  Optical cavities, e.g. as used in organic polariton experiments, often employ
low finesse mirrors or plasmonic structures. The photon lifetime in these
setups is comparable to the timescale of the nuclear dynamics governing the
photochemistry. This highlights the need for including the effect of
dissipation in the molecular simulations. In this study, we perform wave packet
dynamics with the Lindblad master equation, to study the effect of a finite
photon lifetime on the dissociation of the MgH$^+$ molecule model system.
Photon lifetimes of several different orders of magnitude are considered to
encompass an ample range of effects inherent to lossy cavities.
