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arXiv:quant-ph/9912007 · Europhysics Letters (EPL)

Burgers turbulence and the continuous spontaneous localization model

Léa Ferreira dos Santos, Carlos O. Escobar

Published Apr 1, 2001• 3 citations
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Abstract

There is a striking convergence between Burgers turbulence and the continuous spontaneous localization (CSL) model of quantum mechanics. In this paper we exploit this analogy, identify the CSL counterparts of quantities in turbulence, such as the Reynolds number and the injected energy, show that the velocity of a particle subjected to the localization process satisfies Burgers equation and indicate a time region for experimental tests of the CSL models.

DOI
10.1209/epl/i2001-00223-5

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There is a striking convergence between Burgers turbulence and the continuous spontaneous localization (CSL) model of quantum mechanics. In this paper we exploit this analogy, identify the CSL counterparts of quantities in turbulence, such as the Reynolds number and the injected energy, show that the velocity of a particle subjected to the localization process satisfies Burgers equation and indicate a time region for experimental tests of the CSL models.
We find an analogy between turbulence and the dynamics of the continuous spontaneous localization model (CSL) of the wave function. The use of a standard white noise in the localization process gives Richardson's t3{t}^{3}t3 law for the turbulent diffusion, while the introduction of an affine noise in the CSL allows us to obtain the intermittency corrections to this law.
Continuous Spontaneous Localization (CSL) model of Quantum Mechanics modifies Schrödinger equation by adding non-linear stochastic terms due to which the total energy of a system increases with a constant rate which is proportional to the collapse rate λλλ. Thus applying CSL model to cosmological scenarios can change the thermal behaviour of the particles during evolution and we will put constraints on λλλ by considering several cosmological scenarios.
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.
Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schr\"odinger equation, thus (slightly) modifying the dynamics of quantum systems. Experimental bounds on the collapse parameters have been derived from various experiments involving a plethora of different systems, from single atoms to gravitational wave detectors. Here, we give a comprehensive treatment of the continuous spontaneous localization (CSL) model, the most studied among collapse models, for Fermi liquids. We consider both the white and non-white noise case. Application to various astrophysical sources is presented.
Abstract Among the open problems in fundamental physics, few are as conceptually significant as the “measurement problem” in Quantum Mechanics. One of the proposed solutions to this problem is the Continuous Spontaneous Localization (CSL) model, which introduces a non-linear and stochastic modification of the Schrödinger equation. This model incorporates two parameters that can be subjected to experimental constraints. One of the most notable consequences of this theory is the spontaneous heating of massive objects; this anomalous heating is dependent on the CSL parameters. In this work, we will revisit some astrophysical bounds previously found, and introduce new methods for testing the spontaneous heating in a variety of compact objects. Finally, we will compare our different bounds and discuss the benefits and shortcomings of each one.
The continuous spontaneous localization (CSL) model strives to describe the quantum-to-classical transition from the viewpoint of collapse models. However, its original formulation suffers from a fundamental inconsistency in that it is explicitly energy nonconserving. Fortunately, a dissipative extension to CSL has been recently formulated that solves such an energy-divergence problem. We compare the predictions of the dissipative and nondissipative CSL models when various optomechanical settings are used and contrast such predictions with available experimental data, thus building the corresponding exclusion plots.