Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
Page(s) 175 - 197
DOI https://doi.org/10.1051/mmnp/20105408
Published online 12 May 2010
  1. J.E. Avron, A. Raveh, B. Zur. Adiabatic quantum transport in multiply connected systems. Rev. Modern Phys., 60 (1988), No. 4, 873–915. [CrossRef] [MathSciNet]
  2. P. Exner. A duality between Schrödinger operators on graphs and certain Jacobi matrices. Ann. Inst. H. Poincaré Phys. Theor., 66 (1997), No. 4, 359–371. [MathSciNet]
  3. P. Harris. Carbon Nanotubes and Related Structures. Cambridge Univ. Press., Cambridge, 1999.
  4. A. Iantchenko, E. Korotyaev. Periodic Jacobi operators with finitely supported perturbations on the half-line. Preprint, 2009.
  5. S. Iijima. Helical microtubules of graphitic carbon. Nature, 354 (1991), 56–58. [CrossRef]
  6. E. Korotyaev. Effective masses for zigzag nanotubes in magnetic fields. Lett. Math. Phys., 83 (2008), No 1, 83–95. [CrossRef] [MathSciNet]
  7. E. Korotyaev. Resonances for Schrödinger operator with periodic plus compactly supported potentials on the half-line. Preprint, 2008.
  8. E. Korotyaev, A. Kutsenko. Zigzag nanoribbons in external electric Fields. To appear in Asympt. Anal.
  9. E. Korotyaev, A. Kutsenko. Zigzag and armchair nanotubes in external fields. To appear in Diff. Equations: Systems, Applications and Analysis. Nova Science Publishers, Inc.
  10. E. Korotyaev, I. Lobanov. Schrödinger operators on zigzag periodic graphs. Ann. Henri Poincaré, 8 (2007), 1151–1176. [CrossRef] [MathSciNet]
  11. E. Korotyaev, I. Lobanov. Zigzag periodic nanotube in magnetic field. Preprint, 2006.
  12. P. Kuchment, O. Post. On the spectra of carbon nano-structures. Commun. Math. Phys., 275 (2007), 805–826. [CrossRef]
  13. P. van Moerbeke. The spectrum of Jacobi matrices. Invent. Math., 37 (1976), No. 1, 45–81. [CrossRef] [MathSciNet]
  14. D.S. Novikov. Electron properties of carbon nanotubes in a periodic potential. Physical Rev., B 72 (2005), 235428-1-22.
  15. L. Pauling. The diamagnetic anisotropy of aromatic molecules. J. of Chem. Phys., 4 (1936), 673–677. [CrossRef]
  16. K. Pankrashkin. Spectra of Schrödinger operators on equilateral quantum graphs. Lett. Math. Phys., 77 (2006), 139–154. [CrossRef] [MathSciNet]
  17. V. Rabinovich, S. Roch. Essential spectra of difference operators on Zn-periodic graphs. J. Phys. A: Math. Theor., 40 (2007), 10109. [CrossRef]
  18. K. Ruedenberg, C.W. Scherr. Free-electron network model for conjugated systems. I. Theory. J. of Chem. Phys., 21 (1953), 1565–1581. [CrossRef]
  19. R. Saito, G. Dresselhaus, M. Dresselhaus. Physical properties of carbon nanotubes. Imperial College Press, 1998.
  20. G. Teschl. Jacobi operators and completely integrable nonlinear lattices. Providence, RI: AMS, (2000) ( Math. Surveys Monographs, V. 72.)
  21. E.B. Vinberg.A Course in Algebra. Graduate studies in Mathematics, AMS, V. 56.

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