Quantum transport equation for systems with rough surfaces and its application to ultracold neutrons in a quantizing gravity field

Escobar, Mauricio; Meyerovich, A. E.

doi:10.1134/s1063776114120036

Cited by 3 publications

(4 citation statements)

References 31 publications

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“…Large amplitude of roughness in this setup could degrade the usability of the results. One of the possible ways to circumvent these difficulties and produce a much more controllable environment would be the use of a radically new design for a rough mirror which we called an Ising mirror [31,33].…”

Section: Discussionmentioning

confidence: 99%

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Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

Escobar

Meyerovich

2014

Advances in High Energy Physics

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We apply our general theory of transport in systems with random rough boundaries to gravitationally quantized ultracold neutrons in rough waveguides as in GRANIT experiments (ILL, Grenoble). We consider waveguides with roughness in both two and one dimensions (2D and 1D). In the biased diffusion approximation the depletion times for the gravitational quantum states can be easily expressed via each other irrespective of the system parameters. The calculation of the exit neutron count reduces to evaluation of a single constant which contains a complicated integral of the correlation function of surface roughness. In the case of 1D roughness (random grating) this constant is calculated analytically for common types of the correlation functions. The results obey simple scaling relations which are slightly different in 1D and 2D. We predict the exit neutron count for the new GRANIT cell.

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Section: Discussionmentioning

confidence: 99%

“…This scaling is obvious. The dependence on the correlation radius is more elusive and we cannot get an analytical expression similar to (33). The reason is the presence of 1/2 in the argument of (0) 2 (40) in the integrand in (36).…”

Section: Waveguides With 2d Roughnessmentioning

confidence: 98%

Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

Escobar

Meyerovich

2014

Advances in High Energy Physics

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“…There are several ways how to suppress fluctuations and make identification of the correlation function easier. One can average the correlation function over several samples and use the averaged values for identification as in, for example, [38,39]. This is done in the last row in Tables 1 and 2.…”

Section: Identification Of the Correlation Functionmentioning

confidence: 99%

“…The 2D results (Table 4) are different because of different dimensionality and smaller linear sizes of our samples. Here as an observable, which is used to compare the results, we use Φ 2 which describes the neutron count in experiments with 2D roughness [38,41]. The generated rough surfaces are emulating the Gaussian roughness with the correlation function (|x|) = exp(−|x| 2 /8) (i.e., = 1, = 2) for which Φ 2 = 2.58 × 10 3 .…”

Section: Surfaces With Any Predetermined Roughness Correlatorsmentioning

confidence: 99%

Rough Mirror as a Quantum State Selector: Analysis and Design

Escobar

Lamy

Meyerovich

et al. 2014

Advances in High Energy Physics

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We report analysis of rough mirrors used as the gravitational state selectors in neutron beam and similar experiments. The key to mirror properties is its roughness correlation function (CF) which is extracted from the precision optical scanning measurements of the surface profile. To identify CF in the presence of fluctuation-driven fat tails, we perform numerical experiments with computer-generated random surfaces with the known CF. These numerical experiments provide a reliable identification procedure which we apply to the actual rough mirror. The extracted CF allows us to make predictions for ongoing GRANIT experiments. We also propose a radically new design for rough mirrors based on Monte Carlo simulations for the 1D Ising model. The implementation of this design provides a controlled environment with predictable scattering properties.

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Quantum Diffusion of Ultra-Cold Neutrons in a Rough Waveguide in a Gravity Field

Escobar¹

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Quantum transport equation for systems with rough surfaces and its application to ultracold neutrons in a quantizing gravity field

Cited by 3 publications

References 31 publications

Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

Rough Mirror as a Quantum State Selector: Analysis and Design

Quantum Diffusion of Ultra-Cold Neutrons in a Rough Waveguide in a Gravity Field

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