  Using the potential non-relativistic quantum chromodynamics (pNRQCD)
effective field theory, we derive a Lindblad equation for the evolution of the
heavy-quarkonium reduced density matrix that is accurate to next-to-leading
order (NLO) in the ratio of the binding energy of the state to the temperature
of the medium. The resulting NLO Lindblad equation can be used to more reliably
describe heavy-quarkonium evolution in the quark-gluon plasma at low
temperatures compared to the leading-order truncation. For phenomenological
application, we numerically solve the resulting NLO Lindblad equation using the
quantum trajectories algorithm. To achieve this, we map the solution of the
three-dimensional Lindblad equation to the solution of an ensemble of
one-dimensional Schr\"odinger evolutions with Monte-Carlo sampled quantum
jumps. Averaging over the Monte-Carlo sampled quantum jumps, we obtain the
solution to the NLO Lindblad equation without truncation in the angular
momentum quantum number of the states considered. We also consider the
evolution of the system using only the complex effective Hamiltonian without
stochastic jumps and find that this provides a reliable approximation for the
ground state survival probability at LO and NLO. Finally, we make comparisons
with our prior leading-order pNRQCD results and experimental data available
from the ATLAS, ALICE, and CMS collaborations.
