Sadurní, Emerson; Leyvraz, Francois; Stegmann, Thomas; Seligman, Thomas H.; Klein, Dou- glas J. Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene. (English) ✄ ✂  ✁ Zbl 1466.92283 J. Math. Phys. 62, No. 5, 052102, 19 p. (2021). Summary: 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 disconnec- tion 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-naphthalene 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. ©2021 American Institute of Physics MSC: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) 51B10 Möbius geometries Full Text: DOI References: [1] Bargmann, V.; Moshinsky, M., Nucl. Phys., 18, 697 (1960) · Zbl 0096.23902 · doi:10.1016/0029-5582(60)90438-7 [2] Bargmann, V.; Moshinsky, M., Nucl. Phys., 23, 177-199 (1961) · Zbl 0094.43904 · doi:10.1016/0029-5582(61)90253-x [3] Boon, M. H.; Seligman, T. H., J. Math. Phys., 14, 1224-1227 (1973)· doi:10.1063/1.1666470 [4] Fock, V., Z. Phys., 98, 145-154 (1935)· doi:10.1007/bf01336904 [5] Pauli, W., Z. Phys., 36, 336-363 (1926)· doi:10.1007/bf01450175 [6] Louck, J. D.; Moshinsky, M.; Wolf, K. B., J. Math. Phys., 14, 692-695 (1973)· doi:10.1063/1.1666379 [7] Louck, J. D.; Moshinsky, M.; Wolf, K. B., J. Math. Phys., 14, 696-700 (1973)· doi:10.1063/1.1666380 [8] Moshinsky, M.; Patera, J.; Winternitz, P., J. Math. Phys., 16, 82-92 (1975)· doi:10.1063/1.522388 [9] Moshinsky, M.; Patera, J., J. Math. Phys., 16, 1866-1875 (1975)· doi:10.1063/1.522764 [10] Calogero, F., Lett. Nuovo Cimento, 13, 411-416 (1975)· doi:10.1007/bf02790495 [11] Sutherland, B., Phys. Rev. B, 38, 6689 (1988)· doi:10.1103/physrevb.38.668 [12] Khastgir, S. P.; Pocklington, A. J.; Sasaki, R., J. Phys. A: Math. Gen., 33, 9033 (2000) · Zbl 1031.81528 · doi:10.1088/0305- 4470/33/49/303 [13] Sadurní, E.; Hernández-Espinosa, Y., J. Phys. A: Math. Theor., 52, 295204 (2019)· doi:10.1088/1751-8121/ab25b6 [14] Rosado, A. S.; Franco-Villafane, J. A.; Pineda, C.; Sadurní E, E., Phys. Rev. B, 94, 045129 (2016)· doi:10.1103/physrevb.94.045129 [15] Kato, T., Perturbation Theory for Linear Operators (1966), Springer: Springer, Berlin · Zbl 0148.12601 [16] Pechukas, P., Phys. Rev. Lett., 51, 943 (1983)· doi:10.1103/physrevlett.51.943 [17] Gordon, A.; Avron, J. E., Phys. Rev. Lett., 85, 34 (2000)· doi:10.1103/physrevlett.85.34 [18] Steeb, W. H.; van Tonder, A. J.; Villet, C. M.; Brits, S. J. M., Found. Phys. Lett., 1, 147-162 (1988)· doi:10.1007/bf00661855 [19] Weiss, W. D.; Sannino, A. L., J. Phys. A: Math. Gen., 23, 1167-1178 (1990)· doi:10.1088/0305-4470/23/7/022 [20] Heiss, W. D., Czech. J. Phys., 54, 1091-1099 (2004)· doi:10.1023/b:cjop.0000044009.17264.dc [21] Berry, M. V.; Casati, G., Aspects of degeneracy, Chaotic Behaviour in Quantum Systems (1985), Plenum [22] Berry, M. V., Proc. R. Soc. London, Ser. A, 392, 45-57 (1984) · Zbl 1113.81306 · doi:10.1098/rspa.1984.0023 [23] Ortega, A.; Stegmann, T.; Benet, L.; Larralde, H., J. Phys. A: Math. Theor., 53, 445308 (2020)· doi:10.1088/1751-8121/abb513 [24] Nakamura, E.; Tahara, K.; Matsuo, Y.; Sawamura, M., J. Am. Chem. Soc., 125, 2834-2835 (2003)· doi:10.1021/ja029915z Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities © 2021 FIZ Karlsruhe GmbH Page 1