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Axioms
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Stochastic Processes in Quantum Mechanics and Classical Physics
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Stochastic Processes in Quantum Mechanics and Classical Physics

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

Deadline for manuscript submissions: closed (30 August 2024) | Viewed by 3719

Special Issue Editor

Dr. Ilaria Cacciari

E-Mail Website
Guest Editor
Institute of Applied Physics “Nello Carrara” - CNR, Florence, Italy
Interests: stochastic processes; microwave; terahertz and optical propagation; quantum mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to present a new Special Issue in Axioms, entitled “Stochastic Processes in Quantum Mechanics and Classical Physics”.

Stochastic processes, by their nature, can represent an intriguing way to describe a wide range of phenomena. In fact, with stochastic modelling it is possible to give answers to old problems and to offer innovative statements in the current research framework. The first attempts to apply the stochastic theory happened long ago. Today, we have at our disposal powerful mathematical tools suitable for solving a wide variety of applied problems, and this increasingly inspires the interests of mathematicians, physicists and engineers.

The aim of the Special Issue is to publish original research papers and critical reviews that contribute new insights into the development and diffusion of stochastic modelling arising from quantum mechanics and classical physics.

Research areas may include (but are not limited to) the following:

  • Quantum mechanics;
  • Quantum statistics;
  • Quantum field theory;
  • Quantum electrodynamics;
  • Electromagnetism;
  • Thermodynamics;
  • Statistical mechanics.

Dr. Ilaria Cacciari
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

  • stochastic modelling
  • quantum mechanics
  • classical physics
  • Quantum mechanics
  • Quantum field theory

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Published Papers (3 papers)

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Research

16 pages, 337 KiB  
Article
Probability Bracket Notation for Probability Modeling
by Xing M. Wang and Tony C. Scott
Axioms 2024, 13(8), 564; https://doi.org/10.3390/axioms13080564 - 20 Aug 2024
Viewed by 806
Abstract
Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc. Using the PBN, many formulae, such as normalizations and expectations in systems of one or more random variables, can now [...] Read more.
Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc. Using the PBN, many formulae, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, which are easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi’s state function or Peliti’s standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman–Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT. Full article
(This article belongs to the Special Issue Stochastic Processes in Quantum Mechanics and Classical Physics)
12 pages, 1994 KiB  
Article
Modulation Transfer between Microwave Beams: Asymptotic Evaluation of Integrals with Pole Singularities near a First-Order Saddle Point
by Ilaria Cacciari and Anedio Ranfagni
Axioms 2024, 13(3), 178; https://doi.org/10.3390/axioms13030178 - 7 Mar 2024
Viewed by 936
Abstract
Experimental results of delay-time measurements in the transfer of modulation between microwave beams, as reported in previous articles, were interpreted on a competition (interference) between two waves, one of which is modulated and the other is a continuous wave (c.w.). The creation of [...] Read more.
Experimental results of delay-time measurements in the transfer of modulation between microwave beams, as reported in previous articles, were interpreted on a competition (interference) between two waves, one of which is modulated and the other is a continuous wave (c.w.). The creation of one of these waves was attributed to a saddle-point contribution, while the other was attributed to pole singularities. In this paper, such an assumption is justified by a quantitative field-amplitude analysis in order to make the modeling plausible. In particular, two ways of calculating field amplitudes are considered. These lead to results that are quantitatively markedly different, although qualitatively similar. Full article
(This article belongs to the Special Issue Stochastic Processes in Quantum Mechanics and Classical Physics)
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30 pages, 692 KiB  
Article
Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes
by Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko and Yevheniia Anastasiia Rudyk
Axioms 2023, 12(11), 1026; https://doi.org/10.3390/axioms12111026 - 31 Oct 2023
Cited by 2 | Viewed by 1311
Abstract
We consider five types of entropies for Gaussian distribution: Shannon, Rényi, generalized Rényi, Tsallis and Sharma–Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian [...] Read more.
We consider five types of entropies for Gaussian distribution: Shannon, Rényi, generalized Rényi, Tsallis and Sharma–Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian motions, and compare the entropies of one-dimensional distributions of these processes. Full article
(This article belongs to the Special Issue Stochastic Processes in Quantum Mechanics and Classical Physics)
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