Decisiveness of the spectral gaps of periodic Schrodinger operators on the Dumbbell-like metric graph

• Autorzy: Niikuni H.

Identyfikatory

DOI

http://dx.doi.org/10.7494/OpMath.2015.35.2.199

• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider periodic Schrodinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.

Słowa kluczowe

EN

quantum graph; spectral gap; band structure; Hill operator

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 2
• Strony: 199--234
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Niikuni H.

• Maebashi Institute of Technology 460-1 Kaniisadori, Maebashi City Gunma, 371-0816, Japan

Bibliografia

• [1] G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, AMS, Providence, R.I., 2012.
• [2] P. Duclos, P. Exner, O. Turek, On the spectrum of a bent chain graph, J. Phys. A: Math. Theor. 41 (2008), 415206, 18 pp.
• [3] J. Garnett, E. Trubowitz, Gaps and bands of one dimensional periodic Schrodinger operators, Comment. Math. Helv. 59 (1984), 258-312.
• [4] C. Gerard, F. Nier, The Mourre theory for analytically fibered operators, J. Funct. Anal. 152 (1998) 1, 202-219.
• [5] P. Kargaev, E. Korotyaev, Effective masses and conformal mappings, Comm. Math. Phys. 169 (1995), 597-625.
• [6] E. Korotyaev, The inverse problem for the Hill operator. I, Int. Math. Res. Not. 3 (1997), 113-125.
• [7] E. Korotyaev, I. Lobanov, Schrodinger operators on zigzag nanotubes, Ann. Henri Poincare 8 (2007), 1151-1176.
• [8] V. Kostrykin, R. Schrader, Kirchhoff's rule for quantum wires, J. Phys. A: Math. Gen. 32 (1999), 595-630.
• [9] P. Kuchment, O. Post, On the spectra of carbon nano-structures, Comm. Math. Phys. 275 (2007), 805-826.
• [10] W. Magnus, S. Winkler, Hill's Equation, Wiley-Interscience, New York, 1966.
• [11] V. Marchenko, I. Ostrovski, A characterization of the spectrum of the Hill operator, Math. USSR Sb. 26 (1975), 493-554.
• [12] J. Poschel, E. Trubowitz, Inverse Spectral Theory, Academic Press, Orlando, 1987.
• [13] M. Reed, B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Opera­tors, Academic Press, New York, 1978.
• [14] E. Titchmarsh, The Theory of Functions, Second ed., Univ. Press, London, 1975.