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Quantum Reports
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Exploring Information and Complexity Measures in Quantum Systems by Exactly...
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Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models

A special issue of Quantum Reports (ISSN 2624-960X).

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 9022

Special Issue Editors

Prof. Dr. Angelo Plastino

E-Mail Website
Guest Editor
Instituto de Física (IFLP-CCT-CONICET), Universidad Nacional de La Plata, C.C. 727, La Plata 1900, Argentina
Interests: informaton theory; statistical mechanics; quantum information
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Angel Ricardo Plastino

E-Mail Website
Guest Editor
CeBio y Secretaría de Investigación, Universidad Nacional del Noroeste de la Província de Buenos Aires, UNNOBA-Conicet, Roque Saenz Peña 456, 6000 Junin, Argentina
Interests: physics of information; statistical physics and thermodynamics; quantum mechanics; mathematical physics

Special Issue Information

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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Quantum Reports is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

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

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Published Papers (4 papers)

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Research

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15 pages, 357 KiB  
Article
Applications of Supersymmetric Polynomials in Statistical Quantum Physics
by Iryna Chernega, Mariia Martsinkiv, Taras Vasylyshyn and Andriy Zagorodnyuk
Quantum Rep. 2023, 5(4), 683-697; https://doi.org/10.3390/quantum5040043 - 8 Dec 2023
Cited by 3 | Viewed by 1389
Abstract
We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach [...] Read more.
We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for ℓ1(Z0), induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semi-ring structures into this set and discuss their possible physical interpretations. Full article
(This article belongs to the Special Issue Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models)
20 pages, 571 KiB  
Article
Excitation Spectra and Edge Singularities in the One-Dimensional Anisotropic Heisenberg Model for Δ = cos(π/n), n = 3,4,5
by Pedro Schlottmann
Quantum Rep. 2022, 4(4), 442-461; https://doi.org/10.3390/quantum4040032 - 19 Oct 2022
Viewed by 1840
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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8 pages, 593 KiB  
Article
Statistical Quantifiers Resolve a Nuclear Theory Controversy
by 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 3 | Viewed by 2670
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.
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 here that an appeal to a suitable statistical quantifier called thermal efficiency puts an end to the controversy. 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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Review

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22 pages, 447 KiB  
Review
Cramér–Rao, Fisher–Shannon and LMC–Rényi Complexity-like Measures of Multidimensional Hydrogenic Systems with Application to Rydberg States
by Jesús S. Dehesa
Quantum Rep. 2023, 5(1), 116-137; https://doi.org/10.3390/quantum5010009 - 9 Feb 2023
Cited by 3 | Viewed by 1890
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 [...] Read more.
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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