Complexity of multidimensional hydrogenic systems

Abstract: The Cram\'er-Rao, Fisher-Shannon and LMC shape complexity measures have been recently shown to play a relevant role to study the internal disorder of finite many-body systems (e.g., atoms, molecules, nuclei). They highlight amongst the bunch of complexities appeared in the literature by their mathematical simplicity and transparent physical interpretation. They are composed by two spreading measures (variance, Fisher information and Shannon entropies) of the single-particle probability density of the systems. Here we discuss the physico-mathematical knowledge of these two-component complexities for hydrogenic systems with standard ($D = 3$) and non-standard dimensionalities. These systems include not only the hydrogen atom and its isoelectronic series but also a large diversity of quantum systems such as, e.g. exotic atoms, antimatter atoms, some qubits systems and Rydberg atoms, ions and molecules.