The study of finite lumps (droplets) of quark matter plays an important role for the search of the quark gluon plasma (QGP) in relativistic heavy-ion collisions [1]. At low temperatures and densities the quarks are confined into hadrons, but, as the temperature or density increase hadronic matter is expected to undergo phase transitions. It is believed that the QGP lies in the chiral symmetric phase, where all symmetries of the QCD Lagrangian are restored. This motivates a growing activity devoted to the analysis of the thermodynamics of the quark matter, as well as to the study of the QCD phase diagram. Several QCD inspired models have been used to this purpose. The most interesting aspects of such investigations would be to observe signs of phase transitions. This is a challenging topic bearing in mind the results of present and future experiments to which the present lattice calculations are still away from giving definitive answers.

We perform our calculations in the framework of Nambu-Jona-Lasinio type models,

by using a standard bosonization procedure [2,3]. At zero temperature the emphasis is put on investigating droplets formation, which can provide signs indicating a first order phase transition. In fact, the appearance of an absolute minimum of the energy per baryon signifies the possibility for finite droplets to be in mechanical equilibrium with the vacuum at zero pressure. Since for very low temperature the absolute minimum of the energy turns to be at zero density, the phase transition is still first order but the system is unstable against expansion. With increasing temperature we will have a crossover.

We also consider the possibility of bound states in quark matter with the admixture of strange quark matter. We observe that the energy density is reduced by having three Fermi seas instead of just two in the absence of strangeness, and more significant bound states (strangelets) are obtained in this case.

Work supported by Caloust Gulbenkian Foundation (P. Costa), CFT and by FEDER/FCT under projects POCTI/FNU/50326/2003 and POCTI/FP/63412/2005.

[1] F. Karsch and E. Laremann, Phys. Rev. D 50, 6954 (1994); K. Kanaya, Prog. Theor. Phys. Suppl. 129, 197 (1997); C. Lourenço, Nucl. Phys. A 698, 54 (2002).

[2] P. Costa and M. C. Ruivo, Europhys. Lett. 60 (3), 356 (2002); P. Costa, M. C Ruivo, C. A de Sousa and Yu. L. Kalinovsky, Phys. Rev. C 70, 025204 (2004).

[3] P. Costa, M. C. Ruivo, C. A de Sousa and Yu. L. Kalinovsky,

Phys. Rev. D 70, 116013 (2004); Phys. Rev. D 71, 116002 (2005).