On a stochastic Trotter formula with application to spontaneous localization models

TL;DR

This paper establishes a stochastic Trotter formula linking continuous localization models with the discrete GRW wave function collapse model, providing a mathematical foundation for understanding their relationship.

Contribution

It introduces a stochastic Trotter formula that connects continuous and discrete wave function collapse models, expanding the theoretical framework of stochastic Schrödinger evolutions.

Findings

Proves the stochastic Trotter formula for localization models

Shows the continuous models as scaling limits of the GRW process

Complements existing existence results for stochastic Schrödinger evolutions

Abstract

We consider the relation between so called continuous localization models - i.e. non-linear stochastic Schr\"odinger evolutions - and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schr\"odinger evolutions by Holevo and Mora/Rebolledo.