  Strong light-matter coupling between molecules and plasmonic nanoparticles
give rise to new hybrid eigenstates of the coupled system, commonly referred to
as polaritons, or more precisely, plexcitons. Over the last decade it has been
amply shown that molecular electron dynamics and photophysics can be
drastically affected by such interactions, thus paving the way for
light-induced control of molecular excited-state properties and reactivity.
Here, by combining ab initio molecular description and classical or quantum
modelling of arbitrarily-shaped plasmonic nanostructures within Stochastic
Schr\"odinger Equation, we present two approaches, one semi-classical and one
full-quantum, to follow in real-time the electronic dynamics of plexcitons
while realistically taking plasmonic dissipative losses into account. The
full-quantum theory is compared with the semi-classical analogue under
different interaction regimes, showing (numerically and theoretically) that
even in the weak-field and weak-coupling limit a small-yet-observable
difference arises.
