Semiclassical stochastic mechanics for the Coulomb potential with applications to modelling dark matter

DOI10.1063/1.4947180zbMath1342.83543OpenAlexW2407402776MaRDI QIDQ2814208

A. D. Neate, Aubrey Truman

Publication date: 20 June 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://cronfa.swan.ac.uk/Record/cronfa27547/Download/0027547-28042016164354.pdf

zbMATH Keywords

singularitiesHamiltonianJacobi fieldsSchrödinger equationdark mattersemiclassical limitCoulomb potentialKepler's lawsquantum mechanical HamiltonianNelson's stochastic mechanicsBohr correspondence limitFreidlin-Wentzell asymptotic seriesgravitating point massNelson diffusion

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Geometry and quantization, symplectic methods (81S10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Space-time singularities, cosmic censorship, etc. (83C75) Celestial mechanics (70F15) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items (1)

A note on the mechanics emerged from systems with a stochastic process of the time variable

Cites Work

• Conservative diffusions
• A stochastic model for the orbits of planets and satellites: An interpretation of Titius-Bode law
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• The Sharma-Parthasarathy stochastic two-body problem
• A stochastic Burgers-Zeldovich model for the formation of planetary ring systems and the satellites of Jupiter and Saturn
• On the divine clockwork: The spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state
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