Spectral properties of quasiperiodic Kronig-Penney model

Quantum diffusion in the Kronig-Penney model

In this paper we consider the 1D Schrödinger operator H with periodic point interactions. We show an L1 − L∞ bound for the time evolution operator e−itH restricted to each energy band with decay order O(t−1/3) as t → ∞, which comes from some kind of resonant state. The order O(t−1/3) is optimal for our model. We also give an asymptotic bound for the coefficient in the high energy limit. For the...

Remarks on the Spectral Properties of Tight Binding and Kronig-penney Models with Substitution Sequences #

We comment on some recent investigations on the electronic properties of models associated to the Thue-Morse chain and point out that their conclusions are in contradiction with rigorously proven theorems and indicate some of the sources of these misinterpretations. We brieey review and explain the current status of mathematical results in this eld and discuss some conjectures and open problems.

The classical diffusion - limited Kronig - Penney system

We have previously discussed the classical diffusive system of the bounded one-dimensional multitrap using the transfer-matrix method which is generally applied for studying the energy spectrum of the unbounded quantum Kronig-Penney multibarrier. It was shown, by this method, that for certain values of the relevant parameters the bounded multitrap array have unity transmission and a double-peak...

Anomalous properties of the Kronig-Penney model with compositional and structural disorder

We study the localization properties of the eigenstates in the KronigPenney model with weak compositional and structural disorder. The main result is an expression for the localization length that is valid for any kind of selfand inter-correlations of the two types of disorder. We show that the interplay between compositional and structural disorder can result in anomalous localization. Pacs nu...

Two-dimensional effects in nonlinear Kronig-Penney models