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arXiv 1402.0776cond-mat.quant-gasmath-phmath.MPphysics.atom-phquant-ph
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旋量量子气体中的置换对称性:选择规则,守恒定律和关联

Permutation symmetry in spinor quantum gases: selection rules, conservation laws, and correlations

Vladimir A. Yurovsky

摘要:

考虑自旋和空间自由度可分离的全同任意自旋粒子多体系统。它们的本征态可以通过杨氏图进行分类,对应于非平凡的排列对称性(超出了传统的对称-反对称态的范式)。本文得到了(a)附加不可分的选择规则(取决于自旋和坐标)$k$ -体相互作用:与转变的初始和最终状态相关联的杨氏图可以通过在它们的行之间重新定位不超过$k$框而不同;以及(b)相关规则:如果$k$超过相关杨氏图中的列数(对于玻色子)或行数(对于费米子),则$k$粒子的本征态平均局域相关消失。它还阐明了由于置换对称性而守恒的量的物理意义--在1929年,狄拉克确定了那些具有对称群特征的量--将它们与实验上可观察到的几个粒子的相关性联系起来。结果提供了一种控制对称群的多维非阿贝尔表示纠缠态形成的方法。这些状态可以在量子计算和计量学中找到应用。

英文摘要:

Many-body systems of identical arbitrary-spin particles, with separable spin and spatial degrees of freedom, are considered. Their eigenstates can be classified by Young diagrams, corresponding to non-trivial permutation symmetries (beyond the conventional paradigm of symmetric--antisymmetric states). The present work obtains (a) selection rules for additional non-separable (dependent on spins and coordinates) $k$-body interactions: the Young diagrams, associated with the initial and the final states of a transition, can differ by relocation of no more than $k$ boxes between their rows; and (b) correlation rules: eigenstate-averaged local correlations of $k$ particles vanish if $k$ exceeds the number of columns (for bosons) or rows (for fermions) in the associated Young diagram. It also elucidates the physical meaning of the quantities conserved due to permutation symmetry --- in 1929, Dirac identified those with characters of the symmetric group --- relating them to experimentally observable correlations of several particles. The results provide a way to control the formation of entangled states belonging to multidimensional non-Abelian representations of the symmetric group. These states can find applications in quantum computation and metrology.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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