Time propagation of a 2d wavepacket

Localization can be studied by propagating in time an initially well localized wavepacket (with energy approximately 0) and observe how it spreads in time. The propagation is here performed using an expansion of the initial state on the eigenbasis (computed by exact diagonalization).

time_propagation_anderson_model_2d.py L W nr t_max nsteps

L: system size
W: disorder strength
nr: number of disorder realizations
t_max: propagate from time 0 to t_max
nsteps: number of intermediate times where the squared displacement is computed

time_propagation_anderson_model_2d.py 50 3.0 1 10. 50

Look at "squared_displacement.dat". Observe that the dynamics is approximately diffusive at short time. Estimate the diffusion coefficient.

time_propagation_anderson_model_2d.py 50 7.0 1 500. 100

Look at "squared_displacement.dat". Observe that the dynamics is approximately diffusive at short time, then slows down until localization sets in. Observe that it takes a logn time to fully localize. Check that the system is (almost) sufficiently large by running L=60 intead of 50.

N.B.: There is an additional script view_density.py to visualize as a color plot a 2d spatial density.

 __________________________________________________________________________

Warning: For some stupid reason, the CMS of this Web site refuses files with the .py extension. Thus, you have to manually rename the file, changing the final _py to .py