Abstract

We present a possible extension of the usual relativistic nuclear mean field models widely used to describe nuclear matter towards accounting for the influence of possible intrinsic fluctuations caused by the environment. Rather than individually identifying their particular causes we concentrate on the fact that such effects can be summarily incorporated in the changing of the statistical background used, from the usual (extensive) Boltzman-Gibbs one to the nonextensive taken in the form proposed by Tsallis with a dimensionless nonextensivity parameter $q$ responsible for the above mentioned effects (for $q \rightarrow 1$ one recovers the usual BG case). We illustrate this proposition on the example of the QCD-based Nambu - Jona-Lasinio (NJL) model of a many-body field theory describing the behavior of strongly interacting matter presenting its nonextensive version. We check the sensitivity of the usual NJL model to a departure from the BG scenario expressed by the value of $| q - 1|$, in particular in the vicinity of critical points.

Highlights

  • In all studies of relativistic properties of nuclear matter, mean field models are usually the models of first choice [1,2]

  • We present a possible extension of the usual relativistic nuclear mean field models widely used to describe nuclear matter towards accounting for the influence of possible intrinsic fluctuations caused by the environment

  • Rather than individually identifying their particular causes we concentrate on the fact that such effects can be summarily incorporated in the changing of the statistical background used, from the usual Boltzman-Gibbs one to the nonextensive taken in the form proposed by Tsallis with a dimensionless nonextensivity parameter q responsible for the above mentioned effects

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Summary

Introduction

In all studies of relativistic properties of nuclear matter, mean field models are usually the models of first choice [1,2]. In our work [19] we investigated a nonextensive version of another mean field theory, namely the QCD-based Nambu - Jona-Lasinio (NJL) model of a many-body field theory describing the behavior of strongly interacting matter presented recently in [21] This time, unlike in [18], we used the quark rather than the hadronic degrees of freedom and, because of this, we had to consider both the q > 1 and q < 1 cases. This q-NJL model allowed us to discuss the q-dependence of the chiral phase transition in dense quark matter, in particular the quark condensates and the effective quark masses and their influence on the masses of π and σ mesons and on the spinodal decomposition (cf., [19] for details) These results helped us proceed further and consider critical phenomena in strongly interaction matter using q-statistics (these phenomena are of interest nowadays, cf., for example, [23,24], but were so far not investigated in non-equilibrium environment provided by q-statistics). We shall concentrate on the influence of dynamical factors causing nonextensivity and represented by the parameter q in the vicinity of the critical end point (CEP)

The usual NJL model
The q extension of the NJL model - the q-NJL
Results
Summary

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