scholarly journals Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Victor Chulaevsky
Keyword(s):  
Impurity Band ◽  
Dynamical Localization ◽  
Random Schrödinger Operators ◽  
Strong Disorder ◽  
Power Law Decay ◽  
Long Range Interactions ◽  
Surface Localization ◽  
Random Substitution ◽  
Concentration Of Impurities ◽  
Lower Dimensional

We study the random Schrödinger operators in a Euclidean space with the disorder generated by two complementary mechanisms: random substitution in a lower-dimensional layer and random displacements in the bulk, without additional assumptions regarding the reflection symmetry of the site potentials. The latter are assumed to be bounded and have a power-law decay. Complementing earlier results obtained in the strong disorder regime, we establish spectral and strong dynamical localization in the impurity zone near the bottom of spectrum for arbitrarily weak amplitudes of the random displacements, provided the concentration of impurities is sufficiently small.

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.

Fast decay of eigenfunction correlators in long-range continuous random alloys

2019 ◽  
Vol 27 (1) ◽  
pp. 43-51
Author(s):  
Victor Chulaevsky
Keyword(s):  
Long Range ◽  
Exponential Decay ◽  
Interaction Potential ◽  
Dynamical Localization ◽  
Fast Decay ◽  
Euclidean Spaces ◽  
Strong Disorder ◽  
Low Energies ◽  
Media Interaction ◽  
Random Alloys

Abstract We study random Anderson Hamiltonians in Euclidean spaces with a long-range particle-media interaction potential {\mathfrak{u}(r)=r^{-A}} . Improving earlier results, for any {A>2d} , we establish spectral and strong dynamical localization with sub-exponential decay of eigenfunction correlators, both in the strong disorder regime and at low energies.

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.

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