Proof of dynamical localization for perturbations of discrete 1D Schrödinger operators with uniform electric fields

2018 ◽  
Vol 291 (3-4) ◽  
pp. 1525-1541 ◽  
Author(s):  
César R. de Oliveira ◽  
Mariane Pigossi
Keyword(s):  
Electric Fields ◽  
Schrödinger Operators ◽  
Dynamical Localization ◽  
Schrodinger Operators

scholarly journals LOCALIZATION ON A QUANTUM GRAPH WITH A RANDOM POTENTIAL ON THE EDGES

2007 ◽  
Vol 19 (09) ◽  
pp. 923-939 ◽  
Author(s):  
PAVEL EXNER ◽  
MARIO HELM ◽  
PETER STOLLMANN
Keyword(s):  
Multiscale Analysis ◽  
Random Potential ◽  
Schrödinger Operators ◽  
Quantum Graph ◽  
Dynamical Localization ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Cubic Lattice ◽  
Lattice Quantum

We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the well-studied case of random Schrödinger operators.

scholarly journals SPECTRAL PROPERTIES OF DYNAMICAL LOCALIZATION FOR SCHRÖDINGER OPERATORS

2013 ◽  
Vol 25 (09) ◽  
pp. 1350016 ◽  
Author(s):  
FRANÇOIS GERMINET ◽  
AMAL TAARABT
Keyword(s):  
Spectral Properties ◽  
Schrödinger Operators ◽  
Dynamical Localization ◽  
Schrodinger Operators ◽  
Equivalent Properties

We investigate the equivalence between dynamical localization and localization properties of eigenfunctions of Schrödinger Hamiltonians. We introduce three classes of equivalent properties and study the relationships between them. These relationships are optimal as shown by counterexamples.

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