Topology by Dissipation and Majorana Bosons in Metastable Quadratic Markovian Dynamics

Majorana bosons, that is, tight bosonic analogues of the Majorana fermionic quasi-particles of condensed-matter physics, are forbidden for gapped free bosonic matter within a standard Hamiltonian scenario. We show how the interplay between dynamical metastability and non-trivial bulk topology makes their emergence possible in non-interacting bosonic chains undergoing Markovian dissipation. This leads to a distinctive form of topological metastability whereby, consistent with the breakdown of Noether's theorem for open systems, a conserved Majorana boson localized on one edge is paired with a distinct symmetry generator localized on the opposite edge. We argue that Majorana bosons are robust against disorder and identifiable by signatures in the zero-frequency steady-state power spectrum. Our results suggest that symmetry-protected topological phases for free bosons may arise in transient metastable regimes, which are still stable over practical time scales.