Some phenomenological considerations on the nuclear collisions at high energies

TL;DR

This paper applies chaos theory and semiclassical methods to study the dynamics of a relativistic quark system, revealing temperature-dependent behaviors including oscillation, expansion, and partial fragmentation near a critical temperature.

Contribution

It introduces a novel combination of chaos theory, Shannon entropy, and graph theory to analyze phase transitions and fragmentation in high-energy nuclear collisions.

Findings

System can oscillate or expand depending on initial temperature

Partial fragmentation occurs near the critical temperature

Fragmentation degree is quantified using Shannon entropy and graph theory

Abstract

We present some results obtained by applying the chaos theory on the numerical study of one threedimensional, relativistic, many-body quark system. The asymptotic freedom property is introduced by employing a harmonic term in the bi-particle potential. In this context, we used also the outcome of a semiclassical study, applied to the quark constituents of nucleons. Depending on the initial temperature parameter, the system can evolve toward an oscillating or an expansion regime. It is important to notice also a transition region, characterized by a partial fragmentation (higher degree of order). This effect can be observed near the critical temperature and is related to the partial overcoming of the potential barrier (corresponding to the farthest particles from the system). The degree of fragmentation is defined on the Shannon entropy basis and using the graphs theory. For analyzing the expansion tendency of one relativistic many-body system, we employed also the virial coefficient.