The Role of Pairing in Dynamically Stable QBHs

This chapter is dedicated to a set of results specialized to dynamically stable QBHs. In particular, we import mathematical techniques developed for pseudo-Hermitian quantum systems in order to construct a duality transformation that restores number symmetry in dynamically stable QBHs with pairing. We find that the duality transformation is intrinsically related to the covariance matrix of the quasi-particle vacuum of the QBH. Implications for analogue simulation of non-Hermitian quantum dynamics, as well as topological invariants and edge states are discussed. We specialize our results to a general dynamically stable single-band models, exemplified by a gapped harmonic chain, as well as the BKC considered previously.