Anderson localization in dimension 2 and dimension 3

This section describes scripts to solve the Schroedinger equation for the 2D and 3D Anderson model, using various techniques, already used for the 1D Anderson model:

1. Diagonalization of the Hamitonian in a square (or cube) of size L, with periodic boundary conditions.
2. Calculation of the transmission (i.e. total conductance) of a long bar of section M and length L>>M, using the transfer matrix method.
3. Numerical integration of the time-dependent Schroedinger equation in a square (or cube) of size L, with periodic boundary conditions, starting from a wavepacket localized near the origin. Monitoring the squared extension of the wavepacket vs. time gives information on the localization.

Using these scripts, you will be able to observe that Anderson localization is the generic scenario in 2d systems, while, for 3d systems, there is a transition between localized states at low energy (or strong disorder) and delocalized (or diffusive) states at high energy (or weak disorder).