Optical cavities—where spatial confinement can focus electromagnetic excitations—are able to couple matter to light with enough strength that the behaviour of the combined system is best understood in terms of polaritonic states; mixtures of excitations in both light and matter. This polaritonic regime provides a novel approach for modification and control of chemical reactions, and lately, experimental advancements are realising this potential.

There are however many challenges with creating useful theoretical models of the prominent quantum behaviour in these systems, which (with exception of some simple cases) require numerical simulations. In this thesis, we engage with two such challenges from polaritonic chemistry: Modelling cavities containing an ensemble of matter systems, and modelling the open quantum systems that arise from losses in the cavity. We learn what influence an ensemble of atoms has on molecular dissociation, and we characterise multiple physical phenomena in bad cavities.