Modeling of ion-implanted atoms diffusion during the epitaxial growth of the layer

The equation of impurity diffusion due to formation, migration, and dissolution of the pairs "impurity atom - intrinsic point defect" taking into account the nonuniform distributions of nonequilibrium point defects and drift of the pairs in the field of elastic stresses is presented in the coordinate system associated with the moving surface of the growing epitaxial layer. The analytical solution of this equation for the low fluence ion implantation has been obtained.Comment: 3 pages, 2 figure

Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods

Relativistic methods for the Foldy-Wouthuysen transformation of the ``step-by-step'' type already at the first step give an expression for the Hamilton operator not coinciding with the exact result determined by the Eriksen method. The methods agree for the zeroth and first orders in the Planck constant terms but do not agree for the second and higher-order terms. We analyze the benefits and drawbacks of various methods and establish their applicability boundaries.Comment: 20 page

Spin Oscillations in Storage Rings

The dependence of the particle rotation frequency on the particle orbit perturbations is found. The exact equation of spin motion in the cylindrical coordinate system is derived. The calculated formula for the frequency of g-2 precession is in the best agreement with previous results. Nevertheless, this formula contains the additional oscillatory term that can be used for fitting. The influence of spin oscillations on the spin dynamics in the EDM experiment is negligible.Comment: 5 pages. To appear in the proceedings of 16th International Spin Physics Symposium (SPIN 2004), Trieste, Italy, 10-16 Oct 200

On the Relevance of Compton Scattering for the Soft X-ray Spectra of Hot DA White Dwarfs

We re-examine the effects of Compton scattering on the emergent spectra of hot DA white dwarfs in the soft X-ray range. Earlier studies have implied that sensitive X-ray observations at wavelengths $\lambda < 50$ \AA might be capable of probing the flux deficits predicted by the redistribution of electron-scattered X-ray photons toward longer wavelengths. We adopt two independent numerical approaches to the inclusion of Compton scattering in the computation of pure hydrogen atmospheres in hydrostatic equilibrium. One employs the Kompaneets diffusion approximation formalism, while the other uses the cross-sections and redistribution functions of Guilbert. Models and emergent spectra are computed for stellar parameters representative of HZ 43 and Sirius B, and for models with an effective temperature $T_{\rm eff} = 100 000$ K. The differences between emergent spectra computed for Compton and Thomson scattering cases are completely negligible in the case of both HZ 43 and Sirius B models, and are also negligible for all practical purposes for models with temperatures as high as $T_{\rm eff} = 100 000$ K. Models of the soft X-ray flux from these stars are instead dominated by uncertainties in their fundamental parameters.Comment: 7 pages, 5 figures, accepted for publication in A&

Complex masses of resonances and the Cornell potential

Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of relativistic wave equation for the coulombic and linear components of the potential are used to derive the resonance complex-mass formula. The centered masses and total widths of the $\rho$-family resonances are calculated.Comment: 12 pages, 1 figure, 1 tabl

Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics

A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the lower limit of inverse temperature. The authors are of the opinion that the approach proposed may lead to proof of these relations. To this end, the statistical mechanics deformation at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, and it is demonstrated that there is a complete analogy in the construction and properties of quantum mechanics and statistical density matrices at Plank scale (i.e. density pro-matrices). It is shown that an ordinary statistical density matrix occurs in the low-temperature limit at temperatures much lower than the Plank's. The associated deformation of a canonical Gibbs distribution is given explicitly.Comment: 15 pages,no figure

One Upper Estimate on the Number of Limit Cycles of Even Degree Li\'enard Equations in the Focus Case

We give an explicit upper bound for a number of limit cycles of the Li\'enard equation $\dot{x}=y-F(x)$, $\dot{y}=-x$ of even degree in the case its unique singular point $(0,0)$ is a focus.Comment: 10 pages, 1 figur

A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations

Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan, (-1,1)-, quasiassociative, quasialternative, right alternative and Malcev-admissible noncommutative Jordan algebras over the field of characteristic zero. Also, we describe all Leibniz-derivations of semisimple Jordan, right alternative and Malcev algebras

Derivation of Generalized Thomas-Bargmann-Michel-Telegdi Equation for a Particle with Electric Dipole Moment

General classical equation of spin motion is explicitly derived for a particle with magnetic and electric dipole moments in electromagnetic fields. Equation describing the spin motion relatively the momentum direction in storage rings is also obtained.Comment: 7 page

Division algebras of prime degree with infinite genus

The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D'] in the Brauer group Br(F), where D' is a central division F-algebra having the same maximal subfields as D. For any prime p, we construct a division algebra of degree p with infinite genus. Moreover, we show that there exists a field K such that there are infinitely many nonisomorphic central division K-algebras of degree p, and any two such algebras have the same genus.Comment: 4 page