Existence of the Gauge for Fractional Laplacian Schrödinger Operators

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.

Eigenvalue Splitting of Polynomial Order for a System of Schrödinger Operators with Energy-Level Crossing

Communications in Mathematical Physics ◽

10.1007/s00220-021-04123-w ◽

2021 ◽

Author(s):

Marouane Assal ◽

Setsuro Fujiié

Keyword(s):

Energy Level ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

Level Crossing

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

Journal of Mathematical Physics ◽

10.1063/5.0014360 ◽

2021 ◽

Vol 62 (1) ◽

pp. 012105

Author(s):

Vladimir Lotoreichik ◽

Alessandro Michelangeli

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Coulomb Interactions

The scattering of fractional Schrödinger operators with short range potentials

Journal of Functional Analysis ◽

10.1016/j.jfa.2021.109033 ◽

2021 ◽

Vol 281 (2) ◽

pp. 109033

Author(s):

Rui Zhang ◽

Tianxiao Huang ◽

Quan Zheng

Keyword(s):

Short Range ◽

Schrödinger Operators ◽

Schrodinger Operators

Lipschitz estimates for functions of Dirac and Schrödinger operators

Journal of Mathematical Physics ◽

10.1063/5.0017648 ◽

2021 ◽

Vol 62 (1) ◽

pp. 013506

Author(s):

A. Skripka

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Lipschitz Estimates