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arXiv:quant-ph/9812040 · Physical Review A

Enhanced diffusion and the continuous spontaneous localization model

Léa Ferreira dos Santos, Carlos O. Escobar

Published Oct 1, 1999• 5 citations
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Abstract

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 ${t}^{3}$ 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.

DOI
10.1103/physreva.60.2712

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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.
After finding analogies between turbulence and the beable interpretation of the spontaneous collapse model of the wave function, we unravel the underlying Lévy dynamics in such model. Using an affine noise in the collapse process, we obtain the intermittency corrections to Richardson’s t 3 law for the turbulent diffusion. PACS: 05.40.Fb, 03.65.Bz, 02.50.Ey Typeset using REVTEX 1 In studying the phenomenon of enhanced diffusion, Shlesinger et al [1] were led to introduce the concept of a Lévy walk as an extension of the more familiar Lévy flight [2]. The basic difference between a Lévy flight and a Lévy walk is that for the latter, although the walker visits all sites visited by the flight, the jumps do not occur instantaneously, but there may be a time delay before the next jump. Shlesinger et al obtained an integral transport equation involving a scaled memory which is nonlocal in space and time. Contrary to the infinite mean square displacement obtained in a Lévy flight, the solution of such transport
Abstract Models of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system increases, providing a well-defined phenomenology in terms of a non-linearly and stochastically modified Schrödinger equation, which can be tested experimentally. The most popular of such models is the continuous spontaneous localization (CSL) model: in its original version, the collapse is driven by a white noise, and more recently, generalizations in terms of colored noises, which are more realistic, have been formulated. We will analyze how current non-interferometric tests bound the model, depending on the spectrum of the noise. We will find that low frequency purely mechanical experiments provide the most stable and strongest bounds. Graphical abstract
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.
Models of dynamical wave function collapse consistently describe the breakdown of the quantum superposition with the growing mass of the system by introducing non-linear and stochastic modifications to the standard Schrödinger dynamics. Among them, Continuous Spontaneous Localization (CSL) was extensively investigated both theoretically and experimentally. Measurable consequences of the collapse phenomenon depend on different combinations of the phenomenological parameters of the model-the strength λ and the correlation length rC-and have led, so far, to the exclusion of regions of the admissible (λ-rC) parameters space. We developed a novel approach to disentangle the λ and rC probability density functions, which discloses a more profound statistical insight.
Continuous Spontaneous Localization (CSL) is one possible explanation for dynamically induced collapse of the wave-function during a quantum measurement. The collapse is mediated by a stochastic non-linear modification of the Schrödinger equation. A consequence of the CSL mechanism is an extremely tiny violation of energy-momentum conservation, which can, in principle, be detected in the laboratory via the random diffusion of a particle induced by the stochastic collapse mechanism. In a paper in 2003, Collett and Pearle investigated the translational CSL diffusion of a sphere, and the rotational CSL diffusion of a disc, and showed that this effect dominates over the ambient environmental noise at low temperatures and extremely low pressures (about ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis and argue that this stringent condition on pressure can be relaxed, and that the CSL effect can be seen at the pressure of about a pico-Torr. A similar analysis is provided for diffusion produced by gravity-induced decoherence, where the effect is typically much weaker than CSL. We also discuss the CSL induced random displacement of a quantum oscillator. Lastly, we propose possible experimental set-ups justifying that CSL diffusion is indeed measurable with the current technology.