Integrated Density of States in One-Dimensional Problems of Second Order

1992 ◽  
pp. 136-189
Author(s):  
Leonid Pastur ◽  
Alexander Figotin
Keyword(s):  
Density Of States ◽  
Second Order ◽  
Integrated Density Of States ◽  
One Dimensional

scholarly journals Random Schrödinger operators with a background potential

2019 ◽  
Vol 27 (4) ◽  
pp. 253-259
Author(s):  
Hayk Asatryan ◽  
Werner Kirsch
Keyword(s):  
Inverse Scattering ◽  
Density Of States ◽  
Anderson Localization ◽  
Scattering Problem ◽  
Schrödinger Operators ◽  
Inverse Scattering Problem ◽  
Random Schrödinger Operators ◽  
Integrated Density Of States ◽  
Schrodinger Operators ◽  
One Dimensional

Abstract We consider one-dimensional random Schrödinger operators with a background potential, arising in the inverse scattering problem. We study the influence of the background potential on the essential spectrum of the random Schrödinger operator and obtain Anderson localization for a larger class of one-dimensional Schrödinger operators. Further, we prove the existence of the integrated density of states and give a formula for it.

scholarly journals Large Deviation Estimates and Hölder Regularity of the Lyapunov Exponents for Quasi-periodic Schrödinger Cocycles

2020 ◽  
Author(s):  
Rui Han ◽  
Shiwen Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Density Of States ◽  
Large Deviation ◽  
Schrödinger Operators ◽  
Positive Lyapunov Exponent ◽  
Integrated Density Of States ◽  
Holder Continuity ◽  
One Dimensional ◽  
Large Coupling

Abstract We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates, which lead to refined Hölder continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville frequencies.

GAP-LABELLING THEOREMS FOR SCHRÖDINGER OPERATORS ON THE SQUARE AND CUBIC LATTICE

1994 ◽  
Vol 06 (02) ◽  
pp. 319-342 ◽  
Author(s):  
ANDREAS VAN ELST
Keyword(s):  
Density Of States ◽  
Schrödinger Operators ◽  
Integrated Density Of States ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Cubic Lattice ◽  
Higher Dimensional ◽  
K Theory

The spectra of Schrödinger operators on the square and cubic lattice are investigated by means of non-commutative topological K-theory. Using a general gap-labelling theorem, it is shown how to calculate the possible values of the integrated density of states on the gaps of the spectrum, provided some additional conditions hold. If the potential takes on only finitely many values, this reduces to the calculation of frequencies of patterns in the potential sequence. As an example, products of one-dimensional systems and potentials generated by higher-dimensional substitutions are considered.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

One dimensional polymeric photonic crystal doped with second-order nonlinear optical chromophore

2009 ◽  
Author(s):  
Azusa Inoue ◽  
Shin-ichiro Inoue ◽  
Shiyoshi Yokoyama ◽  
Keisuke Kojima ◽  
Kei Yasui ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Nonlinear Optical ◽  
Second Order ◽  
One Dimensional ◽  
Nonlinear Optical Chromophore

Dependence of the Second-order G'-band Profile on the Electronic Structure of Single-wal Nanotubes

2001 ◽  
Vol 706 ◽  
Author(s):  
A. G. Souza Filho ◽  
A. Joribo ◽  
G. Dresselhaus ◽  
M. S. Dresselhaus ◽  
A. K. Swan ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Electronic Structure ◽  
Raman Spectra ◽  
Density Of States ◽  
Resonance Raman ◽  
Second Order ◽  
Electronic Density ◽  
Van Hove Singularities ◽  
Band Profile ◽  
Resonance Raman Spectra

AbstractWe analyze the dependence of the second-order G'-band profile in terms of their (n,m) indices by measuring the resonance Raman spectra of several semiconducting and metalic isolated single wal carbon nanotubes. We show that this profile is very sensitive to the electronic structure, thus making it possible to get structural (n,m) information and to probe the splitting of the van Hove singularities in the electronic density of states due to the trigona warping effect.

scholarly journals The landscape law for the integrated density of states

2021 ◽  
Vol 390 ◽  
pp. 107946
Author(s):  
G. David ◽  
M. Filoche ◽  
S. Mayboroda
Keyword(s):  
Density Of States ◽  
Integrated Density Of States
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