Real-time quantum dynamics of heavy-quark systems at high temperature

On the basis of the closed-time-path formalism of nonequilibrium quantum field theory, we derive the real-time quantum dynamics of heavy-quark systems. Even though our primary goal is the description of heavy quarkonia, our method allows a unified description of the propagation of single heavy quarks as well as their bound states. To make calculations tractable, we deploy leading-order perturbation theory and consider the nonrelativistic limit. Various dynamical equations, such as the master equation for quantum Brownian motion and the time-evolution equation for heavy-quark and quarkonium forward correlators, are obtained from a single operator: the renormalized effective Hamiltonian. We are thus able to reproduce previous results of perturbative calculations of the drag force and the complex potential simultaneously. In addition, we present stochastic time-evolution equations for the heavy-quark and quarkonium wave function, which are equivalent to the dynamical equations.

Figure 1

Closed-time path $\mathcal{C}$ in the complex time plane, parametrized by $s$.