On the number of two-dimensional threshold functions

A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k x k square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such functions only asymptotic bounds are known. We give an exact formula for the number of two-dimensional threshold functions and derive more accurate asymptotics.Comment: 17 pages, 2 figure

Josephson and spontaneous currents at the interface between two d-wave superconductors with transport current in the banks

A stationary Josephson effect in the ballistic contact of two d-wave superconductors with different axes orientation and with tangential transport current in the banks is considered theoretically. We study the influence of the transport current on the current-phase dependence for the Josephson and tangential currents at the interface. It is demonstrated that the spontaneous surface current at the interface depends on the transport current in the banks due to the interference of the angle-dependent current-carrying condensate wave functions of the two superconductors.Comment: to be published in Fiz. Nizk. Temp. (Sov. J. Low Temp. Phys.), Vol.30, No.3 (2004

Pseudoscalar mesons and their radial excitations from the Effective Chiral Lagrangian

Effective Chiral Lagrangian is derived from QCD in the framework of Field Correlator Method. It contains the effects of both confinement and chiral symmetry breaking due to a special structure of the resulting quark mass operator. It is shown that this Lagrangian describes light pseudoscalar mesons, and Gell-Mann-Oakes-Renner relations for pions, eta and K mesons are reproduced. Spectrum of radial excitations of pions and K mesons is found and compared to experimentally known masses.Comment: 6 pages; v3: minor corrections, references adde

Charge ordering and interlayer phase coherence in quantum Hall superlattices

The possibility of the existence of states with a spontaneous interlayer phase coherence in multilayer electron systems in a high perpendicular to the layers magnetic field is investigated. It is shown that phase coherence can be established in such systems only within individual pairs of adjacent layers, while such coherence does not exist between layers of different pairs. The conditions for stability of the state with interlayer phase coherence against transition to a charge-ordered state are determined. It is shown that in the system with the number of layers N\leq 10 these conditions are satisfied at any value of the interlayer distance d. For N>10 there are two intervals of stability: at sufficiently large and at sufficiently small d. For N\to \infty the stability interval in the region of small d vanishesComment: 10 page