Boundary Potential Theory for Schrödinger Operators Based on Fractional Laplacian

2009 ◽  
pp. 25-55 ◽  
Author(s):  
K. Bogdan ◽  
T. Byczkowski
Keyword(s):  
Potential Theory ◽  
Fractional Laplacian ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Boundary Potential

scholarly journals Potential Theory for Schrödinger operators on finite networks

2005 ◽  
pp. 771-818 ◽  
Author(s):  
Enrique Bendito ◽  
Ángeles Carmona ◽  
Andrés Encinas
Keyword(s):  
Potential Theory ◽  
Schrödinger Operators ◽  
Schrodinger Operators

scholarly journals Potential Theory on Minimal Hypersurfaces II: Hardy Structures and Schrödinger Operators

2020 ◽  
Author(s):  
Joachim Lohkamp
Keyword(s):  
Potential Theory ◽  
Schrödinger Operators ◽  
Second Order ◽  
Central Problem ◽  
Schrodinger Operators ◽  
Singular Set ◽  
Minimal Hypersurfaces ◽  
Large Classes ◽  
Fine Control ◽  
Area Minimizing

Abstract Area minimizing hypersurfaces and, more generally, almost minimizing hypersurfaces frequently occur in geometry, dynamics and physics. A central problem is that a general (almost) minimizing hypersurface H contains a complicated singular set Σ. Nevertheless, we manage to develop a detailed potential theory on H ∖Σ applicable to large classes of linear elliptic second order operators. We even get a fine control over their analysis near Σ. This is Part 2 of this two parts work.

scholarly journals Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Luca Fresta
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Local Density Of States ◽  
Weak Disorder ◽  
Cluster Expansions ◽  
Strong Disorder ◽  
Lifshitz Tail

AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

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