A model of sheared nanoribbons
https://doi.org/10.17586/2220-8054-2022-13-1-12-16
Аннотация
In this note, we investigate the spectral properties of the Dirichlet Laplacian defined on an infinite band subject to a “shearing”. We give conditions for which the shear does not produce discret eigenvalue. In a second part we discuss the existence of discrete spectrum.
Список литературы
1. Briet P., Abdou-Soimadou H., Krejcirık D. Spectral analysis of sheared nanoribbons. Z. Angew. Math. Phys., 2019, 70(2), 18 pp.
2. Exner P., Kovarik H. Spectrum of the Schro¨dinger operator in a periodically twisted tube. Lett. Math. Phys., 2005, 73, P. 183-192.
3. Briet P., Raikov G., Kovarik H., Soccorsi E. Eigenvalue asymptotics in a twisted waveguide.Comm. P.D.E., 2009, 34(8).
4. Briet P., Hammedi H., Krejcirık D. Hardy inequality in a globally twisted waveguide. Lett. Math. Phys., 2015, 105, P. 939-958.
5. Briet P., Hammedi H. Twisted waveguide with a Neumann window. Functional Analysis and Operator Theory for Quantum Physics : The Pavel Exner Anniversary Volume, European Mathematical Society, P. 161-175, 2017, EMS Series of Congress Reports, Eur. Math. Soc., Zu¨rich, 2017.
6. Deift P., Hunziker W, Simon B., Vock E. Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems IV.Commun. Math. Phys., 1978, 64, 1-34.
7. Dermenjian Y., Durand D., Iftimie V. Spectral analysis of an acoustic multistratified perturbed cylinder.Commun. P.D.E., 1998, 23(1-2), P. 141-169.
8. Reed M., Simon B. Methods of Modern Mathematical Physics, I: Functional Analysis, Academic Press, New York-London, 1972.
9. Davies E.B. Heat Kernel and Spectral Theory. Univ. Press, Cambridge, 1989.
10. Krejcirık D.D., Lu Z.Z. Location of the essential spectrum in curved quantum layers. J.M.P., 2014, 55, 13 pp.
Рецензия
Для цитирования:
. Наносистемы: физика, химия, математика. 2022;13(1):12-16. https://doi.org/10.17586/2220-8054-2022-13-1-12-16
For citation:
Briet P. A model of sheared nanoribbons. Nanosystems: Physics, Chemistry, Mathematics. 2022;13(1):12-16. https://doi.org/10.17586/2220-8054-2022-13-1-12-16
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