The standard picture of the Coulomb logarithm in the ideal plasma is controversial, the arguments for the lower cut off need revision. The two cases of far subthermal and of far superthermal electron drift motions are accessible to a rigorous analyti
cal treatment. We show that the lower cut off $b_{min}$ is a function of symmetry and shape of the shielding cloud, it is not universal. In the subthermal case shielding is spherical and $b_{min}$ is to be identified with the de Broglie wavelength; at superthermal drift the shielding cloud exhibits cylindrical (axial) symmetry and $b_{min}$ is the classical parameter of perpendicular deflection. In both situations the cut offs are determined by the electron-ion encounters at large collision parameters. This is in net contrast to the governing standard meaning that attributes $b_{min}$ to the Coulomb singularity at vanishing collision parameters $b$ and, consequently, assigns it universal validity. The origin of the contradictions in the traditional picture is analyzed.
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics
is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically low dimens
ional attractor space. This space is determined completely by the unitary operations involved and it is independent of the probabilities with which these unitary operations are applied. Based on this general feature analytical results are presented for the asymptotic dynamics of arbitrarily large cyclic qubit networks whose nodes are coupled by randomly applied controlled-NOT operations.
We present a detailed investigation of minimum detection efficiencies, below which locality cannot be violated by any quantum system of any dimension in bipartite Bell experiments. Lower bounds on these minimum detection efficiencies are determined w
ith the help of linear programming techniques. Our approach is based on the observation that any possible bipartite quantum correlation originating from a quantum state in an arbitrary dimensional Hilbert space is sandwiched between two probability polytopes, namely the local (Bell) polytope and a corresponding nonlocal no-signaling polytope. Numerical results are presented demonstrating the dependence of these lower bounds on the numbers of inputs and outputs of the bipartite physical system.
