Abelian Sandpile Model on the Husimi Lattice of Square Plaquettes

An Abelian sandpile model is considered on the Husimi lattice of square plaquettes. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived. The two-point correlation function for the sites deep inside the Husimi lattice is calculated exactly.Comment: 12 pages, LaTeX, source files and some additional information available at http://thsun1.jinr.dubna.su/~shcher

Friedmann universe with dust and scalar field

We study a spatially flat Friedmann model containing a pressureless perfect fluid (dust) and a scalar field with an unbounded from below potential of the form V(\fii)=W_0 - V_0\sinh(\sqrt{3/2}\kappa\fii), where the parameters $W_0$ and $V_0$ are arbitrary and $\kappa=\sqrt{8\pi G_N}=M_p^{-1}$. The model is integrable and all exact solutions describe the recollapsing universe. The behavior of the model near both initial and final points of evolution is analyzed. The model is consistent with the observational parameters. We single out the exact solution with the present-day values of acceleration parameter $q_0=0.5$ and dark matter density parameter $\Omega_{\rho 0}=0.3$ describing the evolution within the time approximately equal to $2H_0^{-1}$.Comment: 11 pages, 10 figure

Electron-hole symmetry and solutions of Richardson pairing model

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.Comment: 9 pages, 1 figure; accepted for publication in Eur. Phys. J.

CORE 3.1 (COmpendium of RElations, Version 3.1)

The present CORE 3.1 (COmpendium of RElations, Version 3.1) contains various formulas and relations used in the practical calculations in the Standard Model. The properties of the Pauli, Dirac, Gell--Mann matrices, wave functions of free fermions and gauge bosons are considered. We present the full Lagrangian of the Standard Model and the corresponding Feynman rules. The method of the evaluation of the Feynman (loop) integrals and calculations in non-covariant gauges is considered. We discuss in brief the relativistic kinematic and present a large number of the matrix elements of the various processes in the Standard Model.Comment: 80 pages, 21 figures, scripts.sty. arXiv admin note: substantial text overlap with arXiv:hep-ph/950745