Non-Markovian collapse models
Luca Ferialdi · OpenstarTs (Univeristy of Trieste https://www.units.it/) · 2010
Table 1: Table of the collapse constants used in the thesis.L and T denote respectively "length" and "time".α is the inverse of the square root of the correlation length of the GRW model (p.18).m is the mass of the particle considered in the QMUPL model and m 0 is a reference mass (p.30).function undergoes a sudden, spontaneous, and random localization.Such a collapse process is implemented by modifying the linear structure of the Schrödinger equation, introducing suitable non-linear and stochastic terms.Changes of this kind are necessary if one wants to avoid linear superpositions, reproduce quantum indeterminism, and, at the same time, achieve the localization of macroscopic objects.Actually, these requirements imply the structure of the modified Schrödinger equation to be well defined [4]; of course it is possible for the parameters to take very different values, identifying in this way models with physically different features.All the models afore-mentioned are Markovian models: they involve a white noise, i.e. a noise with Dirac-delta temporal correlation function, which implies the absence of memory effects [3].Since it is natural to identify the stochastic field driving the collapse with a physical field in Nature, which is likely to have a cosmological origin, one then needs to go beyond Markovian models since white noises are only mathematical idealizations which do not correspond to any physical noise.For this reason, it is necessary to study non-Markovian collapse models, i.e. models which involve noises with general correlation functions in time [11].The aim of this thesis is to study the non-Markovian generalization of the QMUPL model, both regarding its mathematical features and its physical properties, and to compare them with the known features of the Markovian