Quantum Kinetics of Deconfinement Transitions in Dense Nuclear Matter Dissipation Effects at Low Temperatures

Effects of energy dissipation on quantum nucleation of two-flavor quark matter in dense nuclear matter encountered in neutron star cores are examined at low temperatures. We find that low-energy excitations of nucleons and electrons reduce the nucleation rate exponentially via their collisions with the surface of a quark matter droplet. ∗) E-mail address: [email protected] 1 typeset using PTPTEX.sty The possible existence of quark matter in neutron stars has been studied for the past two decades from the viewpoint of equilibrium phase diagrams (see, e.g., Refs. 1)∼3)). Recently, Glendenning 1) relaxed the constraint of local charge neutrality, as usually assumed, and discovered that a phase where quark matter and nuclear matter in β-equilibrium coexist in a uniform sea of electrons could intervene between bulk quark and nuclear matter phases for a finite range of pressures. This is because the presence of strange and down quarks plays a role in reducing the electron Fermi energy and in increasing the proton fraction of nuclear matter. Glendenning 1) and Heiselberg et al. 2) also claimed that the mixed phase could exhibit spatial structure such as quark matter droplets embedded in nuclear matter as a result of surface and Coulomb effects. As a star whose core consists of nuclear matter in β-equilibrium spins down or accretes matter from a companion star, the central density could become sufficiently large for the mixed phase to be stable. Whether the mixed phase actually appears, however, depends on the occurrence of the dynamical processes leading to its appearance. The first of these processes should be deconfinement; the direct conversion of nuclear matter to three-flavor quark matter that is more stable than two-flavor quark matter is inhibited, since relatively slow weak processes are involved. If quark matter is deconfined from nuclear matter via a first-order phase transition, a droplet of two-flavor quark matter could form in a metastable phase of bulk nuclear matter during the spin-down or accretion. Iida and Sato 4) calculated the rates for the formation of this droplet via quantum tunneling at zero temperature by incorporating the electrostatic energy into the potential for droplet formation. It was found that a droplet formed via quantum fluctuations would develop into bulk matter due to electron screening effects on the Coulomb energy of the droplet itself. This result implies that the mixed phase is unlikely to occur. The effects of energy dissipation on the quantum kinetics of the deconfinement transition, which were ignored in the previous work, 4) may have a decisive role in determining not only the degree of overpressure required to form an up and down quark matter droplet but also the crossover temperature from the nucleation via quantum tunneling to that via thermal activation; its comparison with the temperature of matter in neutron star cores is significant. In this paper, we thus estimate to what extent the rates for droplet formation via quantum tunneling are reduced by the friction exerted on the droplet, according to the work of Burmistrov and Dubovskii 5) that gave useful expressions for such reduction on the basis of a path-integral formalism developed by Caldeira and Leggett. 6) It is found to be the ballistic motion of low-lying excitations of nucleons and electrons that controls the dissipative processes in the situation of interest here. The possible effect of neutron and proton superfluidity, which acts to decrease the number of available quasiparticle states