Quark Probability Distribution at Finite Temperature and Density

Quark deconfinement phase transition at finite temperature and density is investigated in the frame of quantum mechanics. By solving the Schrödinger equation for a heavy quark in a thermal mean field, we calculate the quark probability distribution as a function of temperature and density. The confined wave function in the vacuum expands outward rapidly when the temperature and density are high enough. The obtained phase transition line agrees qualitatively with the result of lattice QCD. It is widely accepted that the collective effect of a multiparton system can change the vacuum structure of Quantum Chromodynamics (QCD)[1], and the partons confined in a hadron bag can move out when the temperature and density are high enough and form a new state of matter, the so called quark-gluon plasma (QGP)[2]. This kind of new matter may be produced in the early stage of a high-energy heavy-ion collision[3]. The dense partons, produced in the vacuum at high temperature or compressed at high baryon density, make the quark wave functions overlap in a space with dimension of the colliding nuclei. An important question in relativistic heavy ion collisions is how to identify the new state of matter if it is created in the early stage. According to the numerical calculation of lattice QCD[4], the critical temperature of quark deconfinement is about 150 MeV when the density effect is excluded. The idea that the overlap of wave functions, or the space extension of wave functions at finite temperature and density is the original reason of quark deconfinement phase transition arises naturally an interesting ques1 tion to study the behavior of quark distribution function in the frame of quantum mechanics. In this letter, we will study a quark moving in a thermal mean field describing multiparton interactions, and obtain the quark probability distribution by solving the Schrödinger equation at finite temperature and density. The temperature and density at which the quark wave function expands outward rapidly can be considered as the critical point of quark deconfinement. Because of the limitation of non-relativistic quantum mechanics, we focus on the motion of a heavy quark at finite temperature and density, corresponding to, for example, the dissociation of J/ψ[5] as a signature of QGP in relativistic heavy ion collisions. In the string-like models[3] that describe the quark confinement well, one uses a linear potential V = kr to express the interaction between two quarks. To simplify the numerical calculation in the following, we use a three dimensional square well