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Types of codes

Static and time-dependent codes

There are two main branches of codes:

  • Static codes st-wslda-?d for solving self-consistently static DFT equations
  • Time-dependent codes td-wslda-?d for solving time dependent DFT equations. The td-wslda-?d codes require starting point for the time evolution (i.e \psi(\vec{r},t=0)) which is typically generated by the static codes.

Codes dimensionality

3D codes

The 3D codes do not impose any restriction for form of the wave-functions. The wave-functions are assumed to be:
\psi=\varphi(x,y,z)

2D codes

In 2D codes the wave-functions are assumed to be:
\psi=\varphi(x,y)\frac{1}{\sqrt{L_z}}e^{ik_z z}
where
k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}
For NZ=1 the code solves 2D problem (there is only one mode in z-directions, which reduces to 1). Note however, that 2D problem requires different prescription for coupling constant regularization than the one implemented in w-SLDA toolkit.

1D codes

In 1D codes the wave-functions are assumed to be:
\psi=\varphi(x)\frac{1}{\sqrt{L_y}}e^{ik_y y}\frac{1}{\sqrt{L_z}}e^{ik_z z}
where
k_y = 0, \pm 1 \frac{2\pi}{L_y}, \pm 2 \frac{2\pi}{L_y}, \ldots , +(N_y-1) \frac{2\pi}{L_y}
k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}
For NY=1 and NZ=1 the code solves 1D problem . Note however, that 1D problem requires different prescription for coupling constant regularization than the one implemented in w-SLDA toolkit.