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Schrödinger evolution of self-gravitating discs

Batygin, Konstantin (2018) Schrödinger evolution of self-gravitating discs. Monthly Notices of the Royal Astronomical Society, 475 (4). pp. 5070-5084. ISSN 0035-8711. doi:10.1093/mnras/sty162.

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An understanding of the long-term evolution of self-gravitating discs ranks among the classic outstanding problems of astrophysics. In this work, we show that the secular inclination dynamics of a geometrically thin quasi-Keplerian disc, with a surface density profile that scales as the inverse square-root of the orbital radius, are described by the time-dependent Schrödinger equation. Within the context of this formalism, nodal bending waves correspond to the eigenmodes of a quasi-particle's wavefunction, confined in an infinite square well with boundaries given by the radial extent of the disc. We further show that external secular perturbations upon self-gravitating discs exhibit a mathematical similarity to quantum scattering theory. Employing this framework, we derive an analytic criterion for the gravitational rigidity of a nearly-Keplerian disc under external perturbations. Applications of the theory to circumstellar discs and Galactic nuclei are discussed.

Item Type:Article
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URLURL TypeDescription Paper
Batygin, Konstantin0000-0002-7094-7908
Alternate Title:Schrödinger evolution of self-gravitating disks
Additional Information:© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. Received: 26 June 2017. Revision Received: 30 December 2017. Accepted: 04 January 2018. I am grateful to G. Laughlin, F. Adams, D. Stevenson, A. Morbidelli, C. Spalding, S. Michalakis, A. Kitaev, S. Tremaine, and J. Touma for illuminating discussions. Additionally, I would like to thank the anonymous referee for providing a thorough and insightful report that has led to a considerable improvement of the manuscript, as well as the David and Lucile Packard Foundation for their generous support.
Group:Astronomy Department, Division of Geological and Planetary Sciences
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Subject Keywords:methods: analytical, protoplanetary discs, Galaxy: nucleus
Issue or Number:4
Record Number:CaltechAUTHORS:20180305-110030629
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Official Citation:Konstantin Batygin; Schrödinger evolution of self-gravitating discs, Monthly Notices of the Royal Astronomical Society, Volume 475, Issue 4, 21 April 2018, Pages 5070–5084,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85094
Deposited By: Ruth Sustaita
Deposited On:05 Mar 2018 19:26
Last Modified:15 Nov 2021 20:25

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