Nucleation of Quark Matter in Neutron Star Cores

We consider the general conditions of quark droplets formation in highdensity neutron matter. The growth of the quark bubble (assumed to contain asufficiently large number of particles) can be described by means of aFokker-Planck equation. The dynamics of the nucleation essentially depends onthe physical properties of the medium it takes place. The conditions for quarkbubble formation are analyzed within the frameworks of both dissipative andnon-dissipative (with zero bulk and shear viscosity coefficients) approaches.The conversion time of the neutron star to a quark star is obtained as afunction of the equation of state of the neutron matter and of the microscopicparameters of the quark nuclei. As an application of the obtained formalism weanalyze the first order phase transition from neutron matter to quark matter inrapidly rotating neutron stars cores, triggered by the gravitational energyreleased during the spinning down of the neutron star. The endothermicconversion process, via gravitational energy absorption, could take place, in avery short time interval, of the order of few tens seconds, in a class of densecompact objects, with very high magnetic fields, called magnetars.Comment: 31 pages, 2 figures, to appear in Ap