arXiv subjects

Hubert Grudzinski

Publications and source records attributed to Hubert Grudzinski.

3 recordsLinked to original sources

arXiv2003

Searching for new conditions for fermion N-representability

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 corresponding necessary conditions for N-representability is obtained for N=3. In this case the new condition is stronger than the known B- and C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N-representable 2-density operator there exists an intrinsic relation between the eigenvalue and the corresponding eigenfunction. keywords: fermion N-representability problem, conditions for N-representability

math-ph↗

arXiv2003

Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator $3P^2_g\wedge I^1\equiv A^3 \sum\limits_{1\leq i < j \leq 3} P^2_g(i,j)A^3$ acting on a 3-particle antisymmetric finite dimensional Hilbert space have been found. Here $P^2_g$ denotes the projection operator onto a 2-particle antisymmetric function $g^2$, while $A^3$ denotes the 3-particle antisymmetrizing operator. keywords: spectral decomposition of operators, fermion 2--body operators

math-ph↗

arXiv1995

The N-representability problem, the pseudo-spectral decomposition of antisymmetric 1-body operators, and collective behaviour

The pseudo--spectral decomposition of an $N$--particle antisymmetric 1--body positive--semidefinite operator that corresponds to the canonical convex decomposition into the extreme elements of the dual cone of the set of fermion $N$--representable $1$--density operators has been derived. An attempt at constucting a mathematical model for collective behaviour of a system of $N$--fermions that originates from the pseudo--spectral decomposition is presented.

quant-ph↗