Quantum information measures: Properties and analysis of structure and dynamics of multielectronic systems

Abstract

This Thesis is a contribution to the research on the Information Theory of multielectronic quantum systems. It focuses on numerous and diverse appli- cations of a range of information-theoretic measures to specific atomic and molecular structures. Relativistic and non relativistic multielectronic atomic systems, the relativistic quantum oscillator, and molecular systems are the principal systems under study in this Thesis. A variety of information- theoretical measures, including complexity and divergence measures, are employed in order to establish how these quantities can be related to dif- ferent physicochemical properties of the systems under consideration. This connections will allow us to reach a better understanding of those systems and propose an alternative methododology of their analysis, which could be applied to other systems in the future.

This Thesis is composed by seven Chapters. The first one is devoted to the description and enumeration of the informational measures used throughout this Thesis. The following five Chapters are focused on the anal- ysis of these mentioned information-theoretic measures applied to atomic systems (Chapters two, three, four and five), molecular systems (Chap- ter six) and the relativistic quantum oscillator or Dirac oscillator (Chapter seven). Each of these Chapters has a specific introduction, which provides the scientific context and motivation of the work. Let us now summarize the contents of this Thesis.

El objetivo principal de este trabajo consiste en establecer una relación directa entre diferentes medidas teórico-informacionales aplicadas a un conjunto variado de sistemas cuánticos, y medidas físico-químicas representativas de dichos sistemas. Concretamente se han estudiado sistemas atómicos, tanto neutros como ionizados, en régimen relativista y no relativista; sistemas moleculares; y el oscilador armónico relativista. Para el estudio se han empleado medidas individuales de la teoría de la información, además de medidas de complejidad y de divergencia.