Universal spectral statistics in quantum graphs

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.Comment: 4 pages, reftex, 1 figure, revised version to be published in PR

Multiparticle production and quantum chromodynamics

The theory of strong interactions, quantum chromodynamics (QCD), is quite successful in the prediction and description of main features of multiparticle production processes at high energies. The general perturbative QCD approach to these processes (mainly to e+e- -annihilation) is briefly formulated and its problems are discussed. It is shown that the analytical calculations at the parton level with the low-momentum cut-off reproduce experimental data on the hadronic final state in multiparticle production processes at high energies surprisingly accurately even though the perturbative expansion parameter is not very small. Moreover, it is important that the perturbative QCD has been able not only to describe the existing data but also to predict many bright qualitatively new phenomena.Comment: 30 pages, LATEX, 12 Figs available at www.ufn.ru; the review pap er to be published in Physics-Uspekhi 45 (5) (2002