arXiv subjects

Askold Duviryak

Publications and source records attributed to Askold Duviryak.

15 recordsLinked to original sources

arXiv2024

Asymptotical dynamics of askew-polarized spinning top under the radiation reaction torque

Rotary dynamics of polarized composite particles as dipole rigid bodies is considered. It is described the Euler equations singularly perturbed by the radiation reaction torque. The Schott term is taken into account, and the reduction procedure lowering higher derivatives is applied. Asymptotic methods of nonlinear mechanics are used to analyze the rotary dynamics of askew-polarized spinning top. Numerical estimates are relevant to the hypothetical DAST-nanocrystals that might possess a huge dipole moment.

physics.class-ph↗

arXiv2022

On the free rotation of a polarized spinning-top as a test of the correct radiation reaction torque

The formula for dipole radiation reaction torque acting on a system of charges, and the Larmor-like formula for the angular momentum loss by this system, differ in the time derivative term which is the analogue of the Schott term in the energy loss problem. In the well-known textbooks this discrepancy is commonly avoided via neglect of the Schott term, and the Larmor-like formula is preferred. In the present paper both formulae are used to derive two different equations of motion of a polarized spinning-top. Both equations are integrable for the symmetric top and lead to quite different solutions. That one following from the Larmor-like formula is physically unplausible, in contrast to another one. This result is accorded with the reinterpretation of Larmor's formula discussed recently in the pedagogical literature. It is appeared, besides, that the Schott term is of not only academic significance, but it may determine the behavior of polarized micro- and nanoparticles in nature or future experiments.

physics.class-ph↗

arXiv2020

Rotary dynamics of the rigid body electric dipole under the radiation reaction

Rotation of a permanently polarized rigid body under the radiation reaction torque is considered. Dynamics of the spinning top is derived from a balance condition of the angular momentum. It leads to the non-integrable nonlinear 2nd-order equations for angular velocities, and then to the reduced 1st-order Euler equations. The example of an axially symmetric top with the longitudinal dipole is solved exactly, with the transverse dipole is analyzed qualitatively and numerically. Physical solutions describe the asymptotic power-law slowdown to stop or the exponential drift to a residual rotation; this depends on initial conditions and a shape of the top.

physics.class-ph↗

arXiv2020

Solvable two-particle systems with time-asymmetric interactions in de Sitter space

The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant descriptions of the models within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the models are de Sitter-invariant and integrable. An explicit solution of equations of motion is derived in quadratures by means of projection operator technique.

gr-qc↗

arXiv2019

Bound states in the tachyon exchange potential

The Klein-Gordon field of imaginary mass is considered as a mediator of particle interaction. The static tachyon exchange potential is derived and its applied meaning is discussed. The Schrödinger equation with this potential is studied by means of variational and numerical methods. Conditions for existence of bound states are analyzed.

physics.gen-ph↗

arXiv2019

Bound states in the compactified gravity

A potential of pointlike mass in the partially compactified multidimensional space is considered. The problem is reduced to the multidimensional Poisson equation with the Dirac comb source in r.h.s. Explicit solutions are built in the cases of 2D and 4D spaces with one compact dimension. The last example of the potential is used in the Schrödinger equation. Bound states of a gravitating test particle on 3D brane of 4D compactified space are studied by means of various approximate methods.

physics.gen-ph↗

arXiv2013

Partially reduced formulation of scalar Yukawa model: Poincare-invariance and unitarity

We consider a scalar Yukawa-like model in the framework of partially reduced quantum field theory. The reduced Lagrangian of the model consists of free scalar field terms and nonlocal current interaction term. Hamiltonian expressions for conserved quantities arose from a Lorentz-invariance of the model in the momentum representation have been found in the first-order approximation with respect to a coupling constant squared. Canonical quantization of the system is performed. It is shown that the obtained conserved quantities and previously founded the Hamiltonian and the momentum of the system satisfy the commutational relations of the Poincare group. The expression for S-matrix in the current approximation is found. Unitarity of this operator is proven by direct calculation.

hep-th↗

arXiv2012

Quantization of almost-circular orbits in the Fokker action formalism. Regge trajectories

A relativistic quark model of mesons formulated within the formalism of Fokker-type action integrals is proposed, in which an interquark interaction is mediated by scalar-vector superposition of higher derivative fields. In the non-relativistic limit the model describes a two-particle system with the linear potential. In order to analyze the model in the essentially relativistic domain the perturbed circular orbit approximation and certain principle of selection of physically meaningful solutions are applied which permit one to perform the canonical quantization of the model. It is shown that the model reproduces well specific features of the light meson spectroscopy.

hep-th↗

arXiv2012

Quantization of almost-circular orbits in the Fokker action formalism. General scheme

General two-particle system is considered within the formalism of Fokker-type action integrals. It is assumed that the system is invariant with respect to the Aristotle group which is a common subgroup of the Galileo and Poincaré groups. It is shown that equations of motion of such system admit circular orbit solutions. The dynamics of perturbations of these solutions is studied. It is described by means of a linear homogeneous set of time-nonlocal equations and is analyzed in terms of eigenfrequencies and eigenmodes. The Hamiltonian description of the system is built in the almost circular orbit approximation. The Aristotle-invariance of the system is exploit to avoid a double count of degrees of freedom and to select physical modes. The quantization procedure and a construction of energy spectrum of the system is proposed.

math-ph↗

arXiv2011

Analysis of inter-quark interactions in classical chromodynamics

The QCD gluon equation of motion is solved approximately by means of the Green function. This solution is used to reformulate the Lagrangian of QCD such that the gluon propagator appears directly in the interaction terms of the Lagrangian. The nature of the interactions is discussed. Their coordinate-space form is presented and analyzed in the static, non-relativistic case.

hep-th↗

arXiv2010

Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model

We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky model. Using an iterative approach and eliminating the mediating field by means of the covariant Green function we arrive at a Lagrangian density containing many-point time-nonlocal interaction terms. In low-order approximations of $ϕ^3{+}ϕ^4$ theory we obtain the usual two-current interaction as well as a three-current interaction of a confining type. The same result is obtained without approximation for a version of the dipole model. The transition to the Hamiltonian formalism and subsequent canonical quantization is performed with time non-locality taken into account approximately. A relativistic three-particle wave equation is derived variationally by using a three-particle Fock space trial state. The non-relativistic limit of this equation is obtained and its properties are analyzed and discussed.

hep-th↗

arXiv2010

Exact two-particle eigenstates in partially reduced QED

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be obtained in the canonical equal-time formalism for the case where there are no free photons. These eigenstates lead to two- and three-body Dirac-like equations with electromagnetic interactions. Perturbative and some numerical solutions of the two-body equations are presented for positronium and muonium-like systems, for various strengths of the coupling.

nucl-th↗

arXiv2008

Solvable Two-Body Dirac Equation as a Potential Model of Light Mesons

The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular structure is found, for which the equation is exactly solvable. On this ground a relativistic potential model of light mesons is constructed and the mass spectrum is calculated. It is compared with experimental data.

hep-ph↗

arXiv2006

Large-j Expansion Method for Two-Body Dirac Equation

By using symmetry properties, the two-body Dirac equation in coordinate representation is reduced to the coupled pair of radial second-order differential equations. Then the large-j expansion technique is used to solve a bound state problem. Linear-plus-Coulomb potentials of different spin structure are examined in order to describe the asymptotic degeneracy and fine splitting of light meson spectra.

math-ph↗

arXiv2002

Heuristic Models of Two-Fermion Relativistic Systems with Field-Type Interaction

We use the chain of simple heuristic expedients to obtain perturbative and exactly solvable relativistic spectra for a family of two-fermionic bound systems with Coulomb-like interaction. In the case of electromagnetic interaction the spectrum coincides up to the second order in a coupling constant with that following from the quantum electrodynamics. Discrepancy occurs only for S-states which is the well-known difficulty in the bound-state problem. The confinement interaction is considered too. PACS number(s): 03.65.Pm, 03.65.Ge, 12.39.Pn

nucl-th↗