Connections and Metrics Respecting Standard Purification

Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.Comment: Latex, 27 page

The Stanley Foundation Bipolar Network: Results of the naturalistic follow-up study after 2.5 years of follow-up in the German centres

The Stanley Foundation Bipolar Network (SFBN) is an international, multisite network investigating the characteristics and course of bipolar disorder. Methods (history, ratings and longitudinal follow-up) are standardized and equally applied in all 7 centres. This article describes demographics and illness characteristics of the first 152 German patients enrolled in them SFBN as well as the results of 2.5 years of follow-up. Patients in Germany were usually enrolled after hospitalisation. More than 72% of the study population suffered from bipolar I disorder and 25% from bipolar 11 disorder. The mean +/- SD age of the study participants was 42.08 +/- 13.5 years, and the mean SD age of onset 24.44 +/- 10.9 years. More than 40% of the sample reported a rapid-cycling course in history, and even more a cycle acceleration overtime. 37% attempted suicide at least once. 36% had an additional Axis I disorder, with alcohol abuse being the most common one, followed by anxiety disorders. During the follow-up period, only 27% remained stable, 56% had a recurrence, 12.8% perceived subsyndromal symptoms despite treatment and regular visits. 27% suffered from a rapid-cycling course during the follow-up period. Recurrences were significantly associated with bipolar I disorder, an additional comorbid Axis I disorder, rapid cycling in history, a higher number of mood stabilizers and the long-term use of typical antipsychotics. Rapid cycling during follow-up was only associated with a rapidcycling course in history, a higher number of mood stabilizers and at least one suicide attempt in history. Copyright (c) 2003 S. Karger AG, Basel

Covariance and Fisher information in quantum mechanics

Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasis that Fisher informations are obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.Comment: LATE

Green-Aware Routing in GMPLS Networks

The increasing amount of traffic in the Internet has been accommodated by the exponential growth of bandwidth provided by the optical networks technologies. However, such a growth has been also accompanied by an increase in the energy consumption and the concomitant green house gases (GHG) emissions. Despite the efforts for improving energy efficiency in silicon technologies and network designs, the large energy consumption still poses challenges for the future development of Internet. In this paper, we propose an extension of the Open Shortest Path First — Traffic Engineering (OSPF-TE) protocol and a green-aware routing and wavelength assignment (RWA) algorithm for minimizing the GHG emissions by routing connection requests through green network elements (NE). The network behavior and the performance of the algorithm are analyzed through simulations under different scenarios, and results show that it is possible to reduce GHGs emissions at the expense of an increase in the path length, and, in some cases, in the blocking probability. The trade-off between emissions and performance is studied. To the authors knowledge, this is the first work that provides a detailed study of a green-aware OSPF protocol

Bures volume of the set of mixed quantum states

We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the boundary of the set M_N and obtain analogous results for the smaller set of all real density matrices. An explicit formula for the Bures-Hall normalization constants is derived for an arbitrary N.Comment: 15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) correcte

Polarized Line Formation in Multi-Dimensional Media.III. Hanle Effect with Partial Frequency Redistribution

In the previous two papers, namely, \citet{anuknn11} and \citet{anuetal11} we solved the polarized radiative transfer (RT) equation in multi-dimensional (multi-D) geometries, with partial frequency redistribution (PRD) as the scattering mechanism. We assumed Rayleigh scattering as the only source of linear polarization ($Q/I, U/I$) in both these papers. In this paper we extend these previous works to include the effect of weak oriented magnetic fields (Hanle effect) on line scattering. We generalize the technique of Stokes vector decomposition in terms of the irreducible spherical tensors $\mathcal{T}^K_Q$, developed in \citet{anuknn11}, to the case of RT with Hanle effect. A fast iterative method of solution (based on the Stabilized Preconditioned Bi-Conjugate-Gradient technique), developed in \citet{anuetal11}, is now generalized to the case of RT in magnetized three-dimensional media. We use the efficient short-characteristics formal solution method for multi-D media, generalized appropriately to the present context. The main results of this paper are the following: (1) A comparison of emergent $(I, Q/I, U/I)$ profiles formed in one-dimensional (1D) media, with the corresponding emergent, spatially averaged profiles formed in multi-D media, shows that in the spatially resolved structures, the assumption of 1D may lead to large errors in linear polarization, especially in the line wings. (2) The multi-D RT in semi-infinite non-magnetic media causes a strong spatial variation of the emergent $(Q/I, U/I)$ profiles, which is more pronounced in the line wings. (3) The presence of a weak magnetic field modifies the spatial variation of the emergent $(Q/I, U/I)$ profiles in the line core, by producing significant changes in their magnitudes.Comment: 31 pages, 14 figures, Submitted to ApJ, Under revie

Ionization by bulk heating of electrons in capacitive radio frequency atmospheric pressure microplasmas

Electron heating and ionization dynamics in capacitively coupled radio frequency (RF) atmospheric pressure microplasmas operated in helium are investigated by Particle in Cell simulations and semi-analytical modeling. A strong heating of electrons and ionization in the plasma bulk due to high bulk electric fields are observed at distinct times within the RF period. Based on the model the electric field is identified to be a drift field caused by a low electrical conductivity due to the high electron-neutral collision frequency at atmospheric pressure. Thus, the ionization is mainly caused by ohmic heating in this "Omega-mode". The phase of strongest bulk electric field and ionization is affected by the driving voltage amplitude. At high amplitudes, the plasma density is high, so that the sheath impedance is comparable to the bulk resistance. Thus, voltage and current are about 45{\deg} out of phase and maximum ionization is observed during sheath expansion with local maxima at the sheath edges. At low driving voltages, the plasma density is low and the discharge becomes more resistive resulting in a smaller phase shift of about 4{\deg}. Thus, maximum ionization occurs later within the RF period with a maximum in the discharge center. Significant analogies to electronegative low pressure macroscopic discharges operated in the Drift-Ambipolar mode are found, where similar mechanisms induced by a high electronegativity instead of a high collision frequency have been identified