PHASE-TRANSITION AND THE NUCLEON AS A SOLITON IN THE NAMBU-JONA-LASINIO MODEL AT FINITE-TEMPERATURE AND DENSITY

We study some bulk thermodynamical characteristics, meson properties a nd the nucleon as a baryon-number-one soliton in hot quark matter in t he NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleon s. In both cases, working in the mean-field approximation, we find a c hiral phase transition from the Goldstone to the Wigner phase. At fini te density the chiral order parameter and the constituent quark mass h ave a non-monotonic temperature dependence - at finite temperatures no t close to the critical one they are less affected than in cold matter . Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter i s much stiffer and the chiral phase transition is very sharp. The ther modynamical variables show large discontinuities which is an indicatio n for a first-order phase transition. We solve the B = 1 solitonic sec tor of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is m ore bound and less swelled than in the case of cold matter. At some cr itical temperature, which for nucleon matter coincides with the critic al temperature for the chiral phase transition, we find no more a loca lized solution. According to this model scenario one should expect a s harp phase transition from nucleon to quark matter.