Collapse models with non-white noises

TL;DR

This paper develops a formalism for spontaneous wave function collapse models driven by general Gaussian noises, extending previous white-noise models and analyzing their collapse dynamics and deviations from standard quantum mechanics.

Contribution

It introduces a general stochastic differential equation framework for collapse models with non-white Gaussian noises and analyzes the collapse process and its quantum probabilities.

Findings

Collapse occurs to eigenstates with correct probabilities

Perturbation expansion for deviations from quantum mechanics

Non-white Gaussian noise can be handled with the imaginary noise trick

Abstract

We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the non-Schrodinger terms of the equation induce the collapse of the wave function to one of the common eigenstates of the collapsing operators, and that the collapse occurs with the correct quantum probabilities. We also develop a perturbation expansion of the solution of the equation with respect to the parameter which sets the strength of the collapse process; such an approximation allows one to compute the leading order terms for the deviations of the predictions of collapse models with respect to those of standard quantum mechanics. This analysis shows that to leading order, the ``imaginary'' noise trick can be used for non-white Gaussian noise.