Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Cấu trúc phổ băng của toán tử Schrödinger định kỳ với hai thế năng trên ống nano zigzag suy biến
Tóm tắt
Trong bài báo này, chúng tôi nghiên cứu phổ của các toán tử Schrödinger định kỳ với hai thế năng trên một đồ thị lượng tử, có liên quan đến ống nano carbon. Chúng tôi chỉ ra rằng phổ có cấu trúc băng. Hơn nữa, chúng tôi giải quyết một vấn đề đồng tồn tại và xem sự khác biệt giữa trường hợp một thế năng và trường hợp hai thế năng.
Từ khóa
#Schrödinger operators #quantum graph #carbon nanotube #spectral band structure #coexistence problem.Tài liệu tham khảo
Berkolaiko, G., Kuchment, P.: Introduction to quantum graphs. AMS, Providence, RI (2012)
Cai, Y., Zhou, M., Zeng, M., Zhang, C., Feng, Y.P.: Adsorbate and defect effects on electronic and transport properties of gold nanotubes. Nanotechnology 22, 215702 (2011)
Carlson, R.: Hill’s equation for a homogeneous tree. Electron. J. Differ. Equ. 23, 1–30 (1997)
Cheon, T., Poghosyan, S.S.: Exotic quantum transport in double-stranded Kronig-Penney model, arXiv:1410.8647
Kuchment, P., Do, Ngoc T.: Quantum graph spectra of a graphyne structure. Nanoscale Syst. 2, 107–123 (2013)
Duclos, P., Exner, P., Turek, Ondřej: On the spectrum of a bent chain graph. J. Phys. A: Math. Theor. 41, 415206 (18pp) (2008)
Enyashin, A.N., Ivanovskii, A.L.: Graphene allotropes: stability, structural and electronic properties from DF-TB calculations. Phys. Status Solidi (b) 248, 1879–1883 (2011)
Gérard, C., Nier, F.: The mourre theory for analytically fibered operators. J. Funct. Anal. 152(1), 202–219 (1998)
Peter, J.F.: Harris, Carbon Nanotube Science. Cambridge University Press, Cambridge (2009)
Katsnelson, M.I.: Graphene: Carbon in Two Dimensions. Cambridge University Press, Cambridge (2012)
Korotyaev, E., Lobanov, I.: Schrödinger operators on zigzag nanotubes. Ann. Henri Poincaré 8, 1151–1176 (2007)
Kostrykin, V., Schrader, R.: Kirchhoff’s rule for quantum wires. J. Phys. A: Math. Gen. 32, 595–630 (1999)
Kostrykin, V., Schrader, R.: A random necklace model. Waves Random Media 13(1), S75–S90 (2004)
Kuchment, P., Post, O.: On the spectra of carbon nano-structures. Commun. Math. Phys. 275, 805–826 (2007)
Levin, B.Ja.: Distribution of zeros of entire functions, American Mathematical Society, Province, R. I., Translations of Mathematical Monographs, Vol. 5, 1964
Magnus, W., Winkler, S.: Hill’s Equation. Wiley, New York (1966)
Malic, E., Knorr, A.: Graphene and Carbon Nanotubes: Ultrafast Optics and Relacation Dynamics. Wiley, New York (2013)
March, N.H., Angilella, G.G.: Electronic states in ordered and disordered quantum networks: with applications to graphene and to boron nanotubes. J. Math. Chem. 46, 532–549 (2009)
Marchenko, V., Ostrovski, I.: A characterization of the spectrum of the hill operator. Math. USSR Sb. 26, 493–554 (1975)
Niikuni, H.: Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph. Opusc. Math. 35, 199–234 (2015)
Niikuni, H.: Spectral band structure of periodic Schrödinger operators on a generalized degenerate zigzag nanotube, submitted
Pauling, L.: The diamagnetic anisotropy of aromatic molecules. J. Chem. Phys. 4, 673–674 (1936)
Platt, J.R., Ruedenberg, K., Scherr, C.W., Ham, N.S., Labhart, H., Lichten, W.: Free-Electron Theory of Conjugated Molecules: A Source Book. Weiley, New York (1964)
Poschel, J., Trubowitz, E.: Inverse Spectral Theory. Academic Press, Orlando (1987)
Reed, M., Simon, B.: Methods of Modern Mathematical Physics, IV. Analysis of Operators. Academic Press, New York (1978)
Shen, S.: Topological Insulators: Dirac Equation in Condensed Matters, Springer Series in Solid-State Sciences 174. Springer, New York (2013)
Titchmarsh, E.: The theory of functions, Sec edn. University Press, London (1975)
Foa Torres, Luis E.F., Roche, Stephan, Charlier, Jean-Christophe: Introduction to Graphene-Based Nanomaterials. Cambridge University Press, Cambridge (2014)
