The Lindblad master equation is a frequently used Markovian approach to describe open quantum
systems in terms of the temporal evolution of a reduced density matrix. Here, the thermal environ-
ment is traced out to obtain an expression to describe the evolution of what is called a system: one
particle or a chain of interacting particles, which is/are surrounded by a thermal heat bath.
In this work, we investigate the formation of non-relativistic bound states, involving the P¨oschl-
Teller potential, in order to discuss the formation time and the thermal equilibrium, applying scales
from nuclear physics. This problem is borrowed from the field of heavy-ion collisions, where the
deuteron is a probe which is measured at temperature regimes around the chemical freeze out
temperature, while the deuteron itself has a binding energy which is much lower. This is known and
often described as a “snowball in hell”.
We use a reformulated Lindblad equation, in terms of a diffusion-advection equation with sources
and therefore provide a hydrodynamical formulation of a dissipative quantum master equation