The Realm of Possibilities

This chapter is devoted to dissecting a series of four models that exemplify the general results of Chap. 8 . The first model is a purely dissipative QBL derived by applying the first recipe of Chap. 7 to the fermionic Kitaev chain (FKC) Hamiltonian. The resulting QBL is topologically metastable in certain parameter regimes that overlap with the topological phase diagram of the FKC and, most importantly, sustains an MB pair that derive from the Majorana edge modes of the FKC. Interestingly, these provide an example of “non-split” MBs, i.e., MBs that are both ZMs and SGs. In this sense, these are the tightest bosonic analogues of Majorana fermions. The second model is a dissipative version of the BKC first explored in Chap. 3 . By completely characterizing the five-parameter topological phase diagram, we uncover three relevant dynamical phases: an anomalously relaxing one, a non-topological dynamically metastable one, and a topologically metastable one. We explore the dynamical features of each phase in detail and, in particular, compute MBs that arise in the topologically metastable phases. The third model once again describes a dissipative BKC. However, in this model, the dissipator is constructed following the second recipe of Chap. 7 , and thus, the resultant QBL possesses a unique, pure steady-state. Additionally, we find that this QBL has a metastable regime. This allows us to explore the interplay between MBs and pure steady states. In particular, we analytically compute the quasi-steady states and uncover surprisingly non-trivial parity dynamics of certain cat-state superpositions. The final model is a number-symmetric QBL that possesses a topologically metastable phase. We explicitly construct the DBs predicted in Chap. 8 . We conclude with an analysis of certain multitime correlation functions in QBLs. We find that, generically, topological metastability may be characterized by the existence of long-live two-time quantum correlation functions between the macroscopically separated MB partners, in addition to the emergence of divergent zero-frequency power-spectral peaks. We further use two-time correlation functions to distinguish the unique features of the models of interest.