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The latest achievements in the development of the concept of radio- and optical systems quasiparticle based on Feynman integrals
Proceedings of SPIE. 2017. Vol. 10342. P. 1–9.
Потапов А. А., Рассадин А. Э.
In a number of previous papers authors have introduced quasiparticle of radio- and optical systems. We have called this quasiparticle by ‘radion’. The basis for this is the representation of Green’s function of equation of quasioptics by Feynman integral. It means that radion has quantum mechanical properties. In particular in approximation of quasioptics one can interprete amplitude of electromagnetic field as amplitude of probability of radion. In the paper presented we describe new features of radion which we have established recently namely we have found some exact solutions of evolutionary equation for field of quantum mechanical averages of momenta of ensemble of radions possessing by average of momentum in initial state depending on average of coordinate in it. We demonstrate three the simplest solutions from this set of exact solutions. These solutions in the form of power series on dimensionless time are applicable up to the moment of gradient catastrophe. For representation of solutions of parabolic equation in approximation of quasioptics Remizov method of quasi-Feynman formulae has been used. All these results due to suggested by us physical analogy are valid for free one-dimensional nonrelativistic quantum mechanical particle too. Also in the framework of Remizov method a number of new formulae for statistical radiophysics and optics has been obtained. ‘Natural’ fractality of radio- and optical systems has been discussed.
Keywords: преобразование Фурье Fourier transformнепрерывная нигде не дифференцируемая функция ТакагиRiemann equationSchrödinger equationуравнение ШрёдингераHeisenberg representationChebyshev-Hermite polynomials the space shift operator bispectrum the Takagi functionпредставление Гейзенбергауравнение Риманаполиномы Чебышёва-Эрмитаоператор пространственного сдвигабиспектр
Dmitriev A., Kornilov V., Batienkov R., Lecture Notes in Civil Engineering 2026 Vol. 886 P. 249–255
Numerous studies have provided compelling evidence that the probability distribution of avalanche sizes follows a power law, and that 1/f noise is present in the stochastic dynamics of landslides. We present a theoretical explanation of these phenomena within the framework of self-organized criticality theory, proposing a discrete-time model in the form of a sandpile cellular ...
Added: October 13, 2026
Dmitriev A., Shulman I., Lebedev A., Studies in Computational Intelligence 2026 Vol. 1265 P. 266–273
A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu ...
Added: October 13, 2026
Arutyunov K., Kharitonov I. A., Petrosyants K. O., JETP Letters 2026 Vol. 124 No. 6 P. 1–16
Superconducting properties of metallic micro- and nanowires can be entirely different from those of bulk superconductors. Of particular interest is the nonequilibrium current-induced state of a quasi-one-dimensional superconducting channel. The most interesting phenomenon here is the stepped I–V characteristic, explained by a process known as phase slip center activation. If the origin of such step-like ...
Added: October 13, 2026
Makarov D. M., Kalikin N., Fashchevsky K. A. et al., Electrochimica Acta 2026 Vol. 579 Article 150159
Machine learning (ML) has become a powerful tool for accelerating the development of carbon-based supercapacitors;
however, most published models assume that a single predictive framework can describe both conventional
porous carbons and hybrid carbon electrodes. Here, we test this assumption using a comprehensive
benchmark dataset and an extended literature-curated dataset enriched with synthesis- and electrolyte-related
descriptors. Three ML algorithms ...
Added: October 13, 2026
Махлуф М., Ozhegov R., Elezov M. et al., Фотоника 2026 Vol. 20 No. 6 P. 414–423
This paper compares the ranging precision of direct time-of-flight (dToF) and non-line-of-sight (NLOS) LiDAR architectures, both using a superconducting nanowire single-photon detector (SNSPD). Both systems operate at 1550 nm with a 50 ps pulsed laser and time-correlated single-photon counting (TCSPC). The dToF configuration achieved approximately 100 µm precision at 10 m, while the NLOS configuration achieved 500 µm precision for ...
Added: October 12, 2026
Singapore: Springer, 2026.
This volume presents the Proceedings of the 34th IUPAP Conference on Computational Physics (CCP2023), held in Kobe, Japan on August 4–8, 2023. It offers a collection of peer-reviewed articles that highlight recent developments in computational and simulation research across various areas of physics. Key topics include the use of data science, quantum computing, and machine ...
Added: October 12, 2026
Goncharov A., Chibisov A., Advanced Theory and Simulations 2023 Vol. 12 No. 13 Article 2200816
Designing stable quantum computers with the ability to correct errors responsibly requires a detailed understanding of the physical processes that underlie these devices. In this study, detailed quantum mechanical simulations of the atomic structure, charge distribution of electron density, and distribution and orientation of magnetic and quantum states as a function of applied external pressure ...
Added: October 11, 2026
Chibisov A., Gnidenko A., Chibisova M. et al., FlatChem 2023 Vol. 41 Article 100533
Manufacturing precise quantum computers with small errors in quantum operations, long coherence times, and low power consumption is the most important challenge in modern nanoelectronics. To understand the operating modes of such calculators in detail, both the optimal arrangement of the qubit system within the structure and changes in its magnetic properties must be comprehensively ...
Added: October 11, 2026
E. M. Novikova, Mathematical notes 2025 Vol. 118 No. 4 P. 794–810
For each integer nonnegative n, in some Hilbert space, we introduce an integral
transform H_n. It is similar to the well-known Hankel (Fourier–Bessel) transform of nth order due
to the fact that it is related to the Fourier transform and its integral kernel is expressed in terms of
the Bessel function J_n. But, unlike the Hankel transform, intended ...
Added: November 25, 2025
Novikov R., Sivkin V., Inverse Problems 2021 Vol. 37 No. 5 Article 055011
We consider phaseless inverse scattering for the multidimensional Schrodinger equation with unknown potential v using the method of known background scatterers. In particular, in dimension d > 2, we show that |f (1)|(2) at high energies uniquely determines v via explicit formulas, where f (1) is the scattering amplitude for v + w (1), w ...
Added: October 22, 2024
Вишняков Г. Н., Yurin A., Minaev V. et al., Известия высших учебных заведений. Прикладная нелинейная динамика 2023 Т. 31 № 4 С. 408–420
The purpose of this work is to analyze the effect of the polarimeter signal processing algorithm on the results of measurements of the optical rotation angle of the polarization plane to improve the accuracy of measurements in differential polarimetry. Methods. The paper considers the methods of polarimetry used for the analysis of optically active substances, ...
Added: July 31, 2023
Romanov I., Shamaev A. S., Mathematical notes 2023 Vol. 113 No. 4 P. 598–600
Problems of local controllability for various systems with distributed parameters often arise in many applied problems, so this field is of significant interest. For classical systems of mechanics (membranes, thin plates), controllability problems are important in the cases where the control action is applied either to the boundary or to a part of the domain. ...
Added: April 25, 2023
A. E. Rassadin, Журнал Средневолжского математического общества 2023 Vol. 25 No. 1 P. 542–533
In the present paper, a nonlinear countable-dimensional system of integrodifferential equations is investigated, whose vector of unknowns is a countable set of functions of two variables. These variables are interpreted as spatial coordinate and time. The nonlinearity of this system is constructed from two simultaneous convolutions: first convolution is in the sense of functional analysis ...
Added: April 4, 2023
Agalarov A. M., Alekseeva E. S., Potapov A. A. et al., , in: 14th Chaotic Modeling and Simulation International Conference.: Springer, 2022. Ch. 3 P. 31–44.
Added: December 7, 2022
Крымский С. Т., Filonov N. D., Алгебра и анализ 2022 Т. 34 № 1 С. 105–122
Рассмотрим уравнение −Δu+Vu=0 в полуцилиндре [0,∞)×(0,2π)d с периодическими краевыми условиями на боковой поверхности. Предполагаем, что потенциал V ограничен. Нас интересует скорость убывания нетривиального решения на бесконечности. Мы покажем, что самое быстрое возможное убывание — как e−cx при d=1 и 2 и как e−cx4/3 при d≥3; здесь x — продольная переменная. ...
Added: October 31, 2022
Marcati C., Rakhuba M., Schwab C., Advances in Computational Mathematics 2022 Vol. 48 No. 3 Article 18
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in ℝ3. We consider functions in countably normed Sobolev spaces with radial weights and analytic- or Gevrey-type control of weighted semi-norms. Several classes of boundary value and eigenvalue problems from science and engineering are discussed whose solutions belong to the ...
Added: October 30, 2022
Chetverikov V., Mamsurov I., , in: Proceedings of 2022 IEEE Moscow Workshop on Electronic and Networking Technologies (MWENT).: M.: IEEE, 2022. P. 1–4.
The solutions of the Schrodinger (Schrodinger – Pauli) equations and the Dirac equation in the 2+1 space for the two-dimensional motion of a charged particle in a uniform and constant magnetic field, as well as the construction of coherent states based on the solutions obtained are considered. A specific feature of this problem is the ...
Added: October 25, 2022
В. П. Спиридонов, Теоретическая и математическая физика 2022 Т. 212 № 3 С. 403–413
We describe a family of quantum states of the Schrödinger cat type as superpositions of the harmonic oscillator coherent states with coefficients defined by the quadratic Gauss sums. These states emerge as eigenfunctions of the lowering operators obtained after canonical transformations of the Heisenberg–Weyl algebra associated with the ordinary and fractional Fourier transformations. The first member of this family is given by the well ...
Added: August 30, 2022
Tikhonov E., Sneps-Sneppe M., International Journal of Open Information Technologies 2019 Vol. 7 No. 4 P. 53–60
The article introduces powerful common tool for the signals analysis – basics of a spectral analysis.
It focuses on decomposition into complex sine waves (harmonic sinusoids) called the Fourier transform.
Based on qualitative review of the natural phenomenon of visible light (that is the electromagnetic field oscillation in a working range of the eyes) decomposition into a ...
Added: April 9, 2022
Galkin O., Galkina S., / Series arXiv "math". 2020. No. 2003.08540.
The functions of the Takagi exponential class are similar in construction to the continuous, nowhere differentiable Takagi function described in 1901. They have one real parameter v∈(−1;1) and at points x∈R are defined by the series Tv(x)=∑∞n=0vnT0(2nx), where T0(x) is the distance between x and the nearest integer point. If v=1/2 then Tv coincides with Takagi's function. In this paper, for different values of the parameter v, we study ...
Added: October 14, 2021
Cohen Y., Zilberman A., Zion Dekel B. et al., , in: Intelligent Decision Technologies. Proceedings of the 12th KES International Conference on Intelligent Decision Technologies (KES-IDT 2020)Vol. 193.: Singapore: Springer, 2020. P. 141–153.
In this work, we present a Real-Time (RT), on-site, machine-learning-based methodology for identifying human cancers. The presented approach is reliable, effective, cost-effective, and non-invasive method, which is based on Fourier Transform Infrared (FTIR) spectroscopy—a vibrational method with the ability to detect changes as a result of molecular vibration bonds using Infrared (IR) radiation in human ...
Added: October 29, 2020
Osipov D., Паршин А. Н., Математический сборник 2020 Т. 211 № 1 С. 125–174
In this work we construct a harmonic analysis on free Abelian groups of rank 2, namely: we construct and investigate spaces of functions and distributions, Fourier transforms and actions of discrete and extended discrete Heisenberg groups. In the case of the rank-2 value group of a two-dimensional local field with finite last residue field we ...
Added: May 20, 2020
Ростов н/Д: Издательство ЮФУ, 2019.
В сборнике представлены доклады участников XVIII Всероссийской конференции-школы молодых исследователей ”СОВРЕМЕННЫЕ ПРОБЛЕМЫ МАТЕМАТИЧЕСКОГО МОДЕЛИРОВАНИЯ”, организованной Институтом прикладной математики им. М.В. Келдыша РАН и Институтом математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета, проходившей с 16 по 21 сентября
2019 года в поселке Абрау-Дюрсо, Новороссийск, Россия. В работе школы приняли участие представители научных центров ...
Added: December 29, 2019
Grushin V. V., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 344–351
Formulas for the asymptotics of some class of integrals of rapidly oscillating functions that generalize the well-known stationary phase method, which were obtained in the previous paper of the author, are applied to integrals arising in the well-known tsunami hydrodynamic piston model in the case of a constant pool bottom. As a result, asymptotic formulas ...
Added: October 14, 2019