Theory of the nuclear excitation by electron transition process near the K-edge

We propose a model for description of the process of Nuclear Excitation by Electron Transition (NEET) near the $K$-shell ionization threshold of an atom. We explain the experimental results for the $^{197}$Au cross section excitation $\sigma_{N^*}$ obtained by S.Kishimoto et al. Phys. Rev. C {\bf 74}, 031301(R) (2006) using synchrotron radiation near the Au $K$-edge. We predict the behavior of $\sigma_{N^*}$ as a function of the incident photon energy for nuclei $^{193}$Ir and $^{189}$Os. We reveal that the $^{189}$Os excitation begins when the energy of incident photons is below the $K$-shell ionization threshold in Os.Comment: 12 pages, 5 figure

On solving Schwinger-Dyson equations for non-Abelian gauge theory

A method for solving Schwinger-Dyson equations for the Green function generating functional of non-Abelian gauge theory is proposed. The method is based on an approximation of Schwinger-Dyson equations by exactly soluble equations. For the SU(2) model the first step equations of the iteration scheme are solved which define a gauge field propagator. Apart from the usual perturbative solution, a non-perturbative solution is found which corresponds to the spontaneous symmetry breaking and obeys infrared finite behaviour of the propagator.Comment: 12 pages, Plain LaTeX, no figures, extended and revised version published in Journal of Physics

Bright solitons in Bose-Fermi mixtures

We consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases confined in a three-dimensional elongated harmonic trap. The Bose and Fermi atoms are assumed to effectively attract each other whereas bosonic atoms repel each other. Strong enough attraction between bosonic and fermionic components can change the character of the interaction within the bosonic cloud from repulsive to attractive making thus possible the generation of bright solitons in the mixture. On the other hand, such structures might be in danger due to the collapse phenomenon existing in attractive gases. We show, however, that under some conditions (defined by the strength of the Bose-Fermi components attraction) the structures which neither spread nor collapse can be generated. For elongated enough traps the formation of solitons is possible even at the ``natural'' value of the mutual Bose-Fermi ($^{87}$Rb -$^{40}$K in our case) scattering length.Comment: 6 pages, 6 figures, 1 tabl

Symmetry Induced 4-Wave Capillary Wave Turbulence

We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two inmiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair $(\eta,\Psi)$. When given the symmetry $z\to-z$, the set of weakly non-linear interacting waves display a Kolmogorov-Zakharov (KZ) spectrum $n_k\sim k^{-4}$ in wave vector space. The wave system was studied experimentally with two inmiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low frequency random forcing. The power spectral density (PSD) and probability density function (PDF) of the local wave amplitude are studied. Both theoretical and experimental results are in fairly good agreement with each other.Comment: 6 pages, 2 figure

On discrete integrable equations of higher order

We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the B\"acklund--Darboux transformations for the lattice equations of Bogoyavlensky type.Comment: 20 pages, 2 figure

Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modelling the strongly nonlinear process of white-capping. Fitting the two experiments, we determined the dissipation function due to wave breaking and found that it depends very sharply on the parameter of nonlinearity (the surface steepness). The onset of white-capping can be compared to a second-order phase transition. This result corroborates with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter