Some Schrödinger Operators with Power-Decaying Potentials and Pure Point Spectrum

1997 ◽  
Vol 186 (2) ◽  
pp. 481-493 ◽  
Author(s):  
Christian Remling
Keyword(s):  
Point Spectrum ◽  
Schrödinger Operators ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Schrodinger Operators

scholarly journals Magnetic Schrödinger Operators with Discrete Spectra on Non-Compact Kähler Manifolds

2012 ◽  
Vol 20 (2) ◽  
pp. 11-20
Author(s):  
Nicolae Anghel
Keyword(s):  
Point Spectrum ◽  
Schrödinger Operators ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Schrodinger Operators ◽  
Type Problem ◽  
Dirac Type ◽  
Discrete Spectra ◽  
Parallel Spinor ◽  
Discreteness Criterion

Abstract We identify a class of magnetic Schrödinger operators on Käler manifolds which exhibit pure point spectrum. To this end we embed the Schröinger problem into a Dirac-type problem via a parallel spinor and use a Bochner-Weitzenböck argument to prove our spectral discreteness criterion

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.

scholarly journals Pure Point Spectrum of the Laplacians on Fractal Graphs

1995 ◽  
Vol 129 (2) ◽  
pp. 390-405 ◽  
Author(s):  
L. Malozemov ◽  
A. Teplyaev
Keyword(s):  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum

scholarly journals Global multiplicity bounds and spectral statistics for random operators

2020 ◽  
Vol 32 (09) ◽  
pp. 2050025
Author(s):  
Anish Mallick ◽  
Krishna Maddaly
Keyword(s):  
Lower Bound ◽  
Separable Hilbert Space ◽  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Positive Lebesgue Measure ◽  
Spectral Multiplicity ◽  
Local Statistics ◽  
Higher Rank ◽  
Spectral Statistics

In this paper, we consider Anderson type operators on a separable Hilbert space where the random perturbations are finite rank and the random variables have full support on [Formula: see text]. We show that spectral multiplicity has a uniform lower bound whenever the lower bound is given on a set of positive Lebesgue measure on the point spectrum away from the continuous one. We also show a deep connection between the multiplicity of pure point spectrum and local spectral statistics, in particular, we show that spectral multiplicity higher than one always gives non-Poisson local statistics in the framework of Minami theory. In particular, for higher rank Anderson models with pure point spectrum, with the randomness having support equal to [Formula: see text], there is a uniform lower bound on spectral multiplicity and in case this is larger than one, the local statistics is not Poisson.

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