theory, we show that the thermodynamics of the NLS are exactly solvable in dimensions three and higher. A number of explicit formulas are derived, with implications for some open questions about blow-up and statistical mechanics of the NLS .

This talk is part of the Partial Differential Equations seminar series.

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