Bjorken sum rule with analytic coupling at low Q2 values

The experimental data obtained for the polarized Bjorken sum rule \Gamma^{(p-n)}_1(Q^2) for small values of Q2 are approximated by the predictions obtained in the framework of analytic QCD up to the 5th order perturbation theory, whose coupling constant does not contain the Landau pole. We found an excellent agreement between the experimental data and the predictions of analytic QCD, as well as a strong difference between these data and the results obtained in the framework of standard QCD.Comment: 9 pages, 1 figur

Level spacing distribution of pseudointegrable billiard

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.Comment: 11 pages, REVTeX file, 3 PostScript Figure

Spectral properties of quantized barrier billiards

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions, number variances, spectral form factors, and the level dynamics is carried out. For a special member of the billiard family, the form factor is calculated analytically for small arguments in the diagonal approximation. All results together are consistent with the so-called semi-Poisson statistics.Comment: 8 pages, 9 figure

Slow relaxation in weakly open vertex-splitting rational polygons

The problem of splitting effects by vertex angles is discussed for nonintegrable rational polygonal billiards. A statistical analysis of the decay dynamics in weakly open polygons is given through the orbit survival probability. Two distinct channels for the late-time relaxation of type 1/t^delta are established. The primary channel, associated with the universal relaxation of ''regular'' orbits, with delta = 1, is common for both the closed and open, chaotic and nonchaotic billiards. The secondary relaxation channel, with delta > 1, is originated from ''irregular'' orbits and is due to the rationality of vertices.Comment: Key words: Dynamics of systems of particles, control of chaos, channels of relaxation. 21 pages, 4 figure

Spin chains from super-models

We construct and study a class of N particle supersymmetric Hamiltonians with nearest and next-nearest neighbor inverse-square interaction in one dimension. We show that inhomogeneous XY models in an external non-uniform magnetic field can be obtained from these super-Hamiltonians in a particular limit decoupling the fermionic degrees of freedom from the kinematic ones. We further consider a suitable deformation of these super-models such that inhomogeneous XXZ Hamiltonians in an external non-uniform magnetic field are obtained in the same limit. We show that this deformed Hamiltonian with rational potential is, (i) mapped to a set of free super-oscillators through a similarity transformation and (ii) supersymmetric in terms of a new, non-standard realization of the supercharge. We construct many exact eigenstates of this Hamiltonian and discuss about the applicability of this technique to other models.Comment: 36 pages, RevTeX, No figures, v1; Corrected typos, Added minor clarifications, v2; Added discussions, version to appear in JPSJ, v