Level spacing and Poisson statistics for continuum random Schrödinger operators

2020 ◽  
Author(s):  
Adrian Dietlein ◽  
Alexander Elgart
Keyword(s):  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Level Spacing ◽  
Poisson Statistics

scholarly journals Poisson statistics for eigenvalues of continuum random Schrödinger operators

2010 ◽  
Vol 3 (1) ◽  
pp. 49-80 ◽  
Author(s):  
Jean-Michel Combes ◽  
François Germinet ◽  
Abel Klein
Keyword(s):  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Poisson Statistics

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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