Are EeV cosmic rays isotropic at intermediate scales?

We study anisotropy of cosmic rays in the energy range 0.2-1.4 EeV at intermediate angular scales using the public data set of the Pierre Auger Observatory. At certain scales, the analysis reveals a number of deviations from the isotropic distribution with the statistical significance above three standard deviations. It also demonstrates that the anisotropy evolves with energy. If confirmed with the complete Auger or Telescope Array data sets, the result can shed new light on the structure of galactic magnetic fields and the problem of transition from galactic to extragalactic cosmic rays.Comment: 9 pages, 2 figure

A solution to the problem posed by Byland and Scialom

Recently, Byland and Scialom studied the evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs universe on the basis of dynamical systems methods (Phys. Rev. D57, 6065 (1998), gr-qc/9802043). In particular, they have pointed out a problem to determine the stability properties of one of the degenerate critical points of the corresponding dynamical system. Here we give a solution, showing that this point is unstable both to the past and to the future. We also discuss the asymptotic behavior of the trajectories in the vicinity of another critical point.Comment: REVTeX, 2 pages; v2: the title changed to avoid ambiguity -- thanks to Brad Woodwort

Dynamical system analysis for the Einstein-Yang-Mills equations

Local solutions of the static, spherically symmetric Einstein-Yang-Mills (EYM) equations with SU(2) gauge group are studied on the basis of dynamical systems methods. This approach enables us to classify EYM solutions in the origin neighborhood, to prove the existence of solutions with the oscillating metric as well as the existence of local solutions for all known formal power series expansions, to study the extendibility of solutions, and to find two new local singular solutions.Comment: 25 pages with 2 figures; v.2: subsec. V.B partially revised, minor style and grammar changes in the rest of the text; the main result unchange

Solutions with negative mass for the SU(2) Einstein-Yang-Mills equations

The aim of this note is to clarify the structure of nontrivial global solutions with nonpositive ADM mass for the static, spherically symmetric Einstein-Yang-Mills equations with SU(2) gauge group. The presented numerical results demonstrate that these solutions have zero number of nodes of the gauge field function. This is a feature that is present neither for particlelike nor for black hole solutions.Comment: 12 pages including 8 figures (harvmac and epsf

On factorized Lax pairs for classical many-body integrable systems

In this paper we study factorization formulae for the Lax matrices of the classical Ruijsenaars-Schneider and Calogero-Moser models. We review the already known results and discuss their possible origins. The first origin comes from the IRF-Vertex relations and the properties of the intertwining matrices. The second origin is based on the Schlesinger transformations generated by modifications of underlying vector bundles. We show that both approaches provide explicit formulae for $M$-matrices of the integrable systems in terms of the intertwining matrices (and/or modification matrices). In the end we discuss the Calogero-Moser models related to classical root systems. The factorization formulae are proposed for a number of special cases.Comment: 42 pages, minor change

Prospects of detecting a large-scale anisotropy of ultra-high-energy cosmic rays from a nearby source with the K-EUSO orbital telescope

KLYPVE-EUSO (K-EUSO) is a planned orbital detector of ultra-high-energy cosmic rays (UHECRs), which is to be deployed on board the International Space Station. K-EUSO is expected to have a uniform exposure over the celestial sphere and register from 120 to 500 UHECRs at energies above 57 EeV in a 2-year mission. We employed the TransportCR and CRPropa 3 packages to estimate prospects of detecting a large-scale anisotropy of ultra-high-energy cosmic rays from a nearby source with K-EUSO. Nearby active galactic nuclei Centaurus A, M82, NGC 253, M87 and Fornax A were considered as possible sources of UHECRs. A minimal model for extragalactic cosmic rays and neutrinos by Kachelriess, Kalashev, Ostapchenko and Semikoz (2017) was chosen for definiteness. We demonstrate that an observation of $\gtrsim300$ events will allow detecting a large-scale anisotropy with a high confidence level providing the fraction of from-source events is $\simeq$10-15%, depending on a particular source. The threshold fraction decreases with an increasing sample size. We also discuss if an overdensity originating from a nearby source can be observed at around the ankle in case a similar anisotropy is found beyond 57 EeV. The results are generic and hold for other future experiments with a uniform exposure of the celestial sphere.Comment: 18 pages; version 2: discussion extended, references added, results unchanged; version 3: numerous changes to address comments of the referee; accepted by JCA

Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations

We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by an arbitrary finite order automorphisms of the underlying Lie algebras. In this way we obtain the spin generalization of the twisted D'Hoker- Phong and Bordner-Corrigan-Sasaki-Takasaki systems. As by product, we construct the corresponding twisted classical dynamical r-matrices and Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms of the Lie algebras.Comment: 35 pages + 2 table

Classification of Isomonodromy Problems on Elliptic Curves

We consider the isomonodromy problems for flat $G$-bundles over punctured elliptic curves $\Sigma_\tau$ with regular singularities of connections at marked points. The bundles are classified by their characteristic classes. These classes are elements of the second cohomology group $H^2(\Sigma_\tau,{\mathcal Z}(G))$, where ${\mathcal Z}(G)$ is the center of $G$. For any complex simple Lie group $G$ and arbitrary class we define the moduli space of flat bundles, and in this way construct the monodromy preserving equations in the Hamiltonian form and their Lax representations. In particular, they include the Painlev\'e VI equation, its multicomponent generalizations and elliptic Schlesinger equations. The general construction is described for punctured curves of arbitrary genus. We extend the Drinfeld-Simpson (double coset) description of the moduli space of Higgs bundles to the case of flat connections. This local description allows us to establish the Symplectic Hecke Correspondence for a wide class of the monodromy preserving equations classified by characteristic classes of underlying bundles. In particular, the Painlev\'e VI equation can be described in terms of ${\rm SL}(2, {\mathbb C})$-bundles. Since ${\mathcal Z}({\rm SL}(2, {\mathbb C}))= {\mathbb Z}_2$, the Painlev\'e VI has two representations related by the Hecke transformation: 1) as the well-known elliptic form of the Painlev\'e VI(for trivial bundles); 2) as the non-autonomous Zhukovsky-Volterra gyrostat (for non-trivial bundles).Comment: 67 pages, minor corrections. arXiv admin note: text overlap with arXiv:1006.070

Yang-Baxter equations with two Planck constants

We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic algebras. Then we proceed to a natural generalization of the Baxter-Belavin quantum $R$-matrix to the case ${\rm Mat}(N,\mathbb C)^{\otimes 2}\otimes {\rm Mat}(M,\mathbb C)^{\otimes 2}$. It can be viewed as symmetric form of ${\rm GL}(NM)$ $R$-matrix in the sense that the Planck constant and the spectral parameter enter (almost) symmetrically. Such type (symmetric) $R$-matrices are also shown to satisfy the Yang-Baxter like quadratic and cubic equations.Comment: 20 pages, minor correction

Quantum Baxter-Belavin R-matrices and multidimensional Lax pairs for Painleve VI

The quantum elliptic $R$-matrices of Baxter-Belavin type satisfy the associative Yang-Baxter equation in ${\rm Mat}(N,\mathbb C)^{\otimes 3}$. The latter can be considered as noncommutative analogue of the Fay identity for the scalar Kronecker function. In this paper we extend the list of $R$-matrix valued analogues of elliptic function identities. In particular, we propose counterparts of the Fay identities in ${\rm Mat}(N,\mathbb C)^{\otimes 2}$. As an application we construct $R$-matrix valued $2N^2\times 2N^2$ Lax pairs for the Painlev\'e VI equation (in elliptic form) with four free constants using ${\mathbb Z}_N\times {\mathbb Z}_N$ elliptic $R$-matrix. More precisely, the four free constants case appears for an odd $N$ while even $N$'s correspond to a single constant.Comment: 16 pages, minor correction