Nonlinear Krönig-Penney model

Two-dimensional effects in nonlinear Kronig-Penney models

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...

Band theory in the context of the Hamilton-Jacobi formulation

In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence postulate of quantum mechanics. Then, without appealing to the wave function properties, we reproduce the well-known dispersion relations which predict the band ...

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...

Calculation of statistical entropic measures in a model of solids

In this work, a one-dimensional model of crystalline solids based on the Dirac comb limit of the Krönig-Penney model is considered. From the wave functions of the valence electrons, we calculate a statistical measure of complexity and the FisherShannon information for the lower energy electronic bands appearing in the system. All these magnitudes present an extremal value for the case of solids...