Open AccessCosmological fluid dynamics in the Schrödinger formalism
Author(s) -
Johnston Rebecca,
Lasenby A. N.,
Hobson M. P.
Publication year - 2010
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2009.16052.x
Subject(s) - physics , formalism (music) , classical mechanics , wave function , boundary value problem , dark matter , quantum , schrödinger equation , homogeneous , piecewise , schrödinger's cat , theoretical physics , statistical physics , mathematical physics , quantum mechanics , mathematical analysis , astrophysics , art , musical , mathematics , visual arts
We investigate the dynamics of a cosmological dark matter fluid in the Schrödinger formulation, seeking to evaluate the approach as a potential tool for theorists. We find simple wave‐mechanical solutions of the equations for the cosmological homogeneous background evolution of the dark matter field, and use them to obtain a piecewise analytic solution for the evolution of a compensated spherical overdensity. We analyse this solution from a ‘quantum mechanical’ viewpoint, and establish the correct boundary conditions satisfied by the wavefunction. Using techniques from multiparticle quantum mechanics, we establish the equations governing the evolution of multiple fluids and then solve them numerically in such a system. Our results establish the viability of the Schrödinger formulation as a genuine alternative to standard methods in certain contexts, and a novel way to model multiple fluids.