Non-Markovian Poissonian Spontaneous Collapse Models

Spontaneous collapse models provide a possible solution to the measurement problem by modifying standard quantum dynamics. The modification consists of adding non-linear and stochastic terms inducing wavefunction collapse in space. Non-Markovian versions of these models are motivated by physical reasons, phenomenological consistency, and potential for relativistic extensions. Here, we investigate a non-Markovian version of the Poissonian Spontaneous Localization (PSL) model, i.e., a model characterized by instantaneous and localized collapse events. We assume that our model is characterized by a typical time scale τ_C so that, given an initial state ρ₀ of standard quantum matter at time t=0, we derive an effective long-time $tgg τ_C$ statistical dynamics in terms of a CPTP map Φ_t. We then show how Φ_t can be made equal to that obtained by non-Markovian CSL models. Moreover, given Φ_t, we obtain the associated time-convolutionless master equation by means of a supercumulant expansion. Finally, we characterize the collapse events process for events with $t gg τ_C$ given an initial quantum state ρ₀ at t=0.