scholarly journals Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

2012 ◽  
Vol 53 (9) ◽  
pp. 095205 ◽  
Author(s):  
Michael Aizenman ◽  
Simone Warzel
Keyword(s):  
Continuous Spectrum ◽  
Random Potential ◽  
Ballistic Transport ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
Tree Graphs ◽  
Quantum Particles

scholarly journals ABSOLUTELY CONTINUOUS SPECTRUM FOR A RANDOM POTENTIAL ON A TREE WITH STRONG TRANSVERSE CORRELATIONS AND LARGE WEIGHTED LOOPS

2009 ◽  
Vol 21 (06) ◽  
pp. 709-733 ◽  
Author(s):  
RICHARD FROESE ◽  
DAVID HASLER ◽  
WOLFGANG SPITZER
Keyword(s):  
Continuous Spectrum ◽  
Binary Tree ◽  
Random Potential ◽  
Random Schrödinger Operators ◽  
Strongly Correlated ◽  
Tree Graph ◽  
Absolutely Continuous Spectrum ◽  
Random Potentials ◽  
Absolutely Continuous ◽  
Tree Graphs

We consider random Schrödinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model, we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.

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