Searching for new conditions for fermion Nrepresentability.pdf

SEARCHING FOR NEW CONDITIONS FOR 3 FERMION N-REPRESENTABILITY 0 0 2 Hubert Grudzi´nski v Department of Physics, Academy of Bydgoszcz, o N 85-072 Bydgoszcz, pl. Weyssenhoffa 11, Poland ( e-mail: hubertg@ab-byd.edu.pl) 6 Jacek Hirsch 1 Institute of Physics, Nicholas Copernicus University, 1 87-100 Toru´n, Poland v 6 (e-mail: jacekh@phys.uni.torun.pl) 2 0 1 1 Abstract 3 0 New elements of the dual cone of the set of fermion N -representable / 2-density operators are proposed. So far, the explicit form of the cor- h p responding necessary conditions for N -representability is obtained for - N = 3. In this case the new condition is stronger than the known B- h and C-conditions for 3-representability. The results provide evidence t a that in the spectral decomposition of the N -representable 2-density m operator there exists an intrinsic relation between the eigenvalue and : the corresponding eigenfunction. v i X keywords: fermion N -representability problem, conditions for N - r representability a 1. Introduction The N-representability problem [1, 5, 13, 18, 19, 23, 25] appears in non- relativistic quantum mechanics of N-fermion systems. The Hamiltonian HN for systems of N-fermions contain only operators