Shannon information entropy for a one-dimensional ionic crystal
Abstract
In this work, we present the information theoretic lengths given by Shannon and Fisher for the lowest-lying stationary state of a one-dimensional ionic crystal modeled by 2N+1 equally spaced attractive and repulsive Dirac delta potentials. The entropic uncertainty relations related to position and momentum spaces are studied as a function of the number of ions and the distance between them. Our results show that the stability of the ionic crystal depends on the number of ions and distance between them. In particular, we show that the position Shannon entropy is always positive and increases as the lattice constant between ions grows, in contrast with the momentum Shannon entropy which decreases and becomes negative beyond a particular lattice constant value.
