Special Issue "Mathematical Physics II"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 October 2019

Special Issue Editor

Guest Editor
Dr. Enrico De Micheli

Consiglio Nazionale delle Ricerche Via De Marini, 6, 16149 Genova, Italy
Website | E-Mail
Interests: mathematical physics; potential theory and harmonic analysis; thermal quantum field theory; quantum computation; regularization theory; special functions of mathematical physics; computational physics

Special Issue Information

Dear Colleagues,

The impressive adequacy of many physical theories with experimental observations has always been a stimulating beacon for mathematical physicists, whose wish is to achieve coherent representations and a coherent understanding of the various branches of physics in terms of mathematically well-defined objects.

The mathematical beauty of the classical theories of the nineteenth century evolved in the first-half of the twentieth century towards the revolutionary ideas of Special Relativity and the puzzling concepts of Quantum Mechanics, which boosted the use and development of sophisticated algebras.

The synthesis of these two paradigms—Quantum Field Theory—provides an outstanding and intriguing theoretical framework for the mathematical formulation of physical theories. Analyticity properties investigation of structure functions and scattering kernels, harmonic analysis of groups, unitary representation theory, algebraic geometry, and operator algebras are just a few examples of the numerous profitable mathematical tools that are normally applied. Mathematical methods that also find fruitful application in Quantum Information Theory are the more recent encounter of quantum ideas with Information Theory and those that allow for the exploration of challenging topics such as entanglement theory, quantum communication channel theory, and algorithm design for quantum computation.

The Guest Editor solicits research papers and reviews that present essentially a mathematical approach to physical problems.

Dr. Enrico De Micheli
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 papers will be 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 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 850 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

  • Mathematical methods in Physics
  • Quantum fields
  • Lie groups in Physics
  • Complex analysis in Physics
  • Spectral analysis
  • Statistical Physics
  • Approximation theory
  • Algebraic geometry in Physics
  • Differential equations
  • Asymptotic methods
  • Operator algebras
  • Quantum Information theory
  • Quantum communication channels

Published Papers (2 papers)

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Research

Open AccessArticle
Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields Q p over Primes p
Mathematics 2019, 7(2), 199; https://doi.org/10.3390/math7020199
Received: 11 December 2018 / Revised: 12 February 2019 / Accepted: 15 February 2019 / Published: 19 February 2019
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Abstract
In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space (LS,τ0) induced by measurable functions on p-adic number fields Qp over primes p. In particular, we are interested in [...] Read more.
In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p . In particular, we are interested in the cases where such free-probabilistic information is affected by primes in given closed intervals of the set R of real numbers by defining suitable “truncated” linear functionals on LS . Full article
(This article belongs to the Special Issue Mathematical Physics II)
Open AccessArticle
The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach
Mathematics 2019, 7(2), 170; https://doi.org/10.3390/math7020170
Received: 4 January 2019 / Revised: 6 February 2019 / Accepted: 7 February 2019 / Published: 13 February 2019
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Abstract
In this paper, the Lax pair of the modified nonlinear Schrödinger equation (mNLS) is derived by means of the prolongation structure theory. Based on the obtained Lax pair, the mNLS equation on the half line is analyzed with the assistance of Fokas method. [...] Read more.
In this paper, the Lax pair of the modified nonlinear Schrödinger equation (mNLS) is derived by means of the prolongation structure theory. Based on the obtained Lax pair, the mNLS equation on the half line is analyzed with the assistance of Fokas method. A Riemann-Hilbert problem is formulated in the complex plane with respect to the spectral parameter. According to the initial-boundary values, the spectral function can be defined. Furthermore, the jump matrices and the global relations can be obtained. Finally, the potential q ( x , t ) can be represented by the solution of this Riemann-Hilbert problem. Full article
(This article belongs to the Special Issue Mathematical Physics II)
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