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Timecrystalline vortices, stagnation points and the Poincare Index Formula

组织者

李淇明

演讲者

Antti Niemi

时间

2024年11月28日 10:00 至 11:30

地点

A6-101

线上

Zoom 462 110 5973 (BIMSA)

摘要

Using the two dimensional Gross-Pitaevskii (a.k.a. nonlinear Schroedinger) equation as a concrete example, we explain the concepts of Hamiltonian time crystals and anyons. Specifically, we first review the phenomenology of the GP equation, the way it describes vortices in cold atom Bose-Einstein condensates. We then expand the conventional point of view, and show that the minimum energy states are time crystalline vortices. We proceed to show that their exchange statistics has anyon structure. We then identify a Kosterlitz-Thouless topological transition and explain how it can be analyzed using the Poincare index formula.