Towards quantum superpositions of a mirror: an exact open systems analysis - calculational details

We give details of calculations analysing the proposed mirror superposition experiment of Marshall, Simon, Penrose and Bouwmeester within different stochastic models for state vector collapse. We give two methods for exactly calculating the fringe visibility in these models, one proceeding directly from the equation of motion for the expectation of the density matrix, and the other proceeding from solving a linear stochastic unravelling of this equation. We also give details of the calculation that identifies the stochasticity parameter implied by the small-displacement Taylor expansion of the CSL model density matrix equation. The implications of the two results are briefly discussed. Two pedagogical appendices review mathematical apparatus needed for the calculations.