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Axioms
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Recent Advances in Quantum Mechanics and Mathematical Physics
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Recent Advances in Quantum Mechanics and Mathematical Physics

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

Deadline for manuscript submissions: 1 October 2025 | Viewed by 2428

Special Issue Editor

Prof. Dr. Espen Gaarder Haug

E-Mail Website
Guest Editor
School of Economics and Business, Norwegian University of Life Sciences, 1430 Ås, Norway
Interests: quantum gravity; uncertainty principle; cosmology; quantum cosmology; Planck scale; mathematical physics; mathematical finance; mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In this issue, we embark on a journey to explore innovative ideas and recent advances in the realms of quantum mechanics, quantum gravity, and mathematical physics. Our primary focus is on uncovering novel foundational concepts, including those that challenge the very bedrock of our understanding of physics. However, we also value contributions that build upon the existing consensus, offering fresh perspectives or enhancing current theories.

It is worth remembering that many concepts now considered central to physics began as speculative ideas with limited foundational support at the time of their initial publication and only later became part of the consensus. Of course, not all speculative ideas stand the test of time. Many have been proven incorrect or have simply faded into obscurity. As editors and referees, we are tasked with the challenging responsibility of discerning which speculative ideas have the potential to spark the next scientific revolution and which may lead to dead ends or be shown to be entirely wrong. Striking the right balance is crucial (but far from easy): being too permissive could dilute the rigor of our discourse, while being too conservative might stifle groundbreaking innovations.

In this issue, we invite you to join us in this delicate and exciting process of scientific discovery. We hope to inspire a dialogue that not only questions the current foundations of physics but also seeks to build upon them, in the hope of fostering a deeper and more comprehensive understanding of the subatomic world as well as the universe.

Prof. Dr. Espen Gaarder Haug
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.

Keywords

  • quantum mechanics
  • Heisenberg’s uncertainty principle
  • entanglement
  • quantum gravity
  • mathematical physics

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

11 pages, 586 KiB  
Article
Theoretical Proof of and Proposed Experimental Search for the Ground Triplet State of a Wigner-Regime Two-Electron ‘Artificial Atom’ in a Magnetic Field
by Marlina Slamet and Viraht Sahni
Axioms 2025, 14(5), 349; https://doi.org/10.3390/axioms14050349 - 3 May 2025
Viewed by 169
Abstract
It is experimentally established that there is no ground triplet state of the natural He atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artificial atom’ or a semiconductor quantum dot [...] Read more.
It is experimentally established that there is no ground triplet state of the natural He atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artificial atom’ or a semiconductor quantum dot in a magnetic field, as described by the Schrödinger–Pauli equation, we provide theoretical proof of the existence of a ground triplet state by deriving an exact analytical correlated wave function solution to the equation. The state exists in the Wigner high-electron-correlation regime. We further explain that the solution satisfies all requisite symmetry and electron coalescence constraints of a triplet state. Since, due to technological advances, such a Wigner crystal quantum dot can be created, we propose an experimental search for the theoretically predicted ground triplet-state spectral line. We note that there exists an analytical solution to the Schrödinger–Pauli equation for a ground singlet state in the Wigner regime for the same value of the magnetic field. The significance to quantum mechanics of the probable experimental observation of the ground triplet state for an ‘artificial atom’ is discussed. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)
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19 pages, 290 KiB  
Article
Fisher Information and Electromagnetic Interacting Dirac Spinors
by Asher Yahalom
Axioms 2025, 14(3), 229; https://doi.org/10.3390/axioms14030229 - 20 Mar 2025
Viewed by 272
Abstract
In earlier works, it was demonstrated that Schrödinger’s equation, which includes interactions with electromagnetic fields, can be derived from a fluid dynamic Lagrangian framework. This approach treats the system as a charged potential flow interacting with an electromagnetic field. The emergence of quantum [...] Read more.
In earlier works, it was demonstrated that Schrödinger’s equation, which includes interactions with electromagnetic fields, can be derived from a fluid dynamic Lagrangian framework. This approach treats the system as a charged potential flow interacting with an electromagnetic field. The emergence of quantum behavior was attributed to the inclusion of Fisher information terms in the classical Lagrangian. This insight suggests that quantum mechanical systems are influenced not just by electromagnetic fields but also by information, which plays a fundamental role in driving quantum dynamics. This methodology was extended to Pauli’s equations by relaxing the constraint of potential flow and employing the Clebsch formalism. Although this approach yielded significant insights, certain terms remained unexplained. Some of these unresolved terms appear to be directly related to aspects of the relativistic Dirac theory. In a recent work, the analysis was revisited within the context of relativistic flows, introducing a novel perspective for deriving the relativistic quantum theory but neglecting the interaction with electromagnetic fields for simplicity. This is rectified in the current work, which shows the implications of the field in the current context. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)
13 pages, 1405 KiB  
Article
Quantum Private Set Intersection Scheme Based on Bell States
by Min Hou, Yue Wu and Shibin Zhang
Axioms 2025, 14(2), 120; https://doi.org/10.3390/axioms14020120 - 7 Feb 2025
Cited by 1 | Viewed by 490
Abstract
In this paper, we introduce a quantum private set intersection (QPSI) scheme that leverages Bell states as quantum information carriers. Our approach involves encoding private sets into Bell states using unitary operations, enabling the computation of the intersection between two private sets from [...] Read more.
In this paper, we introduce a quantum private set intersection (QPSI) scheme that leverages Bell states as quantum information carriers. Our approach involves encoding private sets into Bell states using unitary operations, enabling the computation of the intersection between two private sets from different users while keeping their individual sets undisclosed to anyone except for the intersection result. In our scheme, a semi-honest third party (TP) distributes the first and second qubits of the Bell states to the two users. Each user encodes their private sets by applying unitary operations on the received qubits according to predefined encoding rules. The modified sequence is encrypted and then sent back to TP, who can compute the set intersection without learning any information about the users’ private inputs. The simulation outcomes on the IBM quantum platform substantiate the viability of our scheme. We analyze the security and privacy aspects of the sets, showing that both external attacks and internal threats do not compromise the security of the private inputs. Furthermore, our scheme exhibits better practicality by utilizing easily implementable Bell states and unitary operations, rather than relying on multiple encoded states for set intersection calculations. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)
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11 pages, 293 KiB  
Article
A Kuramoto Model for the Bound State Aharonov–Bohm Effect
by Alviu Rey Nasir, José Luís Da Silva, Jingle Magallanes, Herry Pribawanto Suryawan and Roshin Marielle Nasir-Britos
Axioms 2024, 13(12), 828; https://doi.org/10.3390/axioms13120828 - 27 Nov 2024
Viewed by 836
Abstract
The Aharonov–Bohm effect can be described as a phase difference in interfering charged particles that travel through two distinct pathways oppositely surrounding a perpendicularly-positioned solenoid. The magnetic field emanates from the solenoid but does not intersect the pathways. On the other hand, the [...] Read more.
The Aharonov–Bohm effect can be described as a phase difference in interfering charged particles that travel through two distinct pathways oppositely surrounding a perpendicularly-positioned solenoid. The magnetic field emanates from the solenoid but does not intersect the pathways. On the other hand, the Kuramoto model can be used to identify the synchronization conditions that lead to a particular phase difference by treating the phases as coupled oscillators. Starting with the overall wave function expression for the electron in an Aharonov–Bohm potential, we derive a version of the Kuramoto model describing the phase dynamics of the bound state of the quantum mechanical system. We show that the resulting synchronization condition of the model coincides with the allowable values of the flux parameter for our case to achieve an Aharonov–Bohm effect. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)
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