Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field

A. Iantchenko; E. Korotyaev

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 4, page 175-197
  • ISSN: 0973-5348

Abstract

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We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.

How to cite

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Iantchenko, A., and Korotyaev, E.. "Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field." Mathematical Modelling of Natural Phenomena 5.4 (2010): 175-197. <http://eudml.org/doc/197656>.

@article{Iantchenko2010,
abstract = {We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.},
author = {Iantchenko, A., Korotyaev, E.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {nanotubes; Jacobi operator; periodic; finite support perturbation; resonances},
language = {eng},
month = {5},
number = {4},
pages = {175-197},
publisher = {EDP Sciences},
title = {Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field},
url = {http://eudml.org/doc/197656},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Iantchenko, A.
AU - Korotyaev, E.
TI - Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/5//
PB - EDP Sciences
VL - 5
IS - 4
SP - 175
EP - 197
AB - We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.
LA - eng
KW - nanotubes; Jacobi operator; periodic; finite support perturbation; resonances
UR - http://eudml.org/doc/197656
ER -

References

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  1. J.E. Avron, A. Raveh, B. Zur. Adiabatic quantum transport in multiply connected systems. Rev. Modern Phys., 60 (1988), No. 4, 873–915. 
  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.  
  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. 
  6. E. Korotyaev. Effective masses for zigzag nanotubes in magnetic fields. Lett. Math. Phys., 83 (2008), No 1, 83–95.  
  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. 
  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. 
  13. P. van Moerbeke. The spectrum of Jacobi matrices. Invent. Math., 37 (1976), No. 1, 45–81.  
  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. 
  16. K. Pankrashkin. Spectra of Schrödinger operators on equilateral quantum graphs. Lett. Math. Phys., 77 (2006), 139–154. 
  17. V. Rabinovich, S. Roch. Essential spectra of difference operators on Zn-periodic graphs. J. Phys. A: Math. Theor., 40 (2007), 10109. 
  18. K. Ruedenberg, C.W. Scherr. Free-electron network model for conjugated systems. I. Theory. J. of Chem. Phys., 21 (1953), 1565–1581. 
  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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