Implementation of quark confinement and retarded interactions algorithms for Chaos Many-Body Engine

In Grossu et al. (2012) we presented a Chaos Many-Body Engine (CMBE) toy-model for chaos analysis of relativistic nuclear collisions at 4.5 A GeV/c (the SKM 200 collaboration) which was later extended to Cu ＋Cu collisions at the maximum RHIC-BNL energy. Inspired by existing quark billiards, the main goal of this work was extending CMBE to partons. Thus, we first implemented a confinement algorithm founded on some intuitive assumptions (Grossu et al., 2016): (1) the system can be decomposed into a set of two or three-body quark white clusters; (2) the bi-particle force is limited to the domain of each cluster; (3) the physical solution conforms to the minimum potential energy requirement. Color conservation was also treated as part of the reactions logic module. As an example of use, we proposed a toy-model for p ＋p collisions at s=10 GeV and we compared it with HIJING. Another direction of interest was related to retarded interactions. Following this purpose, we implemented an Euler retarded algorithm and we tested it on a simple two-body system with attractive inverse-square-law force. In this particular test case we noticed the interesting fact that the Virial coefficient is sub-unitary and reaches the expected value (one) as the interaction speed approaches infinity. On the other hand, the time reverse functionality implemented in CMBE v03 could be used together with retardation for analyzing the Loschmidt paradox. Regarding the application design, it is important to mention the code was refactored to SOLID. In this context, we have also written more than one hundred unit and integration tests, which represent an important indicator of application logic validity.