Jensen–Shannon and Kullback–Leibler divergences as quantifiers of relativistic effects in neutral atoms

Monteoliva

2021

Entropy

Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems. In this work we explore the main features of information and information-based complexity indicators in exactly soluble many-fermion models of the Lipkin kind. Models of this kind have been extremely useful in shedding light on the intricacies of quantum many body physics. Models of the Lipkin kind play, for finite systems, a role similar to the one played by the celebrated Hubbard model of solid state physics. We consider two many fermion systems and show how their differences can be best appreciated by recourse to information theoretic tools. We appeal to information measures as tools to compare the structural details of different fermion systems. We will discover that few fermion systems are endowed by a much larger complexity-degree than many fermion ones. The same happens with the coupling-constants strengths. Complexity augments as they decrease, without reaching zero. Also, the behavior of the two lowest lying energy states are crucial in evaluating the system’s complexity.

Section: Introductionmentioning

confidence: 99%

Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models

Monteoliva

2021

Entropy

“…This comparative measure has found deep applications in statistics and many other fields, including entanglement characterization [38], analysis of symbolic sequences or series, and in particular in the study of segmentation of DNA sequences [39]. JSD and some effective generalizations have been used for the study and comparison of one-electron densities [40][41][42][43][44]. For the first time, to the best of our knowledge, this information measure of dissimilarity is applied to the study of two-electron density functions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of correlation and ionization from pair distributions in many-electron systems

et al. 2021

Self Cite

Jensen–Shannon divergence is used to quantify the discrepancy between the Hartree–Fock pair density and the product of its marginals for different N-electron systems, enclosing neutral atoms (with nuclear charge $$Z=N$$ Z = N ) and singly-charged ions ($$N = Z \pm 1$$ N = Z ± 1 ). This divergence measure is applied to determine the interelectronic correlation in atomic systems. A thorough study was carried out, by considering (i) both position and momentum conjugated spaces, and (ii) systems with a nuclear charge as far as $$Z = 103$$ Z = 103 . The correlation among electrons was measured by comparing, for an arbitrary system, the double-variable electron-pair density with the product of the respective one-particle densities. A detailed analysis throughout the Periodic Table highlights the relevance not only of weightiness for the systems considered, but also of their shell structure. Besides, comparative computations between two-electron densities of different atomic systems (neutrals, cations, anions) quantify their dissimilarities, patently governed by shell-filling patterns throughout the Periodic Table.

Int J of Quantum Chemistry

“…In general, it quantifies the question of how different or similar one density is to another. Such distances between electronic charge densities have been related to differences in physical properties between different species, among other applications . KL has also been used in molecular dynamics simulations .…”

Section: Introductionmentioning

confidence: 99%

Entropic Kullback‐Leibler type distance measures for quantum distributions

Laguna

Salazar

Sagar

2019

Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback-Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback-Leibler (CRKL) distance.The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two-variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure.The use of CRKL in measuring distances between orbitals is also discussed. K E Y W O R D S cumulative residual Kullback-Leibler entropy, Kullback-Leibler, quantum distributions, relative entropy