Summary and Outlook

We reflect on the two questions that broadly motivated the work in this thesis. Namely, ‘What are the most salient consequences of the effective non-Hermiticity intrinsic to the equations of motion for closed, non-interacting bosonic systems?’ and ‘To what extent can closed, or open, non-interacting bosons manifest physics associated to SPT phases of non-interacting fermions?’. We concisely summarize the key results uncovered in the pursuit of answers to these questions, and discuss several future directions for this exciting line of research.