Matthieu Verstraete edited text section 3 modelMB.tex  over 9 years ago

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There are also numerical constraints on the wave-functions: space must be represented in a homogeneous hyper-cube, eventually allowing for different particle masses by modifying the Kinetic energy operator for the corresponding directions. All of the grid partitioning algorithms intrinsic to octopus carry over to arbitrary dimensions, which allows for immediate parallelization of the calculations of the ground and excited states. The code is compiled with a fixed upper bound for the (total) number of dimensions, and the complexity and size grow exponentially with the number of particles simulated, as expected. Production runs have been executed up to $d=6$ or $7$.   Most of the additional treatment for Many-Body quantities is actually post-processing of the wave-functions. For each state, the determination of the fermionic or bosonic nature by Young tableau symmetrization is followed (if requested) by the calculation and output of the density (for each given particle type if several are present). The keywords associated to these functionalities are prefixed ``ModelMB'' for Model Many-Body Schr\"odinger equations. Octopus can also output the one-body density matrix,where the latter is  provided in terms of its occupation numbers and natural orbitals. The resulting files contain $d$ dimensional arrays, and the derived quantities are saved into a ``modelmb'' sub-folder, in order to distinguish the one-dimensional density from its $N$ dimensional counterpart, which is output in the normal static folder.