Schrödinger Evolution of Self-Gravitating Disks

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This paper was recently published in the Monthly Notices of the Royal Astronomical Society.

Batygin 2018, Schrödinger Evolution of Self-Gravitating Disks

An understanding of the long-term evolution of self-gravitating disks ranks among the classic outstanding problems of astrophysics. In this work, we show that the secular inclination dynamics of a geometrically thin quasi-Keplerian disk, 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 quasiparticle's wavefunction, confined in an infinite square well with boundaries given by the radial extent of the disk. We further show that external secular perturbations upon self-gravitating disks exhibit a mathematical similarity to quantum scattering theory. Employing this framework, we derive an analytic criterion for the gravitational rigidity of a nearly-Keplerian disk under external perturbations. Applications of the theory to circumstellar disks and Galactic nuclei are discussed.

I am posting this in here, but I am actually more interested in the implications of looking at this the other way around: namely, from a purely mathematical point of view, what are possible mathematical implications for generalizing the Schrödinger equation based on an unsimplified mathematical model of self-gravitating disks?

 

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I read the paper a few days ago. I was honestly quite surprised to see how much can really be surmised about the qualitative features of planetary disks from recasting the dynamical problem into the form of the Schrödinger equation.