A Discrete Version of the Inverse Scattering Problem and the J-matrix Method

The problem of the Hamiltonian matrix in the oscillator and Laguerre basis construction from the S-matrix is treated in the context of the algebraic analogue of the Marchenko method.Comment: 11 pages. The Laguerre basis case is adde

Local density of states at polygonal boundaries of d-wave superconductors

Besides the well-known existence of Andreev bound states, the zero-energy local density of states at the boundary of a d-wave superconductor strongly depends on the boundary geometry itself. In this work, we examine the influence of both a simple wedge-shaped boundary geometry and a more complicated polygonal or faceted boundary structure on the local density of states. For a wedge-shaped boundary geometry, we find oscillations of the zero-energy density of states in the corner of the wedge, depending on the opening angle of the wedge. Furthermore, we study the influence of a single Abrikosov vortex situated near a boundary, which is of either macroscopic or microscopic roughness.Comment: 10 pages, 11 figures; submitted to Phys. Rev.

Associated heavy quarks pair production with Higgs as a tool for a search for non-perturbative effects of the electroweak interaction at the LHC

Assuming an existence of an anomalous triple electro-weak bosons interaction being defined by coupling constant $\lambda$, we calculate its contribution to interactions of the Higgs with pairs of heavy particles. Bearing in mind experimental restrictions $-0.011 < \lambda < 0.011$ we present results for possible effects in processes $p\,p \to W^+ W^- H,\,p\,p \to W^+ Z H,\,p\,p \to W^- Z H,\,p\,p \to \bar t t H$, $p p \to \bar b b H$. Effects could be significant with negative sign of $\lambda$ in associated heavy quarks $t,\,b$ pairs production with the Higgs. In calculations we rely on results of the non-perturbative approach to a spontaneous generation of effective interactions, which defines the form-factor of the three-boson anomalous interaction.Comment: 6 pages, 2 figures, few typos corrected, references adde