Net Fisher information measure versus ionization potential and dipole polarizability in atoms

Abstract

The net Fisher information measure I T , defined as the product of position and momentum Fisher information measures I r and I k and derived from the non-relativistic Hartree-Fock wave functions for atoms with Z = 1−102, is found to correlate well with the inverse of the experimental ionization potential. Strong direct correlations of I T are also reported for the static dipole polarizability of atoms with Z = 1 − 88. The complexity measure, defined as the ratio of the net Onicescu information measure E T and I T , exhibits clearly marked regions corresponding to the periodicity of the atomic shell structure. The reported correlations highlight the need for using the net information measures in addition to either the position or momentum space analogues. With reference to the correlation of the experimental properties considered here, the net Fisher information measure is found to be superior than the net Shannon information entropy.

Statistical measure of complexity and correlated behavior of Fermi systems

“…Figure 4: S cor , D cor and C of electron gas the correlation parameter r s . The lines correspond to the expressions (31), (32), (33), with the parameters derived by the least squares fit method. (40), (41), with the parameters derived by the least squares fit method.…”

“…e S and D [50]. The usefulness of the improved version has been shown in many fields [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]. Moreover, the specific measure is suitably tailored for quantum systems, described by their very nature probabilistically via density distributions in position and momentum spaces, which are necessary for and enable a relatively easy calculation of S and D, entering the formulas C LMC = SD or C = e S D. The motivation of the present work, in the spirit of the above statements, is to extend our previous study of uniform Fermi systems [16], beyond information entropy, in order to include the complexity measure proposed by López-Ruiz et al [22], using probability distributions in momentum space.…”

“…Information-theoretical methods play an important role, not just in the clarification of fundamental concepts of quantum mechanics, but also provide a series of results concerning the information content of systems, the presence of interactions, correlation with experimental measured quantities, extraction of universal relations etc [2,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Additionally, many complexity measures have been proposed as indicators of complex behavior found in different systems scattered in a broad spectrum of fields [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48].…”

“…An alternative definition of complexity is the SDL measure Γ αβ [26] (Shiner, Davison, Landsberg), defined and calculated in an analogous way as the LMC one. It has been applied in atoms as well, starting from [32]. Comments on the validity of SDL and LMC measures are given in detail in Section 4 of [33], where it is stated that a welcome property of a definition of complexity might be the following: If one complicates the system by varying some of its parameters, and this leads to an increase of the adopted measure of complexity, then one could argue that this measure describes the complexity of the system properly.…”

Statistical Complexity. Applications in Electronic Systems

“…The use of these statistical magnitudes to study the electronic structure of atoms is another interesting application [43][44][45][46][47][48][49][50]20]. The basic ingredient to calculate these statistical indicators is the electron probability density, ρ(r), that can be obtained from the numerically derived Hartree-Fock atomic wave function in the non-relativistic case [45,46], and from the Dirac-Fock atomic wave function in the relativistic case [47].…”