Characterization of the one-dimensional fractal structures by correlations, cumulants and moments as applied to high-energy hadronic rapidity correlations.

Abstract

In this dissertation we investigate the question that high energy irregular rapidity events can be generated by finite samples of one dimensional fractal structures. The idea is basically to generate a rapidity histogram by transforming a one-dimensional map of which the histogram is known and simple a one-dimensional map with the desired histogram. Then studying the system in different dynamical regimes we analyse the properties of factorial moments, cumulants and multifractal properties. It is useful to have such models in the sense that one then has a direct ability to check some of the quantitative features that can be distinguished from each other because they refer to different dynamical regimes (i.e. intermittency and chaos). In studying such models we analyse the qualitative and quantitative features of the question of hadronic intermittency in comparison with the same features in those models both theoretically and experimentally. We finally made an analogy with the field theory formalism of hadron production and Quantum Optics in which the question of regularity vs. irregularity has been asked much earlier.