Assumptions that imply quantum dynamics is linear

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrodinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of motion for mean values. Expanded Introductio

Canonical Expansion of PT-Symmetric Operators and Perturbation Theory

Let $H$ be any \PT symmetric Schr\"odinger operator of the type $-\hbar^2\Delta+(x_1^2+...+x_d^2)+igW(x_1,...,x_d)$ on $L^2(\R^d)$, where $W$ is any odd homogeneous polynomial and $g\in\R$. It is proved that $\P H$ is self-adjoint and that its eigenvalues coincide (up to a sign) with the singular values of $H$, i.e. the eigenvalues of $\sqrt{H^\ast H}$. Moreover we explicitly construct the canonical expansion of $H$ and determine the singular values $\mu_j$ of $H$ through the Borel summability of their divergent perturbation theory. The singular values yield estimates of the location of the eigenvalues \l_j of $H$ by Weyl's inequalities.Comment: 20 page

Der internistische Check-up

Zusammenfassung: Viele präventive Maßnahmen bei gesunden Erwachsenen werden in zunehmendem Maße durch Evidenz gestützt oder verworfen. Dabei sind v.a. die Beratung bezüglich Tabakabstinenz, indizierte Impfungen und das Screening in Bezug auf Übergewicht, hohen Blutdruck, Hyperlipidämie, Zervixkarzinom, kolorektales Karzinom und Mammakarzinom bewiesenermaßen wichtig und sinnvoll. Nicht empfohlen wird ein Screening für Bronchial-, Pankreas- und Ovarialkarzinom. Ein Screening für Diabetes mellitus beim jüngeren Erwachsenen, Schilddrüsenerkrankungen und Prostatakarzinom wird nicht routinemäßig empfohlen, sollte aber je nach persönlichem Risikoprofil im Sinne eines sog. "Case findings" erwogen werden. Aus ärztlicher Sicht ist es auch wichtig, auf mögliche nicht deklarierte Beweggründe für eine Check-up-Untersuchung einzugehen, um so mögliche "Hidden Agendas" der Konsultationen aufzudecke

28-jähriger Patient mit erfolgreich behandelter dilatativer Kardiomyopathie

Zusammenfassung: Ein 28-jähriger Patient wurde mit dekompensierter Herzinsuffizienz notfallmäßig zugewiesen. In der Vorgeschichte bestand ein hypogonadotroper Hypogonadismus. Echokardiographisch fand sich eine dilatative Kardiomyopathie. Ein erhöhtes Serumferritin und eine Eisenüberladung in der Leberbiopsie ließen eine hereditäre Hämochromatose vermuten. Die kardiale Beteiligung konnte mittels Magnetresonanztomographie nachgewiesen werden. Genetische Abklärungen ergaben eine homozygote Mutation für G320V und bewiesen eine juvenile Hämochromatose. Eine Aderlasstherapie führte innerhalb eines Jahres zur Normalisierung des Eisenstatus und der kardialen Pumpfunktio

Integrating Data on Ethnicity, Geography, and Conflict: The Ethnic Power Relations Dataset Family.

ArticleThis article introduces the new Family of Ethnic Power Relations (EPR) data sets, version 2014, which is the latest in a series of data sets on ethnicity that have stimulated civil war research in the past decade. The EPR Family provides data on ethnic groups’ access to state power, their settlement patterns, links to rebel organizations, transborder ethnic kin relations, and intraethnic cleavages. The new 2014 version does not only extend the data set’s temporal coverage from 2009 to 2013, but it also offers several new features, such as a new measure of regional autonomy that is independent of national-level executive power and a new data set component coding intraethnic identities and cleavages. Moreover, for the first time, detailed documentation of the EPR data is provided through the EPR Atlas. This article presents these novelties in detail and compares the EPR Family 2014 to the most relevant alternative data sets on ethnicity.Swiss National Science FoundationSwiss Agency for Development and Cooperation (SDC

Free Fermionic Heterotic Model Building and Root Systems

We consider an alternative derivation of the GSO Projection in the free fermionic construction of the weakly coupled heterotic string in terms of root systems, as well as the interpretation of the GSO Projection in this picture. We then present an algorithm to systematically and efficiently generate input sets (i.e. basis vectors) in order to study Landscape statistics with minimal computational cost. For example, the improvement at order 6 is approximately 10^{-13} over a traditional brute force approach, and improvement increases with order. We then consider an example of statistics on a relatively simple class of models.Comment: Standard Latex, 12 page

Stable directions for small nonlinear Dirac standing waves

We prove that for a Dirac operator with no resonance at thresholds nor eigenvalue at thresholds the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues close enough, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schr\"{o}dinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page

A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case

This article is concerned with the derivation and the mathematical study of a new mean-field model for the description of interacting electrons in crystals with local defects. We work with a reduced Hartree-Fock model, obtained from the usual Hartree-Fock model by neglecting the exchange term. First, we recall the definition of the self-consistent Fermi sea of the perfect crystal, which is obtained as a minimizer of some periodic problem, as was shown by Catto, Le Bris and Lions. We also prove some of its properties which were not mentioned before. Then, we define and study in details a nonlinear model for the electrons of the crystal in the presence of a defect. We use formal analogies between the Fermi sea of a perturbed crystal and the Dirac sea in Quantum Electrodynamics in the presence of an external electrostatic field. The latter was recently studied by Hainzl, Lewin, S\'er\'e and Solovej, based on ideas from Chaix and Iracane. This enables us to define the ground state of the self-consistent Fermi sea in the presence of a defect. We end the paper by proving that our model is in fact the thermodynamic limit of the so-called supercell model, widely used in numerical simulations.Comment: Final version, to appear in Comm. Math. Phy