Events for 11/30/2020 from all calendars

Colloquium - Ian Jauslin

Time: 1:00PM - 2:00PM

Location: Zoom

Speaker: Ian Jauslin, Princeton University

Description:
Title: An effective equation to study Bose gases at all densities
Abstract: I will discuss an effective equation, which is used to study the ground state of an interacting system of Bosonic particles. The interactions induce many-body correlations in the system, which makes it very difficult to study, be it analytically or numerically. This system has been the focus of much research in the past twenty years, and yet some of the fundamental questions about it are still open. For instance, there still is no proof of the emergence of a Bose-Einstein condensate at finite density. A very successful approximate approach to this problem is Bogolubov theory, in which a series of approximations are made after which the analysis reduces to a one-particle problem, which incorporates the many-body correlations. The effective equation I will discuss is arrived at by making a very different set of approximations, and, like Bogolubov theory, ultimately reduces to a one-particle problem, in the form of a non-linear and non-local partial differential equation in three dimensions. But, whereas Bogolubov theory is accurate only for very small densities, the effective equation coincides with the many-body Bose gas at both low and high densities. I will discuss some recent results which make this statement more precise, and present numerical evidence that this effective equation is remarkably accurate for all densities, small, intermediate, and large. In other words, the analytical and numerical evidence suggest that this effective equation can capture many-body correlations in a one-particle picture beyond what Bogolubov theor can accomplish. Thus, this effective equation gives an alternative approach to study the low density behavior of the Bose gas, about which there still are many important open questions, such us Bose-Einstein Condensation. In addition, it opens an access to properties of the Bose gas at intermediate densities, which, until now, were only accessible to MC simulations.