Numerical analysis of a spontaneous collapse model for a two-level system

Abstract

We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows to give precise estimates on the regime at which the collapse of the state vector occurs, the reduction and delocalization times, and the reduction probabilities; it also allows to quantify the effect that an Hamiltonian which does not commute with the reducing terms has on the collapse mechanism. We also give a clear picture of the transition from the "microscopic" regime (when the noise terms are weak and the Hamiltonian prevents the state vector to collapse) to the "macroscopic" regime (when the noise terms are dominant and the collapse becomes effective for very long times). Finally, we clarify the distinction between decoherence and collapse.