Bound-state formation and thermalization within the Lindblad approach

We consider a problem borrowed from heavy-ion collisions, namely, the formation of bound states, as for example the deuteron, in the nonrelativistic regime by using the techniques of Lindblad dynamics considering an open quantum system. We show that the position-space Lindblad equation can be reformulated in terms of a diffusion-advection equation with sources and therefore provides a hydrodynamical formulation of a dissipative quantum master equation. Making use of this advanced machinery and these insights, we describe the possible formation of a bound state, which is realized by a P"oschl-Teller-like potential, of a particle in interaction with a heat bath in a one-dimensional setting and discuss general aspects of open quantum systems, such as decoherence, entropy production, purity, thermalization time, and thermalization. Finally, we also show an example of a much deeper potential, where we allow for three bound states, just in the spirit of quarkonia.