scholarly journals Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph

2015 ◽  
Vol 35 (2) ◽  
pp. 199 ◽  
Author(s):  
Hiroaki Niikuni
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Spectral Gaps ◽  
Metric Graph

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.

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