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Spin‑controlled topological phase transition in non‑euclidean space

Frontiers of Optoelectronics 2024年第1期17卷 67-76页

作者： Zhuochen Du Jinze Gao Qiuchen Yan Cuicui Lu Xiaoyong Hu Qihuang Gong State Key Laboratory for Mesoscopic Physics and Department of Physics Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano‑OptoelectronicsBeijing Academy of Quantum Information SciencesPeking UniversityBeijing 100871China Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic SystemsSchool of PhysicsBeijing Institute of TechnologyBeijing 100081China Peking University Yangtze Delta Institute of Optoelectronics Nantong 226010China Collaborative Innovation Center of Extreme Optics Shanxi UniversityTaiyuan 030006China Hefei National Laboratory Hefei 230088China

Modulation of topological phase transition has been pursued by researchers in both condensed matter and optics research fields,and has been realized in euclidean systems,such as topological photonic crystals,topological metamaterials,and coupled resonator ***,the spin-controlled topological phase transition in non-euclidean space has not yet been ***,we propose a non-euclidean configuration based on Mobius rings,and we demonstrate the spin-controlled transition between the topological edge state and the bulk *** Mobius ring,which is designed to have an 8πperiod,has a square cross section at the twist beginning and the length/width evolves adiabatically along the loop,accompanied by conversion from transverse electric to transverse magnetic modes resulting from the spin-locked *** 8πperiod Mobius rings are used to construct Su–Schrieffer–Heeger configuration,and the configuration can support the topological edge states excited by circularly polarized light,and meanwhile a transition from the topological edge state to the bulk state can be realized by controlling circular *** addition,the spin-controlled topological phase transition in non-euclidean space is feasible for both Hermitian and non-Hermitian cases in 2D *** work provides a new degree of polarization to control topological photonic states based on the spin of Mobius rings and opens a way to tune the topological phase in non-euclidean space.

关键词： Topological phase transition non-euclidean space Möbius ring Spin-locked effect

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A Survey of Deep Learning-Based Mesh Processing

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Communications in Mathematics and Statistics 2022年第1期10卷 163-194页

作者： He Wang Juyong Zhang School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026People’s Republic of China

In the past ten years,deep learning technology has achieved a great success in many fields,like computer vision and speech ***,large-scale geometry data become more and more available,and the learned geometry priors have been successfully applied to 3D computer vision and computer graphics *** from the regular representation of images,surface meshes have irregular structures with different vertex numbers and ***,the traditional convolution neural networks used for images cannot be directly used to handle surface meshes,and thus,many methods have been proposed to solve this *** this paper,we provide a comprehensive survey of existing geometric deep learning methods formesh *** first introduce the relevant knowledge and theoretical background of geometric deep learning and some basic mesh data knowledge,including some commonly used mesh ***,we review various deep learning models for mesh data with two different types:graph-based methods and mesh structure-based *** also review the deep learning-based applications for mesh *** the final,we give some potential research directions in this field.

关键词： Geometric deep learning non-euclidean space Mesh Convolution Spectral domain Spatial domain

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