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Mathematics
Special Issues
Recent Advances in Quantum Theory and Its Applications
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Recent Advances in Quantum Theory and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 October 2024 | Viewed by 1946

Special Issue Editor

Dr. Laure Gouba

E-Mail Website
Guest Editor
Abdus Salam International Centre for Theoretical Physics (ICTP), 34151 Trieste, Italy
Interests: noncommutative quantum mechanics; PT-symmetric quantum theories; quantum entanglement; quantization procedures; quantum cosmology; coherent states; non-perturbative study of low dimensional gauge theories

Special Issue Information

Dear Colleagues,

We are pleased to inform you about the forthcoming Special Issue of the journal Mathematics on the topic of “Recent Advances in Quantum Theory and Its Applications”. Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic levels. It has been enormously successful in explaining microscopic phenomena in all branches of physics, and there continue to be many developments in the subject at present.

The aim of this Special Issue is to publish research papers on recent advances in quantum theory and its applications. We hope to attract article contributions from all researchers and experts with regard to the current topics in quantum theory. In addition to original research, review articles are also welcome.

Dr. Laure Gouba
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 information
  • quantum mechanics
  • quantum metrology
  • qubits
  • quantum optics
  • geometric phases
  • quantum gravity
  • quantum cosmology

Published Papers (2 papers)

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Research

45 pages, 461 KiB  
Article
Noncommutativity in Configuration Space Induced by a Conjugate Magnetic Field in Phase Space
by Jan Govaerts
Mathematics 2024, 12(2), 180; https://doi.org/10.3390/math12020180 - 5 Jan 2024
Viewed by 701
Abstract
An external magnetic field in configuration space coupled to quantum dynamics induces noncommutativity in its velocity momentum space. By phase space duality, an external vector potential in the conjugate momentum sector of the system induces noncommutativity in its configuration space. Such a rationale [...] Read more.
An external magnetic field in configuration space coupled to quantum dynamics induces noncommutativity in its velocity momentum space. By phase space duality, an external vector potential in the conjugate momentum sector of the system induces noncommutativity in its configuration space. Such a rationale for noncommutativity is explored herein for an arbitrary configuration space of Euclidean geometry. Ordinary quantum mechanics with a commutative configuration space is revisited first. Through the introduction of an arbitrary positive definite ∗-product, a one-to-one correspondence between the Hilbert space of abstract quantum states and that of the enveloping algebra of the position quantum operators is identified. A parallel discussion is then presented when configuration space is noncommutative, and thoroughly analysed when the conjugate magnetic field is momentum independent and nondegenerate. Once again the space of quantum states may be identified with the enveloping algebra of the noncommutative position quantum operators. Furthermore, when the positive definite ∗-product is adapted to the conjugate magnetic field, the coordinate operators span a Fock algebra of which the coherent states are the analogues of the structureless points in a commutative configuration space. These results generalise and justify a posteriori within ordinary canonical quantisation the heuristic approach to quantum mechanics in the noncommutative Euclidean plane as constructed and developed by F. G. Scholtz and his collaborators. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Theory and Its Applications)
20 pages, 1888 KiB  
Article
Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information
by Fabio Benatti and Giovanni Nichele
Mathematics 2024, 12(1), 37; https://doi.org/10.3390/math12010037 - 22 Dec 2023
Viewed by 818
Abstract
We investigate the divisibility properties of the tensor products Λt(1)⊗Λt(2) of open quantum dynamics Λt(1,2) with time-dependent generators. These dynamical maps emerge from a compound open system [...] Read more.
We investigate the divisibility properties of the tensor products Λt(1)⊗Λt(2) of open quantum dynamics Λt(1,2) with time-dependent generators. These dynamical maps emerge from a compound open system S1+S2 that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing effect: one can have Backflow of Information (BFI) from the environment to S1+S2 without the same phenomenon occurring for either S1 and S2. We shall refer to this effect as the Superactivation of BFI (SBFI). Full article
(This article belongs to the Special Issue Recent Advances in Quantum Theory and Its Applications)
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