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Special Issue "Advances in Quantum Theory and Quantum Computing"

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A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 3501

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Prof. Dr. Jan Sładkowski

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Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, Pl 41-005 Chorzów, Poland
Interests: quantum field theory; quantum computing; mathematical physics; game theory

Special Issue Information

Dear Colleagues,

Even though it is over a hundred years old, quantum theory of information is still highly relevant. Many scientists are looking for a quantum equivalent to the theory of gravity. Therefore, it is difficult to overestimate the importance of quantum aspects in broadly understood science and technology. Even mathematical modeling would be a completely different science without the concepts rooted in quantum theory.

This Special Issue aims to highlight the role of symmetry in pure and applied sciences. We invite contributions of both theoretical and applied types. The authors are encouraged to submit their original research results and, possibly, reviews. The scope of topics includes, but is not limited to, the following:

"standard" quantum mechanics and quantum field theory;
quantum statistical physics;
quantum information processing;
mathematical structure of quantum theory;
quantum games;
quantum decision theory;
quantum aspects of social science.

Prof. Dr. Jan Sładkowski
Guest Editor

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. Axioms is an international peer-reviewed open access monthly 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 2400 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.

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Research

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Open AccessArticle

On the Structure of Quantum Markov Chains on Cayley Trees Associated with Open Quantum Random Walks

and

Axioms 2023, 12(9), 864; https://doi.org/10.3390/axioms12090864 - 07 Sep 2023

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Abstract

Quantum Markov chains (QMCs) and open quantum random walks (OQRWs) represent different quantum extensions of the classical Markov chain framework. QMCs stand as a more profound layer within the realm of Markovian dynamics. The exploration of both QMCs and OQRWs has been a predominant focus over the past decade. Recently, a significant connection between QMCs and OQRWs has been forged, yielding valuable applications. This bridge is particularly impactful when studying QMCs on tree structures, where it intersects with the realm of phase transitions in models naturally arising from quantum statistical mechanics. Furthermore, it aids in elucidating statistical properties, such as recurrence and clustering. The objective of this paper centers around delving into the intricate structure of QMCs on Cayley trees in relation to OQRWs. The foundational elements of this class of QMCs are built upon using classical probability measures that encompass the hierarchical nature of Cayley trees. This exploration unveils the pivotal role that the dynamics of OQRWs play in shaping the behavior of the Markov chains under consideration. Moreover, the analysis extends to their classical counterparts. The findings are further underscored by the examination of notable examples, contributing to a comprehensive understanding of the outcomes. Full article

(This article belongs to the Special Issue Advances in Quantum Theory and Quantum Computing)

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Open AccessArticle

Quasi-Magical Fermion Numbers and Thermal Many-Body Dynamics

Angelo Plastino

Diana Monteoliva

and

Angel Ricardo Plastino

Axioms 2023, 12(5), 493; https://doi.org/10.3390/axioms12050493 - 19 May 2023

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Abstract

This work scrutinizes, using statistical mechanics indicators, important traits displayed by quantum many-body systems. Our statistical mechanics quantifiers are employed, in the context of Gibbs’ canonical ensemble at temperature T. A new quantifier of this sort is also presented here. The present discussion focuses attention on the role played by the fermion number N in many-fermion dynamics, that is, N is our protagonist. We have discovered discovers particular values of N for which the thermal indicators exhibit unexpected abrupt variations. Such a fact reflects an unanticipated characteristic of fermionic dynamics. Full article

(This article belongs to the Special Issue Advances in Quantum Theory and Quantum Computing)

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Open AccessArticle

Certain q-Analogue of Fractional Integrals and Derivatives Involving Basic Analogue of the Several Variable Aleph-Function

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Axioms 2023, 12(1), 51; https://doi.org/10.3390/axioms12010051 - 03 Jan 2023

Cited by 1 | Viewed by 747

Abstract

Using Mellin-Barnes contour integrals, we aim at suggesting a q-analogue (q-extension) of the several variable Aleph-function. Then we present Riemann Liouville fractional q-integral and q-differential formulae for the q-extended several variable Aleph-function. Using the q-analogue of the Leibniz rule for the fractional q-derivative of a product of two basic functions, we also provide a formula for the q-extended several variable Aleph-function, which is expressed in terms of an infinite series of the q-extended several variable Aleph-function. Since the three main formulas presented in this article are so general, they can be reduced to yield a number of identities involving q-extended simpler special functions. In this connection, we choose only one main formula to offer some of its particular instances involving diverse q-extended special functions, for example, the q-extended I-function, the q-extended H-function, and the q-extended Meijer’s G-function. The results presented here are hoped and believed to find some applications, in particular, in quantum mechanics. Full article

(This article belongs to the Special Issue Advances in Quantum Theory and Quantum Computing)

Open AccessArticle

Diffusion Effect in Quantum Hydrodynamics

Moise Bonilla-Licea

Dieter Schuch

and

Moises Bonilla Estrada

Axioms 2022, 11(10), 552; https://doi.org/10.3390/axioms11100552 - 13 Oct 2022

Cited by 1 | Viewed by 762

Abstract

In this paper, we introduce (at least formally) a diffusion effect that is based on an axiom postulated by Werner Heisenberg in the early days of quantum mechanics. His statement was that—in quantum mechanics—kinematical quantities such as velocity must be treated as complex matrices. In the hydrodynamic formulation of quantum mechanics according to Madelung, the complex Schrödinger equation is rewritten in terms of two real equations—a continuity equation and a modified Hamilton–Jacobi equation. Considering seriously Heisenberg’s axiom, the velocity occurring in the continuity equation should be replaced by a complex one, thus introducing a diffusion term with an imaginary diffusion coefficient. Therefore, in quantum mechanics, there should be a diffusion effect showing up in the dynamics. This is the case in the time evolution of the free-motion wave packet under time reversal. The maximum returns to the initial position; however, the width of the wave packet does not shrink to its initial width. This effect is obvious but—as far as we know—it is not mentioned in any textbook. In our paper, we discuss this effect in detail and show the connection with a complex version of quantum hydrodynamics. Full article

(This article belongs to the Special Issue Advances in Quantum Theory and Quantum Computing)

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The Magnificent Realm of Affine Quantization: Valid Results for Particles, Fields, and Gravity

John R. Klauder

and

Riccardo Fantoni

Axioms 2023, 12(10), 911; https://doi.org/10.3390/axioms12100911 (registering DOI) - 25 Sep 2023

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Abstract

Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are extremely close to, and even constructed from, the tools of canonical quantization, are able to fully solve selected problems that using the standard canonical quantization would fail. In particular, improvements can even be found with an affine quantization of fields, as well as gravity. Full article

(This article belongs to the Special Issue Advances in Quantum Theory and Quantum Computing)

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