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: that space 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, 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 and one-body density matrix (for each given particle type if several are present). The resulting files contain $d$ dimensional arrays, or $d^2$ dimensional density matrices. The keywords associated to these functionalities are prefixed ``ModelMB'' for Model Many Body Schr\"odinger equations.  In the following we show a simple example of 1D Lithium, with 3 electrons and a classical (fixed) nucleus.