  We study a topological superconductor capable of exchanging particles with an
environment. This additional interaction breaks particle-number symmetry and
can be modelled by means of an integrable Hamiltonian, building on the class of
Richardson-Gaudin pairing models. The isolated system supports zero-energy
modes at a topological phase transition, which disappear when allowing for
particle exchange with an environment. However, it is shown from the exact
solution that these still play an important role in system-environment particle
exchange, which can be observed through resonances in low-energy and -momentum
level occupations. These fluctuations signal topologically protected Read-Green
points and cannot be observed within traditional mean-field theory.
