偏微分方程式セミナー: Standing waves for the Anderson-Gross-Pitaevskii equation in dimension 1 and 2, Pierre Mackowiak 氏

Time：16:30-17:30

Place：理学部4号館4-501室 (hybrid)

Organizer：黒田 紘敏、浜向 直

Speaker：Pierre Mackowiak 氏 (エコール・ポリテクニーク)

Title：Standing waves for the Anderson-Gross-Pitaevskii equation in dimension 1 and 2

Abstract：The Gross-Pitaevskii equation is a non-linear Schrödinger equation with confining potential that appears in the study of Bose-Einstein condensate. Adding a random potential to this equation is a way to model spatial inhomogeneities during the condensation process. With this in mind, the Anderson-Gross-Pitaevskii, that is the Gross-Pitaevskii with a spatial white noise potential, can be seen as a toy model for spatial inhomogeneities with small correlation length.
In this talk, I will briefly present the outline of the construction of the Anderson-Hermite operator and some of its spectral properties. Then, I will sum up some of the known results on standing waves of the Anderson-Gross-Pitaevskii equation in dimension 1: existence, regularity, localization, stability, bifurcation. I will finish by presenting what is known for 2d standing waves and what still needs to be investigated. This talk is based on an ongoing work.