# Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators

@article{Last1999EigenfunctionsTM, title={Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schr{\"o}dinger operators}, author={Yoram Last and Barry Simon}, journal={Inventiones mathematicae}, year={1999}, volume={135}, pages={329-367} }

Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators

## 230 Citations

On Instability of the absolutely continuous spectrum of dissipative Schrödinger operators and Jacobi matrices

- Mathematics
- 2006

The absence of the absolutely continuous spectrum is proved for dissipative Schrödinger operators and Jacobi matrices with slowly decaying imaginary part of the potential. §

Embedded singular continuous spectrum for one-dimensional Schrödinger operators

- Mathematics
- 1999

We investigate one-dimensional Schrödinger operators with sparse potentials (i.e. the potential consists of a sequence of bumps with rapidly growing barrier separations). These examples illuminate…

Uniform Spectral Properties of One-Dimensional Quasicrystals, I. Absence of Eigenvalues

- Mathematics
- 1999

Abstract:We consider discrete one-dimensional Schrödinger operators with Sturmian potentials. For a full-measure set of rotation numbers including the Fibonacci case, we prove absence of eigenvalues…

Dynamics and spectral theory of quasi-periodic Schrödinger-type operators

- Mathematics, PhysicsErgodic Theory and Dynamical Systems
- 2016

We survey the theory of quasi-periodic Schrödinger-type operators, focusing on the advances made since the early 2000s by adopting a dynamical systems point of view.

Uniform Singular Continuous Spectrum for the Period Doubling Hamiltonian

- Mathematics
- 2001

Abstract. We consider the ergodic family of Schrödinger operators generated by the period doubling substitution and we prove that every element of this family has purely singular continuous spectrum.

Destruction of Absolutely Continuous Spectrum by Perturbation Potentials of Bounded Variation

- Mathematics
- 2007

We show that absolutely continuous spectrum of one-dimensional Schrödinger operators may be destroyed by adding to them decaying perturbation potentials of bounded variation.

On the Lyapounov Exponents of Schrödinger Operators Associated with the Standard Map

- Mathematics
- 2013

It is shown that Schrodinger operators defined from the standard map have positive (mean) Lyapounov exponents for almost all energies.

Cantor singular continuous spectrum for operators along interval exchange transformations

- Mathematics
- 2007

It is shown that Schrodinger operators, with potentials along the shift embedding of Lebesgue almost every interval exchange transformations, have Cantor spectrum of measure zero and pure singular…

Absolutely Continuous Spectrum For Schr\"odinger Operators With Random Decaying Matrix Potentials on The Strip

- Mathematics
- 2022

We consider a family of random Schrödinger operators on the discrete strip with decaying random ` matrix potential. We prove that the spectrum is almost surely pure absolutely continuous, apart from…

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