Quantum to classical parton dynamics in QCD media

We study the time evolution of the density matrix of a high energy quark propagating in a dense QCD medium where it undergoes elastic collisions (radiation is ignored in the present study). The medium is modeled as a stochastic color field with a Gaussian correlation function. This allows us to eliminate the medium degrees of freedom and obtain a simple master equation for the evolution of the reduced density matrix of the high energy quark, making use of approximations that are familiar in the description of open quantum systems. This master equation is solved analytically, and we demonstrate that its solution can be reconstructed from a simple Langevin equation. At late times, one finds that only the color singlet component of the density matrix survives the quark's propagation through the medium. The off-diagonal elements of the density matrix are suppressed successively in transverse position space and in momentum space, and become independent of the details of the initial condition. This behavior is reflected in the corresponding von Neumann entropy, whose growth at late time is related to the increase of the classical phase space explored by the high energy quark in its motion through the medium. The interpretation of the Wigner transform as a classical distribution is further supported by the fact that the associated classical entropy coincides at late time with the von Neumann entropy.