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SUMMARY:Bose-Einstein condensation and probabilistic methods for the nonli
 near Schrödinger equation - Kay Kirkpatrick (Paris IX Dauphine\, Urbana-C
 hampaign)
DTSTART:20101122T160000Z
DTEND:20101122T170000Z
UID:TALK28025@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:Near absolute zero\, a gas of quantum particles can condense i
 nto an unusual state of matter\, called Bose-Einstein condensation\, that 
 behaves like a giant quantum particle. Recently we've been able to make th
 e rigorous probabilistic connection between the physics of the microscopic
  dynamics and the mathematics of the macroscopic model\, the cubic nonline
 ar Schrödinger equation (NLS).\n\nI'll discuss new work with Sourav Chatt
 erjee about a phase transition for invariant measures of the focusing NLS.
  Using techniques from probability theory\, we show that the thermodynamic
 s of the NLS are exactly solvable in dimensions three and higher. A number
  of explicit formulas are derived\, with implications for some open questi
 ons about blow-up and statistical mechanics of the NLS.\n\n\n\n
LOCATION:CMS\, MR5
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