Seminar Talk - An effective equation to study Bose gases at all densities

Mathematical and Theoretical Physics Seminar (MTPS):

An effective equation to study Bose gases at all densities

Ian Jauslin (Princeton University)

Abstract: I will discuss an effective equation, which is used to study the ground state of the interacting Bose gas. The interactions induce many-body correlations in the system, which makes it very difficult to study, be it analytically or numerically. A very successful approach to solving 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. 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 at high densities. I will show some theorems which make this statement more precise, and present numerical evidence that this effective equation is remarkably accurate for all densities, small, intermediate, and large. That is, the analytical and numerical evidence suggest that this effective equation can capture many-body correlations in a one-particle picture beyond what Bogolubov 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). In addition, it opens an avenue to understand the physics of the Bose gas at intermediate densities, which, until now, were only accessible to Monte Carlo simulations.

Please note the unusual time of this lecture! April 1, 2021, 16:00-17:00 (online)

Talks organized by Stefan Kettemann, Sören Petrat, and Peter Schupp

Usual time: Thursdays, 13:00-14:00

Location: for most of the semester the seminar will be online (access data will be sent around to the mailing list shortly before the talks; please write an email to Sören Petrat (s.petrat@jacobs-university.de) for the access data to specific talks or to be added to the mailing list).
All times are German time zone.