Spectral properties of combinatorial Schrödinger operators on infinite weighted graphs

2011 ◽  
Vol 74 (1-2) ◽  
pp. 1-31 ◽  
Author(s):  
Sofiane Akkouche
Keyword(s):  
Spectral Properties ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Weighted Graphs

On the spectrum and the distribution of singular values of Schrödinger operators with a complex potential

1983 ◽  
Vol 388 (1794) ◽  
pp. 195-218 ◽  
Keyword(s):  
Complex Potential ◽  
Spectral Properties ◽  
Polynomial Growth ◽  
Schrödinger Operators ◽  
Singular Values ◽  
Negative Real Part ◽  
Adjoint Problem ◽  
Schrodinger Operators ◽  
Asymptotic Estimates ◽  
Integrability Conditions

This paper is concerned with spectral properties of the Schrödinger operator ─ ∆+ q with a complex potential q which has non-negative real part and satisfies weak integrability conditions. The problem is dealt with as a genuine non-self-adjoint problem, not as a perturbation of a self-adjoint one, and global and asymptotic estimates are obtained for the corresponding singular values. From these estimates information is obtained about the eigenvalues of the problem. By way of illustration, detailed calculations are given for an example in which the potential has at most polynomial growth.

scholarly journals LOCALIZATION FOR ONE DIMENSIONAL LONG RANGE RANDOM HAMILTONIANS

1999 ◽  
Vol 11 (01) ◽  
pp. 103-135 ◽  
Author(s):  
VOJKAN JAKŠIĆ ◽  
STANISLAV MOLCHANOV
Keyword(s):  
Long Range ◽  
Spectral Properties ◽  
Schrödinger Operators ◽  
Pure Point ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Free Part ◽  
Random Hamiltonians

We study spectral properties of random Schrödinger operators hω=h0+vω(n) on l2(Z) whose free part h0 is long range. We prove that the spectrum of hω is pure point for typical ω whenever the off-diagonal terms of h0 decay as |i-j|-γ for some γ>8.

Spectral properties of k p schrödinger operators in one space dimension

2000 ◽  
Vol 21 (3-4) ◽  
pp. 379-409 ◽  
Author(s):  
U. Bandelow ◽  
H. -Chr. Kaiser ◽  
Th. Koprucki ◽  
J. Rehberg
Keyword(s):  
Spectral Properties ◽  
Space Dimension ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Space Dimension
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