QED calculation of the 2p3/2-2p1/2 transition energy in five-electron ion of argon

We perform ab initio QED calculation of the (1s)^2(2s)^22p_{3/2} - (1s)^2(2s)^22p_{1/2} transition energy in the five-electron ion of argon. The calculation is carried out by perturbation theory starting with an effective screening potential approximation. Four different types of the screening potentials are considered. The rigorous QED calculations of the two lowest-order QED and electron-correlation effects are combined with approximate evaluations of the third- and higher-order electron-correlation contributions. The theoretical value for the wavelength obtained amounts to 441.261(70) (nm, air) and perfectly agrees with the experimental one, 441.2559(1) (nm, air).Comment: 10 pages, 3 figures, 1 tabl

Vector solitons in nearly-one-dimensional Bose-Einstein condensates

We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped trap. The system is obtained by means of the variational approximation, starting from the coupled 3D Gross-Pitaevskii equations and assuming, as usual, the factorization of 3D wave functions. The system can be obtained in a tractable form under a natural condition of symmetry between the two species. A family of vector (two-component) soliton solutions is constructed. Collisions between orthogonal solitons (ones belonging to the different components) are investigated by means of simulations. The collisions are essentially inelastic. They result in strong excitation of intrinsic vibrations in the solitons, and create a small orthogonal component ("shadow") in each colliding soliton. The collision may initiate collapse, which depends on the mass and velocities of the solitons.Comment: 7 pages, 6 figures; Physical Review A, in pres

Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions

The light-induced frequency shift due to the hyperpolarizability (i.e. terms of second-order in intensity) is studied for a forbidden optical transition, $J$=0$\to$$J$=0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.Comment: 4 pages, RevTeX4, 2 eps fig

Symbiotic Solitons in Heteronuclear Multicomponent Bose-Einstein condensates

We show that bright solitons exist in quasi-one dimensional heteronuclear multicomponent Bose-Einstein condensates with repulsive self-interaction and attractive inter-species interaction. They are remarkably robust to perturbations of initial data and collisions and can be generated by the mechanism of modulational instability. Some possibilities for control and the behavior of the system in three dimensions are also discussed

Nekhoroshev theorem for the periodic Toda lattice

The periodic Toda lattice with $N$ sites is globally symplectomorphic to a two parameter family of $N-1$ coupled harmonic oscillators. The action variables fill out the whole positive quadrant of $\R^{N-1}$. We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space.Comment: 28 page

On the dispersionless Kadomtsev-Petviashvili equation in n+1 dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking

We study the (n+1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi one dimensional waves in n+1 dimensions, and arising in several physical contexts, like acoustics, plasma physics and hydrodynamics. For n=2, this equation is integrable, and it has been recently shown to be a prototype model equation in the description of the two dimensional wave breaking of localized initial data. We construct an exact solution of the n+1 dimensional model containing an arbitrary function of one variable, corresponding to its parabolic invariance, describing waves, constant on their paraboloidal wave front, breaking simultaneously in all points of it. Then we use such solution to build a uniform approximation of the solution of the Cauchy problem, for small and localized initial data, showing that such a small and localized initial data evolving according to the (n+1)-dimensional dKP equation break, in the long time regime, if and only if n=1,2,3; i.e., in physical space. Such a wave breaking takes place, generically, in a point of the paraboloidal wave front, and the analytic aspects of it are given explicitly in terms of the small initial data.Comment: 20 pages, 10 figures, few formulas adde

Solitary waves in mixtures of Bose gases confined in annular traps

A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically. The derived solutions are shown to be unique. The corresponding dispersion relation that generalizes the case of a single-component system shows interesting features.Comment: 4 pages, 1 figur

Territorial structure of the denominational space of the South-East Baltic

The South-East Baltic is a meeting place of three branches of Christianity: Orthodoxy, Catholicism, and Lutheranism. Dominant in the Baltic region, these religious confessions define the cultural landscape of the area. At the same time, they have an indirect effect on socio-economic development. In this study, we aim to identify the main components of the territorial structure and the formation and transformation factors of the denominational space in the South-East Baltic. The complexity of the denominational structure of the local population stems from the centuries-long position of this region as a political buffer zone. We calculate the potential denominational structure and the potential religious fractionalisation index at the level of basic territorial units and regions southeast of the Baltic Sea. Based on this, we identify the main components of the territorial structure of the denominational space, which includes three denominational shields and contact zones between them. From a practical viewpoint, these components suggest a new variant of the territorial differentiation of the Baltic region. This variant has only limited relevance to ethnic and socioeconomic zoning

Tri-hamiltonian vector fields, spectral curves and separation coordinates

We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to its symplectic leaves. The frameworks is applied to Lax equations with spectral parameter, for which not only it unifies the separation techniques of Sklyanin and of Magri, but also provides a more efficient ``inverse'' procedure not involving the extraction of roots.Comment: 49 pages Section on reduction revisite

Squared Eigenfunctions for the Sasa-Satsuma Equation

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a $3\times 3$ system, while its linearized operator is a $2\times 2$ system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: first is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying respectively the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.Comment: 18 page