Many-atom systems partitioning approach

To consider next the partitioning approach for many-atom systems, we start again with the full density operator f(t), describing both electrons and nuclei. We describe a procedure useful in a first principles dynamics where the nuclear motions are described in an eikonal approximation with Q = Q(t), so that the electronic part of the problem involves the calculation of an electronic density operator r[Q(f), Q t), f] = pei t). This satisfies an electronic L-vN equation... 

The OOA, also known as Kugel-Khomskii approach, is based on the partitioning of a coupled electron-phonon system into an electron spin-orbital system and crystal lattice vibrations. Correspondingly, Hilbert space of vibronic wave functions is partitioned into two subspaces, spin-orbital electron states and crystal-lattice phonon states. A similar partitioning procedure has been applied in many areas of atomic, molecular, and nuclear physics with widespread success. It s most important advantage is the limited (finite) manifold of orbital and spin electron states in which the effective Hamiltonian operates. For the complex problem of cooperative JT effect, this partitioning simplifies its solution a lot. 

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