Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products.
Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products.
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通过一维对象及其点/叉积将涌现现象和对称性破缺联系起来。
DOI：
10.1088/1361-6633/ac97aa
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Cheong SW
中科院分区：
文献类型：
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作者：
Cheong SW
整个实验装置的对称性，包括特定的样品环境和可测量的，可以与可观察到的物理现象的标本进行比较。我们，首先，专注于一维（1D）的实验设置，独立于围绕一个方向的任何空间旋转，并表明，八种1D对象（四个;矢量，其他四个;导演），定义的对称性，和他们的点和交叉产品是一种有效的方式的对称性考虑。点积构成一个具有Abel加法运算的Z2 × Z2 × Z2群，叉积构成一个具有Abel加法运算的Z2 × Z2群或一个8阶非Abel群Q8，这取决于它们的符号.这些1D物体与特征物理现象相关联。当3D样本具有与具有特定现象的1D对象的对称性操作相似性（SOS）（相同或低于但不高于）时，3D样本可以表现出该现象。这种SOS方法可以成为一种变革性和非传统的途径，用于指导材料的设计和发现。
The symmetry of the whole experimental setups, including specific sample environments and measurables, can be compared with that of specimens for observable physical phenomena. We, first, focus on one-dimensional (1D) experimental setups, independent from any spatial rotation around one direction, and show that eight kinds of 1D objects (four; vector-like, the other four; director-like), defined in terms of symmetry, and their dot and cross products are an effective way for the symmetry consideration. The dot products form a Z 2× Z 2× Z 2 group with Abelian additive operation, and the cross products form a Z 2× Z 2 group with Abelian additive operation or Q 8, a non-Abelian group of order eight, depending on their signs. Those 1D objects are associated with characteristic physical phenomena. When a 3D specimen has symmetry operational similarity (SOS) with (identical or lower, but not higher, symmetries than) an 1D object with a particular phenomenon, the 3D specimen can exhibit the phenomenon. This SOS approach can be a transformative and unconventional avenue for symmetry-guided materials designs and discoveries.