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I start by an update of vortices, as described by the Gross-Pitaevskii (GP) equation, explaining why there is room for new phenomena. I describe what a time crystal is in Hamiltonian context. Then, I show that minimal energy vortex solutions of GP equation are timecrystalline. Furthermore, I show that these vortices have anyonic exchange. I conclude with a topological analysis of multi-vortex systems and identify a topological phase transition akin the Kosterlitz-Thouless transition, using the Poincaré index formula. At the end, I very shortly comment on three imensional extensions such as closed and possibly knotted vortex lines.
Professor Antti J. Niemi received his Ph.D. degree in Theoretical High Energy Physics in 1983, from Department of Physics, Massachusetts Institute of Technology, Cambridge, USA. Currently, he is a tenured professor at the Nordic Institute for Theoretical Physics. He also holds professor positions at the Uppsala University and Beijing Institute of Technology and is the Directeur de Recherche (DR1), CNRS at the Institut Denis Poisson, Tours, France. He also held a number of professor and research positions in the USA, Brazil, Finland, and China. He collaborates with scientists worldwide. He is a member of Royal Society of Sweden (since 1994) and of the Finnish Society of Sciences and Letters (since 2000). He authored or co-authored 200 papers. Professor Niemi’s research interests concentrate on Mathematical Physics, from High Energy to Biological Physics. He developed a unique theory of protein folding, which is based on the concept of dark-soliton solutions of Discrete Nonlinear Schroedinger Equation. Recently he directed his interests towards time crystals, in which field he tightly collaborates with Professor Frank Wilczek, now a part-time Professor at Stockholm University.
Tencent Meeting link: https://meeting.tencent.com/dm/EbkEjJ1l5mSn Meeting ID: 703 713 951, no password