A new framework for numerical simulations of structure formation
  The diversity of structures in the Universe (from the smallest galaxies to
the largest superclusters) has formed under the pull of gravity from the tiny
primordial perturbations that we see imprinted in the cosmic microwave
background. A quantitative description of this process would require
description of motion of zillions of dark matter particles. This impossible
task is usually circumvented by coarse-graining the problem: one either
considers a Newtonian dynamics of "particles" with macroscopically large masses
or approximates the dark matter distribution with a continuous density field.
There is no closed system of equations for the evolution of the matter density
field alone and instead it should still be discretized at each timestep. In
this work we describe a method of solving the full 6-dimensional Vlasov-Poisson
equation via a system of auxiliary Schroedinger-like equations. The complexity
of the problem gets shifted into the choice of the number and shape of the
initial wavefunctions that should only be specified at the beginning of the
computation (we stress that these wavefunctions have nothing to do with quantum
nature of the actual dark matter particles). We discuss different prescriptions
to generate the initial wave functions from the initial conditions and
demonstrate the validity of the technique on two simple test cases. This new
simulation algorithm can in principle be used on an arbitrary distribution
function, enabling the simulation of warm and hot dark matter structure
formation scenarios.
