Ciftja Orion, Batle Josep, Hafez Mohamed Ahmed
Department of Physics, Prairie View A&M University, Prairie View, TX 77446, USA.
Departament de Física and Institut d'Aplicacions Computacionals de Codi Comunitari (IAC3), University of the Balearic Islands, E-07122 Palma de Mallorca, Spain.
Nanomaterials (Basel). 2025 May 21;15(10):771. doi: 10.3390/nano15100771.
Structures composed of classical dipoles in higher-dimensional space present a unique opportunity to venture beyond the conventional paradigm of few-body or cluster physics. In this work, we consider the six convex regular polychora that exist in an Euclidean four-dimensional space as a theoretical benchmark for hte investigation of dipolar systems in higher dimensions. The structures under consideration represent the four-dimensional counterparts of the well-known Platonic solids in three-dimensions. A dipole is placed in each vertex of the structure and is allowed to interact with the rest of the system via the usual dipole-dipole interaction generalized to the higher dimension. We use numerical tools to minimize the total interaction energy of the systems and observe that all six structures represent dipole clusters with a zero net dipole moment. The minimum energy is achieved for dipoles arranging themselves with orientations whose angles are commensurate or irrational fractions of the number π.
由高维空间中的经典偶极子组成的结构为突破少体或团簇物理的传统范式提供了独特的契机。在这项工作中，我们将欧几里得四维空间中存在的六个凸正多胞体视为研究高维偶极系统的理论基准。所考虑的结构是三维中著名的柏拉图立体在四维的对应物。在结构的每个顶点放置一个偶极子，并允许其通过推广到高维的通常偶极 - 偶极相互作用与系统的其余部分相互作用。我们使用数值工具来最小化系统的总相互作用能，并观察到所有六个结构都代表净偶极矩为零的偶极子团簇。当偶极子以其角度为π的整数比或无理分数的取向排列时，可实现最小能量。
