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Coherent States in a Problem with Infinitely Multiple Spectrum
P. 1–4.
Chetverikov V., Mamsurov I.
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 presence of a discrete spectrum with infinite multiplicity of degeneracy. Two pairs of creation and annihilation operators allow one to construct coherent states which are a special superposition of the states of two oscillators. The influence of the multiplicity of the spectrum on the average values of coordinates and momenta due to the appearance of two pairs of creation and annihilation operators is shown. The constructed coherent states depending on two complex numbers lead to two independent Poisson distributions for two types of vibration quanta. The introduced operators allow one to represent the solutions of the Dirac equation in the 2+1 space for the discrete spectrum problem under consideration in a simple form.
In book
M.: IEEE, 2022.
Sofia Rumyantseva, Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 Article 5
This paper investigates the Lorentz invariance of the multidimensional Dirac–Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the coordinates. We examine two distinct approaches: the tensor formulation and the spinor formulation. We first present a detailed examination of the four-dimensional Dirac–Hestenes equation, comparing both transformation approaches. These results are subsequently ...
Added: December 19, 2025
Glutsyuk A., Александров А. А., Горский А. С., / Series arXiv "math". 2025.
In this study, we discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrodinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the ...
Added: June 23, 2025
Sofia Rumyantseva, Shirokov D., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 24
It is easier to investigate phenomena in particle physics geometrically by exploring a real solution to the Dirac-Hestenes equation instead of a complex solution to the Dirac equation. The present research outlines the multidimensional Dirac-Hestenes equation. Since the matrix representation of the complexified (Clifford) geometric algebra ℂ⊗Cℓ1,n depends on a parity of n, we explore even and odd ...
Added: November 8, 2024
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
Hohage T., Novikov R., Sivkin V., Inverse Problems 2024 Vol. 40 No. 10 Article 105007
We consider the problem of finding a compactly supported potential in the multidimensional Schr & ouml;dinger equation from its differential scattering cross section (squared modulus of the scattering amplitude) at fixed energy. In the Born approximation this problem simplifies to the phase retrieval problem of reconstructing the potential from the absolute value of its Fourier ...
Added: October 22, 2024
Fedor Ozhegov, Reviews in Mathematical Physics 2024 Vol. 36 No. 7 Article 2450017
In this paper, we study Feynman checkers, one of the most elementary models of electron motion. It is also known as a one-dimensional quantum walk or an Ising model at an imaginary temperature. We add the simplest non-trivial electromagnetic field and find the limits of the resulting model for small lattice step and large time, ...
Added: May 17, 2024
Skopenkov M., Ustinov A., Analysis and Mathematical Physics 2024 Vol. 14 Article 38
We present a new completely elementary model that describes the creation, annihilation, and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names
Feynman checkers or one-dimensional quantum walk. It can be viewed as a six-vertex model with certain complex weights of the vertices. The discrete model is consistent ...
Added: March 24, 2024
Marchuk N., М.: Издательская группа URSS, 2023.
В книге изучаются релятивистские уравнения теории поля, в частности рассматриваются свойства ковариантности и симметрии уравнений Дирака—Максвелла и Дирака—Янга—Миллса. Вводится ряд новых систем уравнений, называемых модельными уравнениями теории поля. Эти системы уравнений воспроизводят основные свойства стандартных систем уравнений теории поля. В то же время модельные уравнения имеют ряд отличий от стандартных уравнений теории поля, в частности обладают новой внутренней симметрией ...
Added: January 3, 2024
Потапов А. А., Рассадин А. Э., Proceedings of SPIE 2017 Vol. 10342 P. 1–9
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 ...
Added: December 17, 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
Skopenkov M., Ustinov A., / Cornell University. Серия arXiv "math". 2022.
We present a new completely elementary model which describes creation, annihilation and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names Feynman checkers, or one-dimensional quantum walk, or Ising model at imaginary temperature. The discrete model is consistent with the continuum quantum field theory, ...
Added: October 23, 2022
М. Б. Скопенков, А. В. Устинов, Успехи математических наук 2022 Т. 77 № 3(465) С. 73–160
We survey and develop the most elementary model of electron motion introduced by R.Feynman. In this game, a checker moves on a checkerboard by simple rules, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk or an Ising model at imaginary temperature. We solve mathematically a problem by R.Feynman ...
Added: August 12, 2022
Remizov I., Starodubtseva M., Математические заметки 2018 Т. 104 № 5 С. 790–795
краткое сообщение - нет аннотации ...
Added: September 29, 2018
Remizov I., Математические заметки 2016 Т. 100 № 3 С. 477–480
Краткое сообщение. ...
Added: March 9, 2018
Shirokov D., , in: Proceedings of the Nineteenth International Conference on Geometry, Integrability and QuantizationVol. 19.: Sofia: Avangard Prima, 2018. Ch. 1 P. 11–53.
We discuss some well-known facts about Clifford algebras: matrix representations, Cartan’s periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in <span data-mathml="nn dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the ...
Added: January 31, 2018
Shirokov D., Marchuk N., Reports on Mathematical Physics 2016 Vol. 78 No. 3 P. 305–326
We find general solutions of some field equations (systems of equations) in pseudo-Euclidian spaces (so-called primitive field equations). These equations are used in the study of the Dirac equation and Yang-Mills equations. These equations are invariant under orthogonal O(p,q) coordinate transformations and invariant under gauge transformations, which depend on some Lie groups. In this paper ...
Added: September 27, 2016
K.I. Kugel, Rodionov Y. I., Nori F., Physical Review B: Condensed Matter and Materials Physics 2015 Vol. 92 No. 19 P. 195117-1–195117-15
We study dc conductivity of a Weyl semimetal with uniaxial anisotropy (Fermi velocity ratio ξ = v⊥/v = 1)
considering the scattering of charge carriers by a wide class of impurity potentials, both short- and long-range.We
obtain the ratio of transverse and longitudinal (with respect to the anisotropy axis) conductivities as a function of
both ξ and temperature. ...
Added: March 11, 2016
Vybornyi E., Наноструктуры. Математическая физика и моделирование 2015 Т. 13 № 2 С. 43–54
We conceder semiclassical asymptotics of the energy levels shift of the Schrödinger operator discrete spectrum with a one-dimensional single-well potential that appears due to a deformation of the potential in the classically forbidden region. Since such a deformation of the potential effects on the quantum particle only due to the tunneling effects, then the corresponding ...
Added: February 18, 2016
Vybornyi E., Наноструктуры. Математическая физика и моделирование 2015 Т. 12 № 1 С. 5–84
We consider the problem of constructing semiclassical asymptotic expansions of discrete spectrum and the corresponding stationary states of one-dimensional Schrödinger operator in the case of resonance tunneling. We consider two basic models: tunneling in an asymmetric double-well potential on a line and momentum tunneling of a particle in a potential field on a circle. For ...
Added: February 12, 2016