We consider two non-interacting systems embedded in a heat bath. If they remain dynamically independent, physical inconsistencies are avoided only if the single-system reduced dynamics is completely positive also beyond the weak-coupling limit.

We consider the reduced density matrix $\rho_{A}^{(m)}$ of a bipartite system $AB$ dimensionality $mn$ in Gaussian ensemble random, complex pure states composite system. For given $m$ subsystem $A$, eigenvalues $\lambda_{1}^{(m)},\ldots, \lambda_{m}^{(m)}$ are correlated random variables because their sum equals unity. The following quantities known, among others: joint probability function (PD...

We investigate here how some results of Hanzon and Ober [6] can be used to obtain reduced order controllers. The idea is to apply the principle of Nehari extension, which generates optimally robust stabilizing controllers, to functions which have multiple maximal singular values. It is well known that in this case the controller has a drop in degree. Using the parametrization of [6], we obtain ...