Monotone complexity measures of multidimensional quantum systems with central potentials
Affiliation:
1. Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada , 18071 Granada, Spain and , 18071 Granada, Spain
2. Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada , 18071 Granada, Spain and , 18071 Granada, Spain
Abstract
In this work, we explore the (inequality-type) properties of the monotone complexity-like measures of the internal complexity (disorder) of multidimensional non-relativistic electron systems subject to a central potential. Each measure quantifies the combined balance of two spreading facets of the electron density of the system. We show that the hyperspherical symmetry (i.e., the multidimensional spherical symmetry) of the potential allows Cramér–Rao, Fisher–Shannon, and Lopez-Ruiz, Mancini, Calbet–Rényi complexity measures to be expressed in terms of the space dimensionality and the hyperangular quantum numbers of the electron state. Upper bounds, mutual complexity relationships, and complexity-based uncertainty relations of position–momentum type are also found by means of the electronic hyperangular quantum numbers and, at times, the Heisenberg–Kennard relation. We use a methodology that includes a variational approach with a covariance matrix constraint and some algebraic linearization techniques of hyperspherical harmonics and Gegenbauer orthogonal polynomials.
Funder
Agencia Estatal de Investigación
European Regional Development Fund
Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía
Vicerrectorado de Investigación y Transferencia, Universidad de Granada
Subject
Mathematical Physics,Statistical and Nonlinear Physics