Dissipative extension of the Ghirardi-Rimini-Weber model

TL;DR

This paper extends the Ghirardi-Rimini-Weber model by incorporating dissipation, preventing energy divergence, and enabling a realistic finite-temperature collapse noise, while maintaining effective wavefunction localization.

Contribution

The authors introduce a dissipative extension of the GRW model with new momentum-dependent jump operators, ensuring finite energy and realistic collapse noise, while preserving localization and amplification mechanisms.

Findings

Energy relaxes exponentially to a finite value

Collapse remains effective at low temperatures

Model can be described by a stochastic differential equation

Abstract

In this paper we present an extension of the Ghirardi-Rimini-Weber model for the spontaneous collapse of the wavefunction. Through the inclusion of dissipation, we avoid the divergence of the energy on the long time scale, which affects the original model. In particular, we define new jump operators, which depend on the momentum of the system and lead to an exponential relaxation of the energy to a finite value. The finite asymptotic energy is naturally associated to a collapse noise with a finite temperature, which is a basic realistic feature of our extended model. Remarkably, even in the presence of a low temperature noise, the collapse model is effective. The action of the new jump operators still localizes the wavefunction and the relevance of the localization increases with the size of the system, according to the so-called amplification mechanism, which guarantees a unified description of the evolution of microscopic and macroscopic systems. We study in detail the features of our model, both at the level of the trajectories in the Hilbert space and at the level of the master equation for the average state of the system. In addition, we show that the dissipative Ghirardi-Rimini-Weber model, as well as the original one, can be fully characterized in a compact way by means of a proper stochastic differential equation.