# 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.