Astrophysical disks are among the most ubiquitous objects in the universe, and span a staggering range of astronomical scales. Within the broader category of flattened structures, galactic nuclei, black hole accretion disks, protoplanetary nebulae, and proto-satellite disks all share a common feature - they all encircle objects that are much more massive than the disks themselves. The resulting dominance of the central body’s gravity leads to nearly-Keplerian motion that resembles planetary orbits on short (orbital) time-scales, but can exhibit highly non-trivial behaviour over much longer (secular) periods of time, due to the self-gravitation of the disk.
In Batygin (2018), I demonstrated that the long-term inclination evolution of self-gravitating discs can be modeled with the time-dependent Schrödinger equation - a cornerstone of quantum mechanics. Within the context of this formalism, propagation of warps within disks is analogous to the motion of a quantum quasi-particle's wave function, confined within an infinite square well, with boundaries given by the inner and outer edges of the disk. The parallel does not end there - as it turns out, external perturbations upon self-gravitating discs exhibit a mathematical similarity to quantum scattering theory, and by borrowing well-known solutions from quantum mechanics, it is possible to construct an analytic criterion for the gravitational rigidity of a nearly-Keplerian disc under external perturbations.