Spectral theory of corrugated surfaces
Journées équations aux dérivées partielles (2001), article no. 8, 11 p.

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.

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     author = {Jak\v{s}i\'c, Vojkan},
     title = {Spectral theory of corrugated surfaces},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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     publisher = {Universit\'e de Nantes},
     year = {2001},
     doi = {10.5802/jedp.592},
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Jakšić, Vojkan. Spectral theory of corrugated surfaces. Journées équations aux dérivées partielles (2001), article  no. 8, 11 p. doi : 10.5802/jedp.592. http://archive.numdam.org/articles/10.5802/jedp.592/

[A] Aizenman M Localization at Weak Disorder: Some Elementary Bounds Rev. Math. Phys., 6, 1163 1994. | MR | Zbl

[AM] Aizenman M., Molchanov S Localization at Large Disorder and at Extreme Energies: An Elementary Derivation Commun. Math. Phys. 157, 245 1993. | MR | Zbl

[BBP] Bentosela F., Briet Ph., Pastur L, In preparation.

[CS] Chahrour A. Sahbani J, On the Spectral and Scattering Theory of the Schrödinger Operator with Surface Potential Rev. Math. Phys. 12, 561 (2000). | MR | Zbl

[CFKS] Cycon H., Froese R., Kirsch W., Simon B., Schrödinger Operators. Springer-Verlag Berlin-Heidelberg 1987. | MR | Zbl

[G] Grinshpun V Localization for Random Potentials Supported on a Subspace Lett. Math. Phys. 34, 103 1995. | MR | Zbl

[GJMS] Gordon Y., Jakšić, V., Molchanov S., Simon B. Spectral Properties of Random Schrödinger Operators with Unbounded Potentials Commun. Math. Phys. 157, 23 1993. | MR | Zbl

[DJ] Derezinski J., Jakšić, V Spectral Theory of Pauli-Fierz Hamiltonians J. Funct. Anal. 180, 243 (2001). | MR | Zbl

[DS] Davies E.B., Simon B Scattering Theory for Systems with Different Spatial Asymptotics on the Left and Right Commun. Math. Phys. 63, 277 1978. | MR | Zbl

[FP] Figotin A., Pastur L An Exactly Solvable Model of Multidimensional Incommensurate Structure Commun. Math. Phys. 95, 410 1984. | MR | Zbl

[JL1] Jakšić, V.,Last Y Corrugated Surfaces and A.C. Spectrum Rev. Math. Phys. 12, 1465 (2000). | MR | Zbl

[JL2] Jakšić, V., Last Y, Spectral Structure of Anderson Type Hamiltonians Invent. Math. 141, 561 (2000). | MR | Zbl

[JL3] Jakšić, V., Last Y, Surface States and Spectra Commun. Math. Phys. 218, 459 (2001). | MR | Zbl

[JM1] Jakšić, V., Molchanov S, On the Spectrum of the Surface Maryland Model Lett. Math. Phys. 45, 185 1998. | MR | Zbl

[JM2] Jakšić, V., Molchanov S, On the Surface Spectrum in Dimension Two Helv. Phys. Acta 71, 629 1999. | MR | Zbl

[JM3] Jakšić, V., Molchanov S, Localization of Surface Spectra Commun. Math. Phys. 208, 153 1999. | MR | Zbl

[JM4] Jakšić, V., Molchanov S, Wave Operators for the Surface Maryland Model J. Math. Phys. 41, 4452 (2000). | MR | Zbl

[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. | MR | Zbl

[KMP] Kirch W., Molchanov S., Pastur L One-dimensional Schrödinger Operator with Unbounded Potential Func. Anal. Prilozhen. 24, 14 1990. | MR | Zbl

[KP] Khoruzenko B.A. Pastur L, The Localization of Surface States: An Exactly Solvable Model Physics Reports 288, 109-126 1997. | Zbl

[M1] Molchanov S., Lectures given at Caltech, Spring 1990.

[M2] Molchanov S. Lectures on Random Media. In Lectures on Probability ed. P. Bernard, Lecture Notes in Mathematics, 1581, Springer-Verlag, Heidelberg 1994. | MR | Zbl

[MV1] Molchanov S., Vainberg B, unpublished.

[MV2] Molchanov S., Vainberg B private communication.

[SW] Simon B., Wolff T Singular Continuous Spectrum Under Rank One Perturbations and Localization for Random Hamiltonians Commun. Pure Appl. Math. 39, 75 1986. | MR | Zbl

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