The Mourre Estimate for Dispersive N-Body Schrodinger Operators

1990 ◽  
Vol 317 (2) ◽  
pp. 773 ◽  
Author(s):  
Jan Derezinski
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Mourre Estimate

scholarly journals Rellich’s theorem and N-body Schrödinger operators

2016 ◽  
Vol 28 (05) ◽  
pp. 1650010 ◽  
Author(s):  
K. Ito ◽  
E. Skibsted
Keyword(s):  
Functional Calculus ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Singular Potentials ◽  
Localization Technique ◽  
Atoms And Molecules ◽  
Infinite Mass ◽  
Mourre Estimate ◽  
Rellich’S Theorem ◽  
Finite Extent

We show an optimal version of Rellich’s theorem for generalized [Formula: see text]-body Schrödinger operators. It applies to singular potentials, in particular, to a model for atoms and molecules with infinite mass and finite extent nuclei. Our proof relies on a Mourre estimate [10] and a functional calculus localization technique.

Coincidence of weighted Hardy spaces associated with higher-order Schrödinger operators

2021 ◽  
pp. 103031
Author(s):  
Trong Ngoc Nguyen ◽  
Truong Xuan Le ◽  
Tan Duc Do
Keyword(s):  
Hardy Spaces ◽  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators ◽  
Weighted Hardy Spaces

scholarly journals Existence of the Gauge for Fractional Laplacian Schrödinger Operators

2021 ◽  
Author(s):  
Michael W. Frazier ◽  
Igor E. Verbitsky
Keyword(s):  
Fractional Laplacian ◽  
Schrödinger Operators ◽  
Schrodinger Operators

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.

scholarly journals Faber–Krahn inequalities for Schrödinger operators with point and with Coulomb interactions

2021 ◽  
Vol 62 (1) ◽  
pp. 012105
Author(s):  
Vladimir Lotoreichik ◽  
Alessandro Michelangeli
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Coulomb Interactions
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