Results 1  10
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12
Transport properties of quasifree Fermions
 J. MATH. PHYS
, 2007
"... Using the scattering approach to the construction of NonEquilibrium Steady States proposed by Ruelle we study the transport properties of systems of independent electrons. We show that Landauer–Büttiker and GreenKubo formulas hold under very general conditions. ..."
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Cited by 20 (4 self)
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Using the scattering approach to the construction of NonEquilibrium Steady States proposed by Ruelle we study the transport properties of systems of independent electrons. We show that Landauer–Büttiker and GreenKubo formulas hold under very general conditions.
INTEGRATED DENSITY OF STATES AND WEGNER ESTIMATES FOR RANDOM SCHRÖDINGER OPERATORS
, 2003
"... We survey recent results on spectral properties of random Schrödinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a selfaveraging IDS which is general enough to be applicable to random Schrödinger and LaplaceBeltrami operators ..."
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Cited by 12 (2 self)
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We survey recent results on spectral properties of random Schrödinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a selfaveraging IDS which is general enough to be applicable to random Schrödinger and LaplaceBeltrami operators on manifolds. Subsequently we study more specific models in Euclidean space, namely of alloy type, and concentrate on the regularity properties of the IDS. We discuss the role of the integrated density of states and its regularity properties for the spectral analysis of random Schrödinger operators, particularly in relation to localisation. Proofs of the central results are given in detail. Whenever there are alternative proofs, the different approaches are compared.
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.
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.
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.
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
, 2002
"... Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems ..."
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Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems
unknown title
, 2002
"... Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems ..."
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Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems
ABSENCE OF CONTINUOUS SPECTRAL TYPES FOR CERTAIN NONSTATIONARY RANDOM MODELS
, 2004
"... 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 ra ..."
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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.