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SUMMARY:Gibbs Measures of Nonlinear Schrödinger Equations and Many-Body Q
 uantum Mechanics
DTSTART:20190503T141500
DTSTAMP:20260928T194117Z
UID:c7b90c09f5294241c857a59dc9ed20189333c21316f721441019527b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Antti KNOWLES\, University of Geneva\nAbstract:\nMany ti
 me-dependent nonlinear Schrödinger equations admit an invariant Gibbs mea
 sure\, which is a probability measure on the space of distributions that i
 s left invariant by the time evolution. Such measures have been extensivel
 y studied as tool to construct global solutions of time-dependent nonlinea
 r Schrödinger equations with rough initial data. I review some recent pro
 gress on deriving these measures in dimensions 1\,2\,3 as high-temperature
  limits of many-body quantum mechanics. In one dimension\, I also explain 
 how time-dependent correlation functions of the nonlinear Schrödinger equ
 ation arise as limits of corresponding quantum many-body correlation funct
 ions.
LOCATION:MA B1 11 https://plan.epfl.ch/?room=MAB111
STATUS:CONFIRMED
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