Advances in Quantum Theory Methods and Applications in Computational Mathematics and Physics

Dear Colleagues,

In 2025, we celebrate the centenary of quantum mechanics by proclaiming this year as the International Year of Quantum Science and Technology. Quantum science is not just a theory; it is a force that has significantly transformed the world around us. From quantum mechanics to quantum physics of atoms, molecules, nanotechnology and nanomaterials, nuclear energy, medicine to quantum mathematics, informatics, communications, cryptography, quantum computing, and quantum intelligent systems, quantum science and quantum systems and technologies are unlocking new possibilities, bringing us closer to a more sustainable future.

Achieving goals these goals requires innovative strategies for the development and implementation of new ideas, mathematical concepts, and numerical methods across various areas, including quantum mechanics and quantum electrodynamics, quantum geometry and algebra, relativistic quantum field theory (including axiomatic quantum field theory), quantum information science and statistics, quantum modeling, computing  and optimal governing, and quantum intelligent systems. Additionally, it calls for the application of new methods and computational algorithms in various fields of computational mathematics, physics, etc.

The purpose of this Special Issue is to highlight high-quality articles on new theoretical, mathematical,  and methodological advances in quantum mechanics, quantum electrodynamics, quantum field theory (including axiomatic quantum field theory), and mathematical physics. We emphasize the application of new ideas, concepts, axioms, methods, and algorithms of quantum theory in theoretical, computational physics, mathematics, etc., to develop and apply new quantum approaches in modern theoretical atomic and molecular spectroscopy, quantum optics, precision description of relativistic effects in modern quantum physics, further development of mathematical aspects of modern density functional theory, ab initio approaches based on wave functions, and the development and implementation of new optimal mathematical analysis and mathematical physics methods to describe complex quantum systems, quantum artificial intelligence, quantum modelling, and optimal governing and control.

We hope that this issue will provide timely and in-depth coverage of the latest fundamental theoretical and mathematical advancements in the theory and applications of quantum systems. This Special Issue aims to serve as a basis for evaluating and generating new ideas in the broad fields of quantum theory, computational mathematics, mathematical physics, and computer science. This issue will be of particular interest to researchers focused on the development and application of new theoretical, mathematical, axiomatic, and computational approaches in quantum science.

Topics of interest include (but are not limited to) the following research areas:

• New mathematical ideas, concepts, and methods in quantum mechanics and quantum electrodynamics;
• Advances in quantum geometry, algebra, and new computational algorithms for solving master quantum equations;
• New approaches in quantum field theory, including an axiomatic quantum field theory;
• New mathematical and methodical advances in density functional theory and wavefunction-based ab initio treatments;
• Relativistic effects in quantum physics: new and advanced available approaches;
• New mathematical approaches to finite Fermi (atoms, molecules, nuclei) and Bose systems in strong fields;
• New quantum methods and numerical analysis and computational codes in mathematical and computational physics, including theoretical atomic and molecular spectroscopy;
• New theoretical methods and mathematical models in quantum informatics and quantum statistics;
• New mathematical concepts and algorithms in quantum systems, quantum computing, quantum artificial intelligence, quantum modelling, and optimal governing.

We look forward to receiving your contributions.

Sincerely yours,

Prof. Dr. Alexander V. Glushkov
Prof. Dr. Andrey A. Svinarenko
Prof. Dr. Olga Y. Khetselius
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. 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.

• quantum geometry and algebra, mathematical analysis, computational algorithms of solving quantum equations
• theoretical quantum mechanics and quantum electrodynamics
• relativistic effects in quantum physics
• quantum field theory, axiomatic quantum field theory
• numerical modelling Fermi and Bose systems in strong fields
• wavefunction-based ab initio treatments
• density functional theory
• mathematical analysis, computational mathematics, theoretical and mathematical physics
• computational codes in theoretical atomic and molecular spectroscopy
• quantum informatics and quantum statistics
• quantum modelling and optimal governing
• quantum artificial intelligence