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Journal of Mathematical Physics : On the divine clockwork: The spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state

By Richard Durran, Andrew Neate, Aubrey Truman, and Feng-Yu Wang

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Book Id: WPLBN0002169533
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 8 October 2008

Title: Journal of Mathematical Physics : On the divine clockwork: The spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state  
Author: Richard Durran, Andrew Neate, Aubrey Truman, and Feng-Yu Wang
Volume: Issue : October 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Journal of Mathematical Physics Collection
Historic
Publication Date:
Publisher: American Institute of Physics

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Andrew Neate, Aubrey Truman, And Feng-Yu Wan, R. D. (n.d.). Journal of Mathematical Physics : On the divine clockwork: The spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state. Retrieved from http://worldlibrary.in/


Description
Description: The correspondence limit of the atomic elliptic state in three dimensions is discussed in terms of Nelson’s stochastic mechanics. In previous work we have shown that this approach leads to a limiting Nelson diffusion, and here we discuss in detail the invariant measure for this process and show that it is concentrated on the Kepler ellipse in the plane z = 0. We then show that the limiting Nelson diffusion generator has a spectral gap; thereby proving that in the infinite time limit the density for the limiting Nelson diffusion will converge to its invariant measure. We also include a summary of the Cheeger and Poincaré inequalities, both of which are used in our proof of the existence of the spectral gap.

 

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