Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states

Abstract: Gibbs measures of nonlinear Schr¨odinger equations are a fundamental object used to\nstudy low-regularity solutions with random initial data. In the dispersive PDE community,\nthis point of view was pioneered by Bourgain in the 1990s. We study the problem of the\nderivation of Gibbs measures as mean-field limits of Gibbs states in many-body quantum\nmechanics.\nWe present two approaches to this problem. The first one is based on a perturbative\nexpansion in the interaction. This expansion is then analysed by means of Borel resummation techniques and a graphical representation. The second approach is based on a\nfunctional integral representation. The latter can be interpreted as a rigorous version of\nan infinite-dimensional stationary phase argument. This is joint work with J¨urg Fr¨ohlich,\nAntti Knowles, and Benjamin Schlein.

analysis of PDEs

Audience: researchers in the topic

MIT PDE/analysis seminar spring 2020

Series comments: At the time of adding this to mathseminars.org, 7 talks had already taken place. Check the website for details and abstracts math.mit.edu/seminars/pde-analysis/

Not publicly viewable (Zoom room needs a password).