论文标题
通过一维对象及其点/跨产品连接新兴现象和破碎的对称性
Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products
论文作者
论文摘要
可以将整个实验设置的对称性（包括特定的样品环境和可测量物品）与可观察到的物理现象的标本进行比较。首先，我们专注于一维（1D）实验设置，独立于一个方向围绕一个方向的任何空间旋转，并表明八种1D对象（四个；矢量类，其他四个；类似于对称的导演），它们的点和点和交叉产物是对称性考虑的有效方法。 DOT产品形成了一个具有Abelian添加剂操作的Z2XZ2XZ2组，跨产品形成了一个Z2XZ2组，其Abelian添加剂操作或Q8（Q8）是第8订单的非阿布尔式订单组，具体取决于其标志。那些1D对象与特征物理现象有关。当3D试样具有具有特定现象的1D对象（相同或更低但不高的对称性）的对称性操作相似性（SOS）时，3D标本可以表现出现象。这种SOS方法可能是对称性引导的材料设计和发现的变革性和非常规的途径。
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; vectorlike, 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 Z2xZ2xZ2 group with Abelian additive operation, and the cross products form a Z2xZ2 group with Abelian additive operation or Q8, 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.
