勷勤数学•专家报告

题      目：Dimensional reduction for anyons in the average-field approximation

报  告  人：杨绮云 博士  (邀请人：徐欣)

                                             Basque Center for Applied Mathematics (BCAM)

时      间： 12月18日  15：30-16:30

地     点：数科院东楼401

报告人简介:

          杨绮云现为西班牙毕尔巴鄂巴斯克应用数学中心（Basque Center for Applied Mathematics, BCAM）博士后研究员，博士毕业于法国里昂高等师范学校（École normale supérieure de Lyon）。其主要研究方向为与任意子（anyons）相关的偏微分方程问题，涵盖多体量子系统、Chern–Simons–Schrödinger方程以及不同数学模型之间的联系；同时研究费米子系统，涉及Hartree–Fock方程、Lipkin模型等。目前已在Annales Henri Poincaré等国际学术期刊发表论文三篇。

摘      要：

        We study Abelian anyons at the mean-field/almost-bosonic level, whose dynamics are governed by the Chern–Simons–Schrödinger system. We consider the dimensional reduction of this 2D model by introducing an anisotropic trapping potential and derive an effective 1D model after tracing out the tightly confined direction, whose dynamics are described by a quintic defocusing nonlinear Schrödinger equation. We rigorously establish this reduction for ground-state energies and time-dependent solutions, under a uniform H^2 well-posedness assumption. This provides a natural way to understand how the statistical structure of a 2D anyon system is reflected in its 1D effective description.

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