Seminars & Colloquia Calendar
Analysis of a non-linear, non-local PDE to study Bose gases at all densities
Ian Jauslin, Princeton University
Date & time: Wednesday, 16 December 2020 at 3:30PM - 4:30PM
In this talk, I will discuss a partial differential equation that arises in the study of interacting systems of Bosonic particles. This equation arises in the study of interacting systems of Bosonic particles. The non-linearity and non-locality of the self-convolution term and of the multiplication by e make this equation rather difficult to study. I will first introduce a set of tools that have allowed us to prove a number of properties of this equation, which we have shown to be relevant to our understanding of the interacting Bose gas. In particular, the solution to this equation is shown to make accurate predictions for various physical observables of the Bose gas both when the particle density is low, and when it is high. Until now, the only means to accomplish this was to carry out difficult and computationally intensive numerical computations.