Spectral theory of corrugated surfaces

Vojkan Jakšić

Journées équations aux dérivées partielles (2001)

  • page 1-11
  • ISSN: 0752-0360

Abstract

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We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.

How to cite

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Jakšić, Vojkan. "Spectral theory of corrugated surfaces." Journées équations aux dérivées partielles (2001): 1-11. <http://eudml.org/doc/93419>.

@article{Jakšić2001,
abstract = {We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.},
author = {Jakšić, Vojkan},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-11},
publisher = {Université de Nantes},
title = {Spectral theory of corrugated surfaces},
url = {http://eudml.org/doc/93419},
year = {2001},
}

TY - JOUR
AU - Jakšić, Vojkan
TI - Spectral theory of corrugated surfaces
JO - Journées équations aux dérivées partielles
PY - 2001
PB - Université de Nantes
SP - 1
EP - 11
AB - We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.
LA - eng
UR - http://eudml.org/doc/93419
ER -

References

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  1. [A] Aizenman MLocalization at Weak Disorder: Some Elementary Bounds Rev. Math. Phys., 6, 1163 1994. Zbl0843.47039MR1301371
  2. [AM] Aizenman M., Molchanov SLocalization at Large Disorder and at Extreme Energies: An Elementary Derivation Commun. Math. Phys. 157, 245 1993. Zbl0782.60044MR1244867
  3. [BBP] Bentosela F., Briet Ph., Pastur L, In preparation. 
  4. [CS] Chahrour A.Sahbani J, On the Spectral and Scattering Theory of the Schrödinger Operator with Surface Potential Rev. Math. Phys. 12, 561 ( 2000). Zbl1044.81034MR1763841
  5. [CFKS] Cycon H., Froese R., Kirsch W., Simon B., Schrödinger Operators. Springer-Verlag Berlin-Heidelberg 1987. Zbl0619.47005MR883643
  6. [G] Grinshpun VLocalization for Random Potentials Supported on a Subspace Lett. Math. Phys. 34, 103 1995. Zbl0831.47052MR1335579
  7. [GJMS] Gordon Y., Jakšić, V., Molchanov S., Simon B.Spectral Properties of Random Schrödinger Operators with Unbounded Potentials Commun. Math. Phys. 157, 23 1993. Zbl0788.60077MR1244857
  8. [DJ] Derezinski J., Jakšić, VSpectral Theory of Pauli-Fierz Hamiltonians J. Funct. Anal. 180, 243 ( 2001). Zbl1034.81016MR1814991
  9. [DS] Davies E.B., Simon BScattering Theory for Systems with Different Spatial Asymptotics on the Left and Right Commun. Math. Phys. 63, 277 1978. Zbl0393.34015MR513906
  10. [FP] Figotin A., Pastur LAn Exactly Solvable Model of Multidimensional Incommensurate Structure Commun. Math. Phys. 95, 410 1984. Zbl0582.35101MR767188
  11. [JL1] Jakšić, V.,Last YCorrugated Surfaces and A.C. Spectrum Rev. Math. Phys. 12, 1465 ( 2000). Zbl0979.60050MR1809458
  12. [JL2] Jakšić, V., Last Y,Spectral Structure of Anderson Type Hamiltonians Invent. Math. 141, 561 ( 2000). Zbl0962.60056MR1779620
  13. [JL3] Jakšić, V., Last Y, Surface States and Spectra Commun. Math. Phys. 218, 459 ( 2001). Zbl1163.81308MR1828849
  14. [JM1] Jakšić, V., Molchanov S, On the Spectrum of the Surface Maryland Model Lett. Math. Phys. 45, 185 1998. Zbl0916.47027MR1641176
  15. [JM2] Jakšić, V., Molchanov S, On the Surface Spectrum in Dimension Two Helv. Phys. Acta 71, 629 1999. Zbl0939.60074MR1669046
  16. [JM3] Jakšić, V., Molchanov S, Localization of Surface Spectra Commun. Math. Phys. 208, 153 1999. Zbl0952.60059MR1729882
  17. [JM4] Jakšić, V., Molchanov S, Wave Operators for the Surface Maryland Model J. Math. Phys. 41, 4452 ( 2000). Zbl0983.82007MR1765613
  18. [JMP] Jakšić, V., Molchanov S., Pastur L., On the Propagation Properties of Surface Waves Wave Propagation in Complex Media, IMA Vol. Math. Appl. 96, 143 1998. Zbl0905.65107MR1489748
  19. [KMP] Kirch W., Molchanov S., Pastur LOne-dimensional Schrödinger Operator with Unbounded Potential Func. Anal. Prilozhen. 24, 14 1990. Zbl0747.47023MR1082027
  20. [KP] Khoruzenko B.A.Pastur L, The Localization of Surface States: An Exactly Solvable Model Physics Reports 288, 109-126 1997. Zbl1001.82526
  21. [M1] Molchanov S., Lectures given at Caltech, Spring 1990. 
  22. [M2] Molchanov S.Lectures on Random Media. In Lectures on Probability ed. P. Bernard, Lecture Notes in Mathematics, 1581, Springer-Verlag, Heidelberg 1994. Zbl0814.60093MR1307415
  23. [MV1] Molchanov S., Vainberg B, unpublished. 
  24. [MV2] Molchanov S., Vainberg B private communication. 
  25. [SW] Simon B., Wolff TSingular Continuous Spectrum Under Rank One Perturbations and Localization for Random Hamiltonians Commun. Pure Appl. Math. 39, 75 1986. Zbl0609.47001MR820340

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