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Special Issue "Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models"

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Dear Colleagues,

The study of quantum systems has been enriched in recent years with the incorporation of new mathematical tools inspired by information theory. In particular, information measures and complexity measures have been successfully applied to elucidate various aspects of the physics of atoms, molecules, etc.

Unfortunately, quantum systems rarely admit exact treatment and most studies must rest heavily on the numerical solution of the equations describing the system.

Therefore, exactly soluble models play an essential role when exploring and testing the above-mentioned new statistical techniques. The aim of the present Special Issue is to apply information techniques to investigate the properties of exactly soluble quantum systems, including discrete systems like the celebrated Lipkin model and continuous systems based on exactly solvable quantum potentials.

Prof. Dr. Angelo Plastino
Prof. Dr. Angel Ricardo Plastino
Guest Editors

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Keywords

quantum mechanics
finite fermion systems
statistical treatment of fermion-systems
finite temperatures
fermion models that can be exactly solved without undue effort

Published Papers (3 papers)

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Research

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Open AccessArticle

Excitation Spectra and Edge Singularities in the One-Dimensional Anisotropic Heisenberg Model for Δ = cos(π/n), n = 3,4,5

Pedro Schlottmann

Quantum Rep. 2022, 4(4), 442-461; https://doi.org/10.3390/quantum4040032 - 19 Oct 2022

Viewed by 1181

Abstract

The

T = 0

excitation spectra of the antiferromagnetic (

J > 0

) anisotropic Heisenberg chain of spins 1/2 are studied using the Bethe Ansatz equations for

Δ = cos (π / n)

n = 3, 4

and [...] Read more.

The

T = 0

excitation spectra of the antiferromagnetic (

J > 0

) anisotropic Heisenberg chain of spins 1/2 are studied using the Bethe Ansatz equations for

Δ = cos (π / n)

n = 3, 4

and 5. The number of unknown functions is

n - 1

for

Δ = cos (π / n)

and can be solved numerically for a finite external field. The low-energy excitations form a Luttinger liquid parametrized by a conformal field theory with conformal charge of

c = 1

. For higher energy excitations, the spectral functions display deviations from the Luttinger behavior arising from the curvature in the dispersion. Adding a corrective term of the form of a mobile impurity coupled to the Luttinger liquid modes corrects this difference. The “impurity” is an irrelevant operator, which if treated non-perturbatively, yields the threshold singularities in the one-spinwave particle and hole Green’s function correctly. Full article

(This article belongs to the Special Issue Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models)

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Open AccessFeature PaperArticle

Statistical Quantifiers Resolve a Nuclear Theory Controversy

Diana Monteoliva

Angelo Plastino

and

Angel Ricardo Plastino

Quantum Rep. 2022, 4(1), 127-134; https://doi.org/10.3390/quantum4010009 - 22 Feb 2022

Cited by 2 | Viewed by 1978

Abstract

We deal here with an exactly solvable N-nucleon system that has been used to mimic typical features of quantum many-body systems. There is in the literature some controversy regarding the possible existence of a quantum phase transition in the model. We show [...] Read more.

(This article belongs to the Special Issue Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models)

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Review

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Open AccessReview

Cramér–Rao, Fisher–Shannon and LMC–Rényi Complexity-like Measures of Multidimensional Hydrogenic Systems with Application to Rydberg States

Jesús S. Dehesa

Quantum Rep. 2023, 5(1), 116-137; https://doi.org/10.3390/quantum5010009 - 09 Feb 2023

Viewed by 1136

Abstract

Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information–theoretical analysis of chemical reactions. This potential will be shown in hydrogenic systems by means of the monotone complexity measures of Cramér–Rao, Fisher–Shannon and LMC(Lopez-Ruiz, Mancini, Calbet)–Rényi types. These quantities are shown to be analytically determined from first principles, i.e., explicitly in terms of the space dimensionality D, the nuclear charge and the hyperquantum numbers, which characterize the system’ states. Then, they are applied to several relevant classes of particular states with emphasis on the quasi-spherical and the highly excited Rydberg states, obtaining compact and physically transparent expressions. This is possible because of the use of powerful techniques of approximation theory and orthogonal polynomials, asymptotics and generalized hypergeometric functions. Full article

(This article belongs to the Special Issue Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models)

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Special Issue "Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models"

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