环并苯与莫比乌斯环并苯中的隐藏对偶性与偶然简并
Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene
AI总结：
本文提出分段概念解释环并苯和莫比乌斯环并苯的偶然简并，并用紧束缚模型连续极限与切比雪夫多项式给出简并条件。
摘要：
环并苯中以三重态和四重态形式出现的偶然简并，可借助分段概念加以解释；本文引入这一概念，旨在描述这些有机化合物中π轨道的有效断开。对于具有时间反演对称性的周期系统，研究表明涌现的节点域将原子链分割为更简单的碳结构，类似于苯环、二烯丙基链、蒽（三并苯）链以及四甲基萘骨架形式。这些分段共有的电子能级被识别为整体系统简并多重态的成员。莫比乌斯环并苯特有的简并同样可通过分段来解释。最后一部分表明，环并苯能量的多重性可通过研究紧束缚模型的连续极限来预测；简并条件以切比雪夫多项式表示。本研究所得结果对有机导线中的电子输运物理及其人工实现均具有重要意义。
英文摘要：
The accidental degeneracy appearing in cycloacenes as triplets and quadruplets is explained with the concept of segmentation, introduced here with the aim of describing the effective disconnection of $π$ orbitals on these organic compounds. For periodic systems with time reversal symmetry, the emergent nodal domains are shown to divide the atomic chains into simpler carbon structures analog to benzene rings, diallyl chains, anthracene (triacene) chains and tetramethyl-naphtalene skeletal forms. The common electronic levels of these segments are identified as members of degenerate multiplets of the global system. The peculiar degeneracy of Möbius cycloacene is also explained by segmentation. In the last part, it is shown that the multiplicity of energies for cycloacene can be foreseen by studying the continuous limit of the tight-binding model; the degeneracy conditions are put in terms of Chebyshev polynomials. The results obtained in this work have important consequences on the physics of electronic transport in organic wires, together with their artificial realizations.
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