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Mathematical Physics Seminar

Derivation of 1d and 2d Gross-Pitaevskii equations for strongly confined 3d bosons

Lea Bossmann - University of Tübingen

Location:  Hill 705
Date & time: Thursday, 31 October 2019 at 2:00PM - 3:00PM

Abstract:   We study the dynamics of a system of N interacting bosons in a cigar- or disc-shaped trap, which initially exhibit Bose--Einstein condensation and interact via a non-negative interaction potential in the Gross--Pitaevskii scaling regime. The trap is realized by an external potential, which confines the bosons in two/one spatial dimensions to a region of order \(\varepsilon\). We study the simultaneous limit \((N,\varepsilon)\to(\infty,0)\) and show that the N-body dynamics preserve condensation. The time-evolved condensate wave function is the solution of a one/two-dimensional Gross--Pitaevskii equation.

This is based on joint work with Stefan Teufel.

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