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

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.