Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds
Dita, Petre
arXiv, 0305156 / Harvested from arXiv
Text on arXiv
In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of arbitrary $n$-dimensional operators, operators that may be considered either as Hamiltonians, or density matrices for finite-level quantum systems. It is shown that the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices, each one generated by a complex $n-k$-dimensional unit vector, $k=0,1,...,n-2$. As a byproduct, an alternative and simple parameterization of Stiefel and Grassmann manifolds is obtained.
Publié le : 2003-05-26
Classification:  Quantum Physics,  High Energy Physics - Phenomenology,  High Energy Physics - Theory,  Mathematical Physics 
@article{0305156,
     author = {Dita, Petre},
     title = {Finite-level systems, Hermitian operators, isometries, and a novel
  parameterization of Stiefel and Grassmann manifolds},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0305156}
}

Dita, Petre. Finite-level systems, Hermitian operators, isometries, and a novel
  parameterization of Stiefel and Grassmann manifolds. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0305156/