Weak coupling asymptotics of schrodinger operators with stark effect

1991 ◽  
pp. 185-195 ◽  
Author(s):  
Xue-Ping Wang
Keyword(s):  
Weak Coupling ◽  
Stark Effect ◽  
Schrödinger Operators ◽  
Schrodinger Operators

AN ABSTRACT RADIATION CONDITION AND APPLICATIONS TO N-BODY SYSTEMS

2000 ◽  
Vol 12 (05) ◽  
pp. 767-803 ◽  
Author(s):  
JACOB SCHACH MØLLER
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stark Effect ◽  
Schrödinger Operators ◽  
Radiation Condition ◽  
Schrodinger Operators ◽  
Limiting Absorption Principle ◽  
Inhomogeneous Schrödinger Equation

In the setting of Mourre [18] we characterize the "outgoing" and "incoming" solutions, to the abstract inhomogeneous Schrödinger equation (H-E)u=v, given by the Limiting Absorption Principle. The characterization is in terms of an abstract radiation condition and as an application we give a characterization, in the framework of weighted L2-spaces, of the outgoing and incoming solutions for N-body Schrödinger operators with and without Stark effect. The abstract radiation condition translates in the application into a radiation condition considered by Isozaki in [13].

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.

Sign in / Sign up

Export Citation Format

Share Document