scholarly journals Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions

1993 ◽  
Vol 158 (1) ◽  
pp. 45-66 ◽  
Author(s):  
Anton Bovier ◽  
Jean-Michel Ghez
Keyword(s):  
Spectral Properties ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional

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 Sparse Schrödinger Operators

1997 ◽  
Vol 09 (03) ◽  
pp. 315-341
Author(s):  
Claire Guille-Biel
Keyword(s):  
Dynamical System ◽  
Spectral Properties ◽  
Schrödinger Operators ◽  
Negative Integer ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Discrete Operators ◽  
Ergodic Dynamical System

We study spectral properties of a family [Formula: see text], indexed by a non-negative integer p, of one-dimensional discrete operators associated to an ergodic dynamical system (T,X,ℬ,μ) and defined for u in ℓ2(ℤ) and n in ℤ by [Formula: see text], where Vx(n)=f(Tnx) and f is a real-valued measurable bounded map on X. In some particular cases, we prove that the nature of the spectrum does not change with p. Applications include some classes of random and quasi-periodic substitutional potentials.

scholarly journals Reflection Probabilities of One-Dimensional Schrödinger Operators and Scattering Theory

2017 ◽  
Vol 18 (6) ◽  
pp. 2075-2085 ◽  
Author(s):  
Benjamin Landon ◽  
Annalisa Panati ◽  
Jane Panangaden ◽  
Justine Zwicker
Keyword(s):  
Scattering Theory ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional

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.

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