What can we learn about hadronic intermittency from finite fractal sets?

Abstract

The formalism recently introduced in hadronic intermittency is used to understand the dynamics of one-dimensional fractal sets. We examine the translation invariance, factorial and cumulant moments, and the fractal dimensions of the phase space as the nonlinearity of the sets is changed in a broad range from intermittent to chaotic. We show that the dynamical content of the sets is strongly interwoven with the magnitude of the fractal dimensions of the phase-space correlations. We simulate events by properly transforming the logistic map so that relevant density histograms of hadronic particle distributions are qualitatively produced. We use this as a toy model to understand the rapidity phase-space behavior of these distributions. By studying the fractal dimensions of these models we show that the hadronic data show very weak intermittency in the rapidity phase space.