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Pinning of Fermionic occupation numbers

Thursday 17th October 2013 - 14:00 to 15:00
INI Seminar Room 1
Co-authors: David Gross (University of Freiburg), Matthias Christandl (ETH Zurich)

The problem of determining and describing the family of 1-particle reduced density operators (1-RDO) arising from N-fermion pure states (via partial 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. Our findings suggest a generalization of the Hartree-Fock approximation.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons