The problem of determining and describing the family of 1-particle reduced density operators (1-RDO) arising from N-fermion pure states (viapartial trace) is known as the fermionic quantum marginal problem. We present its solution, a multitude of constraints on the eigenvalues of the 1-RDO, generalizing the Pauli exclusion principle. To explore the relevance of these constraints we study an analytically solvable model of N fermions in a harmonic potential and determine the spectral `trajectory' corresponding to the ground state as function of the fermion-fermion interaction strength.Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasi-pinned). Our findings suggest a generalization of the Hartree-Fock approximation.
see also: http://arxiv.org/abs/1210.5531