2008/05/09 by Richard Durran, Andrew Neate, Aubrey Truman +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Diffusion #Diffusion and Search Dynamics #Diffusion process #Ellipse #Elliptic operator #Generator (circuit theory) #Invariant (physics) #Invariant measure #Limit (mathematics) #Limiting #Quantum chaos and dynamical systems #Spectral gap #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/1.2988715
30 pages, 5 figures, submitted to J. Math. Phys
arxiv created 2008/05/09 · openalex publication_date 2008/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.