Monday, 07/24: Writing a pm-code - AIP

Setting up cosmological ICs 40
The displacement vector S is given by the discrete Fourier transform (e.g.,
Padmanabhan 1993, p.294):
S(q) = α
k∑
max
k x,y,z =−k max
ik c k exp (ik · q) ;
k x,y,z = 2π
N g
l, m, n; l, m, n = 0, ±1, ..., ±N p,1 /2; k 2 = k 2 x + k 2 y + k 2 z ≠ 0.
Here, α is the power spectrum normalization. The summation is over all
possible wavenumbers from the fundamental mode with wavelentgh equal to
the box size to the smallest “Nyquist” wavelength with the wavenumber of
N p,1 /2. The real and imaginary components of the Fourier coefficients,
c k = (a k − ib k )/2 are independent gaussian random numbers with the mean
zero and dispersion σ 2 = P (k)/k 4 :
a k = √ P (k)
Gauss(0, 1)
k 2 , b k = √ P (k)
Gauss(0, 1)
k 2 .
Note that c k should satisfy condition c k = c ∗ −k = (a k − ib k )/2.