Reduction Groups and Automorphic Lie Algebras

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates the name automorphic Lie algebras. For automorphic Lie algebras we present bases in which they are quasigraded and all structure constants can be written out explicitly. These algebras have a useful factorisations on two subalgebras similar to the factorisation of the current algebra on the positive and negative parts.Comment: 21 pages, standard LaTeX2e, corrected typos, accepted for publication in CMP - Communications in Mathematical Physic

Single photoeffect on helium-like ions in the non-relativistic region

We present a generalization of the pioneering results obtained for single K-shell photoionization of H-like ions by M. Stobbe [Ann. Phys. 7 (1930) 661] to the case of the helium isoelectronic sequence. The total cross section of the process is calculated, taking into account the correlation corrections to first order of the perturbation theory with respect to the electron-electron interaction. Predictions are made for the entire non-relativistic energy domain. The phenomenon of dynamical suppression of correlation effects in the ionization cross section is discussed.Comment: to be published in Physics Letters

Excitation of K-shell electrons by electron impact

The universal scaling behavior for the electron-impact excitation cross sections of the $2s$ states of hydrogen- and helium-like multicharged ions is deduced. The study is performed within the framework of non-relativistic perturbation theory, taking into account the one-photon exchange diagrams. Special emphasis is laid on the near-threshold energy domain. The parametrical relationship between the cross sections for excitation of multicharged ions with different number of electrons is established.Comment: to be published in Physics Letters

History-sensitive accumulation rules for life-time prediction under variable loading

This is the post-print version of the article. The official published version can be obtained from the link below - Copyright @ 2011 SpringerA general form of temporal strength conditions under variable creep loading is employed to formulate several new phenomenological accumulation rules based on the constant-loading durability diagram. Unlike the well-known Robinson rule of linear accumulation of partial life-times, the new rules allow to describe the life-time sensibility to the load sequence, observed in experiments. Comparison of the new rules with experimental data shows that they fit the data much more accurately than the Robinson rule

Nonrelativistic double photoeffect on lithiumlike ions at high energies

The total cross section for double ionization of lithiumlike ions by a high-energy photon is calculated in leading order of the nonrelativistic perturbation theory. The partial contributions due to simultaneous and sequential emissions of two electrons are taken into account. The cross section under consideration is shown to be related to those for double photoeffect on the ground and excited 2^{1,3}S states of heliumlike ions. The double-to-single ionization ratio is equal to R = 0.288/Z^2 for lithiumlike ions with moderate nuclear charge numbers Z. However, even for the lightest three-electron targets such as Li and Be^+, analytical predictions are found to be in good agreement with the numerical calculations performed within the framework of different rather involved approaches.Comment: 12 pages, 2 figures. to be published in Physics Letters

Maximally nonabelian Toda systems

A detailed consideration of the maximally nonabelian Toda systems based on the classical semisimple Lie groups is given. The explicit expressions for the general solution of the corresponding equations are obtained.Comment: 28 pages, LaTeX file. A few references and appendix B are added; this version will appear in Nuclear Physics

Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the interaction properties of polarized kink solutions.Comment: 14 pages; 4 picture

Asymmetric Gluon Distributions and Hard Diffractive Electroproduction

The ``asymmetric'' matrix element that appears in the pQCD description of hard diffractive electroproduction does not coincide with that defining the gluon distribution function f_g(x). I outline a pQCD formalism based on a concept of the double distribution F_g(x,y), which specifies the fractions xp, yr, (1-y)r of the initial proton momentum p and the momentum transfer r, resp., carried by the gluons. For $t \equiv r^2 =0$, r is proportional to p: $r = \zeta p$, and it is convenient to parameterize the matrix element by an asymmetric distribution function ${\cal F}_{\zeta}^g (X)$ depending on the total fractions $X \equiv x+y \zeta$ and $X-\zeta = x- (1-y) \zeta$ of the initial hadron momentum p carried by the gluons.I formulate evolution equations for ${\cal F}_{\zeta}^g (X)$, study some of their general properties and discuss the relationship between ${\cal F}_{\zeta}^g (X)$, F_g(x,y) and f_g(x).Comment: Definition of asymmetric gluon distribution is corrected to conform with the reduction formula

Two ground-state modifications of quantum-dot beryllium

Exact electronic properties of a system of four Coulomb-interacting two-dimensional electrons in a parabolic confinement are reported. We show that degenerate ground states of this system are characterized by qualitatively different internal electron-electron correlations, and that the formation of Wigner molecule in the strong-interaction regime is going on in essentially different ways in these ground states.Comment: 5 pages, incl 5 Figures and 2 Table

Scaling Limit of Deeply Virtual Compton Scattering

I outline a perturbative QCD approach to the analysis of the deeply virtual Compton scattering process $\gamma^* p \to \gamma p'$ in the limit of vanishing momentum transfer $t= (p' - p)^2$. The DVCS amplitude in this limit exhibits a scaling behaviour described by a two-argument distributions $F(x,y)$ which specify the fractions of the initial momentum $p$ and the momentum transfer $r \equiv p'-p$ carried by the constituents of the nucleon.The kernel $R(x,y;\xi,\eta)$ governing the evolution of the non-forward distributions $F(x,y)$ has a remarkable property: it produces the GLAPD evolution kernel $P(x/\xi)$ when integrated over $y$ and reduces to the Brodsky-Lepage evolution kernel $V(y,\eta)$ after the $x$-integration. This property is used to construct the solution of the one-loop evolution equation for the flavour non-singlet part of the non-forward quark distribution.Comment: gziped, tar file of LaTeX paper plus 2 postscript figures,10 pages; some changes in new terminolog