ABSENT SPECTRAL GAPS OF THE GENERALIZED KRONIG-PENNEY HAMILTONIANS

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...

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.

Band Spectra of Kronig-Penney Model with Generalized Con- tact Interaction

We extend the standard Kronig-Penney model with periodic δ potentials to the cases with generalized contact interactions under the assumption that the system has time-reversal symmetry. By applying Bloch theorem, the eigenvalue equation which determines the dispersion relation for onedimensional periodic array of the generalized contact interactions is deduced within the framework of the transf...

Two-dimensional effects in nonlinear Kronig-Penney models