Collapse models with non-white noises II: particle-density coupled noises

TL;DR

This paper analyzes collapse models driven by non-white Gaussian noise coupled to particle density, deriving reduction rates and Fokker-Planck equations, with implications for cosmological noise sources.

Contribution

It introduces a detailed analysis of non-white noise in collapse models, deriving general reduction rates and equations, and explores cosmological noise implications.

Findings

Density matrix diagonalization and state reduction governed by same rate parameters

Derived Fokker-Planck equations for stochastic Schrödinger equation

Dependence of reduction dynamics on noise autocorrelator and cosmological factors

Abstract

We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schr\"odinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and qantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.