Optical cavities are structures where excitations in the electromagnetic field (photons of light) are confined and generally long-lived. The spatial confinement will enhance interactions with any matter systems in the cavity, such that the behaviour of a 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 the modification and control of chemical reactions, and a multitude of experimental advancements are beginning to realise this potential. There are however many challenges with creating useful theoretical models of the prominent quantum-mechanical behaviour in these systems, where model complexities regularly require numerical simulations.

In this thesis, we especially engage with two challenges from the field: One is to model cavities that contain ensembles of matter systems that interact collectively with the confined light. Another is to implement models based on open quantum systems, which is a dominant framework to include environment interactions.

With this work, we aim to deepen the understanding of the physics in these polaritonic chemistry systems. Our strategy is to isolate critical processes in order to study their significance and impact. In different contexts, this either allows us to identify potential obstacles to avoid or highlights opportunities to achieve desired experimental conditions and technological objectives.