Bound states in a nonlinear 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...

Two-dimensional effects in nonlinear Kronig-Penney models

ar X iv : c on d - m at / 9 70 80 35 v 1 5 A ug 1 99 7 Bound states in a nonlinear Kronig Penney model

We study the bound states of a Kronig Penney potential for a nonlinear one-dimensional Schrodinger equation. This potential consists of a large, but not necessarily infinite, number of equidistant δ-function wells. We show that the ground state can be highly degenerate. Under certain conditions furthermore, even the bound state that would be normally the highest can have almost the same energy ...

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...

Suppression of localization in Kronig-Penney models with correlated disorder.

We consider the electron dynamics and transport properties of one-dimensional continuous models with random, short-range correlated impurities. We develop a generalized Poincare map formalism to cast the Schrodinger equation for any potential into a discrete set of equations, illustrating its application by means of a specific example. We then concentrate on the case of a Kronig-Penney model wi...