scholarly journals Lifshitz tails for generalized alloy-type random Schrödinger operators

2010 ◽  
Vol 3 (4) ◽  
pp. 409-426 ◽  
Author(s):  
Frédéric Klopp ◽  
Shu Nakamura
Keyword(s):  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Lifshitz Tails ◽  
Alloy Type

scholarly journals Internal Lifshitz tails for discrete Schrödinger operators

2006 ◽  
Vol 2006 ◽  
pp. 1-8
Author(s):  
Hatem Najar
Keyword(s):  
Density Of States ◽  
Present Model ◽  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Integrated Density Of States ◽  
Periodic Operator ◽  
Schrodinger Operators ◽  
Spectral Gaps ◽  
Lifshitz Tails ◽  
Discrete Schrödinger Operators

We consider random Schrödinger operatorsHωacting onl2(ℤd). We adapt the technique of the periodic approximations used in (2003) for the present model to prove that the integrated density of states ofHωhas a Lifshitz behavior at the edges of internal spectral gaps if and only if the integrated density of states of a well-chosen periodic operator is nondegenerate at the same edges. A possible application of the result to get Anderson localization is given.

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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