Results 1  10
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15
Wegner Estimate for Sparse and Other Generalized Alloy Type Potentials
, 2002
"... We prove a Wegner estimate for generalized alloy type models at negative energies (Theorems 8 and 13). The single site potential is assumed to be non positive. The random potential does not need to be stationary with respect to translations from a lattice. Actually, the set of points to which t ..."
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Cited by 10 (2 self)
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We prove a Wegner estimate for generalized alloy type models at negative energies (Theorems 8 and 13). The single site potential is assumed to be non positive. The random potential does not need to be stationary with respect to translations from a lattice. Actually, the set of points to which the individual single site potentials are attached, needs only to satisfy a certain density condition. The distribution of the coupling constants is assumed to have a bounded density only in the energy region where we prove the Wegner estimate.
On the spectrum of Schrödinger operator with periodic surface potential
, 2000
"... We consider a discrete Schrödinger operator H = +V acting in l 2 (Z d ), with periodic potential V supported by the subspace "surface" f0g Z d2 . We prove that the spectrum of H is purely absolutely continuous, and that surface waves (see [8] for denition) oscillate in the longitu ..."
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Cited by 9 (0 self)
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We consider a discrete Schrödinger operator H = +V acting in l 2 (Z d ), with periodic potential V supported by the subspace "surface" f0g Z d2 . We prove that the spectrum of H is purely absolutely continuous, and that surface waves (see [8] for denition) oscillate in the longitudinal directions to the "surface". We find also an explicit formula for the generalized spectral shift function introduced in [4].
Surface States and Spectra
, 2000
"... Let Z d+1 + = Z d Z+,letH 0 be the discrete Laplacian on the Hilbert space l 2 (Z d+1 + ) with a Dirichlet boundary condition, and let V be a potential supported on the boundary #Z d+1 + .We introduce the notions of surface states and surface spectrum of the operator H = H 0 + V and ex ..."
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Cited by 6 (1 self)
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Let Z d+1 + = Z d Z+,letH 0 be the discrete Laplacian on the Hilbert space l 2 (Z d+1 + ) with a Dirichlet boundary condition, and let V be a potential supported on the boundary #Z d+1 + .We introduce the notions of surface states and surface spectrum of the operator H = H 0 + V and explore their properties. Our main result is that if the potential V is random and if the disorder is either large or small enough, then in dimension two H has no surface spectrum on #(H 0 ) with probability one. To prove this result we combine AizenmanMolchanov theory with techniques of scattering theory.
Anderson localization and Lifshits tails for random surface potentials, Preprint 2004
"... ABSTRACT. We consider Schrödinger operators on L 2 (R d) with a random potential concentrated near the surface R d1 × {0} ⊂ R d. We prove that the integrated density of states of such operators exhibits Lifshits tails near the bottom of the spectrum. From this and the multiscale analysis by Boutet ..."
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Cited by 3 (2 self)
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ABSTRACT. We consider Schrödinger operators on L 2 (R d) with a random potential concentrated near the surface R d1 × {0} ⊂ R d. We prove that the integrated density of states of such operators exhibits Lifshits tails near the bottom of the spectrum. From this and the multiscale analysis by Boutet de Monvel and Stollmann [Arch. Math. 80 (2003) 87] we infer Anderson localization (pure point spectrum and dynamical localization) for low energies. Our proof of Lifshits tail relies on spectral properties of Schrödinger operators with partially periodic potentials. In particular, we show that the lowest energy band of
Absence of continuous spectral types for certain nonstationary random Schrödinger operators
, 2005
"... We consider continuum random Schrödinger operators of the type Hω = −∆+V0 + Vω with a deterministic background potential V0. We establish criteria for the absence of continuous and absolutely continuous spectrum, respectively, outside the spectrum of − ∆ +V0. The models we treat include random sur ..."
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Cited by 3 (1 self)
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We consider continuum random Schrödinger operators of the type Hω = −∆+V0 + Vω with a deterministic background potential V0. We establish criteria for the absence of continuous and absolutely continuous spectrum, respectively, outside the spectrum of − ∆ +V0. The models we treat include random surface potentials as well as sparse or slowly decaying random potentials. In particular, we establish absence of absolutely continuous surface spectrum for random potentials supported near a onedimensional surface (“random tube”) in arbitrary dimension.
Spectral Theory of Corrugated Surfaces
, 2001
"... We discuss spectral and scattering theory of the discrete Laplacian limited to a halfspace. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics. 1. ..."
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Cited by 2 (0 self)
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We discuss spectral and scattering theory of the discrete Laplacian limited to a halfspace. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics. 1.
The bandedge behavior of the density of surfacic states
 Math. Phys. Anal. Geom
"... Abstract. This paper is devoted to the asymptotics of the density of surfacic states near the spectral edges for a discrete surfacic Anderson model. Two types of spectral edges have to be considered: fluctuating edges and stable edges. Each type has its own type of asymptotics. In the case of fluctu ..."
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Cited by 2 (2 self)
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Abstract. This paper is devoted to the asymptotics of the density of surfacic states near the spectral edges for a discrete surfacic Anderson model. Two types of spectral edges have to be considered: fluctuating edges and stable edges. Each type has its own type of asymptotics. In the case of fluctuating edges, one obtains Lifshitz tails the parameters of which are given by the initial operator suitably “reduced ” to the surface. For stable edges, the surface density of states behaves like the surface density of states of a constant (equal to the expectation of the random potential) surface potential. Among the tools used to establish this are the asymptotics of the surface density of states for constant surface potentials.
unknown title
, 2005
"... Large time behavior of the solutions to the difference wave operators. ..."
ABSENCE OF CONTINUOUS SPECTRAL TYPES FOR CERTAIN NONSTATIONARY RANDOM MODELS IN MEMORY OF
"... Abstract. We consider continuum random Schrödinger operators of the type Hω = − ∆ + V0 + Vω with a deterministic background potential V0. We establish criteria for the absence of continuous and absolutely continuous spectrum, respectively, outside the spectrum of − ∆ + V0. The models we treat includ ..."
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Abstract. We consider continuum random Schrödinger operators of the type Hω = − ∆ + V0 + Vω with a deterministic background potential V0. We establish criteria for the absence of continuous and absolutely continuous spectrum, respectively, outside the spectrum of − ∆ + V0. The models we treat include random surface potentials as well as sparse or slowly decaying random potentials. In particular, we establish absence of absolutely continuous surface spectrum for random potentials supported near a onedimensional surface (“random tube”) in arbitrary dimension. 1.
unknown title
, 2008
"... Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others ..."
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Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others