Event

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

Event Date: Jul 12, 2024

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.