Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems

• DOI: 10.48550/arxiv.1904.02462
• Publication Date: 2019-01-01
• Authors: Yuguo Su; Fei Yao; Yanming Che; Libin Fu; Xiaoguang Wang
• Keywords: Representation

By describing the evolution of a quantum state with trajectories Majorana stars on Bloch sphere, Majorana's stellar representation provides an intuitive geometric perspective to comprehend system high-dimensional Hilbert space. However, problem two-spin coupling sphere has not been solved satisfactorily yet. Here, we present practical method resolve for mixed-spin $(s, 1/2)$ system. The can be decomposed into two spins: spin-$(s+1/2)$ and spin-$(s-1/2)$ at bases, which regarded as independent spins. Besides, may write any pure superposition orthonormal states one other state. Thus, whole pseudo spin-$1/2$. In this way, mixed spin decomposes three Therefore, represent by $(2s+1)+(2s-1)+1=4s+1$ sets sphere. Finally, demonstrate our theory, give some examples that indeed show laconic symmetric patterns unveil properties high-spin analyzing