Dissipative Continuous Spontaneous Localization (CSL) model.

Andrea Smirne,Angelo Bassi

doi:10.1038/srep12518

Abstract

Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system’s evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.

Highlights

The superposition principle lies at the core of quantum mechanics
That we have clarified the problem of the Continuous Spontaneous Localization (CSL) model we want to work out, as well as the features that must be preserved, we are in the position to formulate a new, dissipative CSL model
We consider the following non-linear stochastic differential equation:

Summary

Introduction

The superposition principle lies at the core of quantum mechanics. The last years have experienced a huge progress in the theoretical and experimental investigation aimed at preparing and observing quantum superpositions of large systems[1,2,3,4,5,6,7]. The full characterization of such a noise calls for a new fundamental theory, which departs from quantum mechanics and can explain the classical nature of the noise, as well as its non-hermitian and non-linear coupling with matter[13,17] In this respect, the CSL model, like every collapse model, should be seen as a phenomenological model expressing the influence of the noise field in an effective way. We modify the defining stochastic differential equation via the introduction of new operators, which depend on the momentum of the system This determines the occurrence of dissipation[26,27,28], leading to the relaxation of the energy to a finite asymptotic value. Contrary to a common misconception, the steady increase of the energy is not an unavoidable trait of collapse models inducing localization in space: in our dissipative model there is a continuous localization of the wavefunction, while the mean energy of the system will typically decrease

Methods

Results

Conclusion