scholarly journals Growth of Sobolev norms for linear Schrödinger operators

2021 ◽  
Vol 4 ◽  
pp. 1595-1618
Author(s):  
Laurent Thomann
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Sobolev Norms

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

scholarly journals The scattering of fractional Schrödinger operators with short range potentials

2021 ◽  
Vol 281 (2) ◽  
pp. 109033
Author(s):  
Rui Zhang ◽  
Tianxiao Huang ◽  
Quan Zheng
Keyword(s):  
Short Range ◽  
Schrödinger Operators ◽  
Schrodinger Operators
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