### Abstract

The Pauli exclusion principle is a constraint on the occupation numbers of fermionic quantum states. Just a few years ago a multitude of further and stronger constraints on these numbers have been found. We explore the physical relevance of those generalized Pauli constraints by studying a physical system of N-fermions in a harmonic trap with harmonic interaction. Intriguingly, for each N we find that the occupation numbers of the ground state are very close to the boundary of the allowed region. This effect of so-called quasi-pinning is physically relevant in the sense that it corresponds to a very specific and simplified structure of the corresponding N-fermions quantum state.

### Related Links

- http://prl.aps.org/abstract/PRL/v110/i4/e040404 - The 3-fermion case, studied by Christian Schilling