arXiv subjects
Publications and source records attributed to D. U. Matrasulov.
The Casimir effects for one-dimensional fractal networks, so-called quantum graphs is studied. Based on the Green function approach for quantum graphs zero-point energy for some simplest topologies is written explicitly.
Finite-temperature spectra of heavy quarkonia are calculated by combining potential model and thermofield dynamics formalisms. The mass spectra of the heavy quarkonia with various quark contents are calculated. It is found that binding mass of the quarkonium decreases as temperature increases.
The quantum chaos in the finite-temperature Yang-Mills-Higgs system is studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs is calculated within thermofield dynamics. Level statistics of the spectra is studied by plotting nearest-level spacing distribution histograms. It is found that finite temperature effects lead to a strengthening of chaotic effects, i.e. spectrum which has Poissonian distribution at zero temperature has Gaussian distribution at finite-temperature.
The binding energy spectra of the heavy quarkonia are calculated by solving the Schrödinger equations with Coulomb plus confining potentials. Statistical properties of the obtained spectra are studied by plotting nearest level spacing distribution histograms.
Classical regular and chaotic dynamics of the particle bound in the Coulomb plus linear potential under the influence of time-periodical perturbations is treated using resonace analysis. Critical value of the external field at which chaotization will occur is evaluated analytically based on the Chirikov criterion of stochasticity.
Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. Schrödinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form. Using those formulas, the energy spectra of doubly heavy baryons with various quark compositions are calculated analytically.
Chaotization of supercritical (Z>137) hydrogenlike atom in the monochromatic field is investigated. A theoretical analysis of chaotic dynamics of the relativistic electron based on Chirikov criterion is given. Critical value of the external field at which chaotization will occur is evaluated analytically. The diffusion coefficient is also calculated.
Chaotic autoionization of the relativistic two-electron atom is investigated. A theoretical analysis of chaotic dynamics of the relativistic outer electron under the periodic perturbation due to the inner electron, based on Chirikov criterion, is given. The diffusion coefficient, the ionization rate and time are calculated.
A general expression for the cross sections of inelastic collisions of fast (including relativistic) multicharged ions with atoms which is based on the genelazition of the eikonal approximation is derived. This expression is applicable for wide range of collision energy and has the standard nonrelativistic limit and in the ultrarelativistic limit coincides with the Baltz's exact solution ~\cite{art13} of the Dirac equation. As an application of the obtained result the following processes are calculated: the excitation and ionization cross sections of hydrogenlike atom; the single and double excitation and ionization of heliumlike atom; the multiply ionization of neon and argon atoms; the probability and cross section of K-vacancy production in the relativistic $U^{92+} - U^{91+}$ collision. The simple analytic formulae for the cross sections of inelastic collisions and the recurrence relations between the ionization cross sections of different multiplicities are also obtained. Comparison of our results with the experimental data and the results of other calculations are given.
Stochastic ionization of highly excited relativistic hydrogenlike atom in the monochromatic field is investigated. A theoretical analisis of chaotic dynamics of the relativistic electron based on Chirikov criterion is given for the cases of one- and three-dimensional atoms. Critical value of the external field is evaluated analitically. The diffusion coefficient and ionization time are calculated.
Dirac equation for the finite dipole potential is solved by the method of the join of the asymptotics. The formulas for the near continuum state energy term of a relativistic electron-dipole system are obtained analytically. Two cases are considered: $Z < 137$ and $Z >137$