Simple approach to characterizing band topology in bosonic pairing Hamiltonians

We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. show this can be rigorously addressed by a smooth and local adiabatic mapping procedure to number conserving Hamiltonian. In contrast generic fermionic pairing Hamiltonian, such always constructed for bosons. Our approach shows non-conserving classified using known approaches models. It also provides simple means identifying calculating appropriate topological invariants. explicitly study dynamically stable but non-positive definite (as arise frequently driven photonic systems). case, each gap is characterized two distinct