Axiom System and Completeness Expression for Quantum Mechanics

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. Using a plausible principle P1, about the role of probability in a physical theory, and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a generalization of P2, a principle P3. It is thus made plausible that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed.Comment: 20 pages, no figure

Figura...or Face? Reflections on Two Sociopragmatic Key Concepts in the Light of a Recent Media Conflict Between Italians and Germans and Its Negotiation in Italian Internet Forums

This study will contrast the notions of figura and face. It reflects two Sociopragmatic Key Concepts in the Light of a Recent Media Conflict between Italians and Germans and its Negotiation in Italian Internet Forums

Localization of strongly correlated electrons as Jahn-Teller polarons in manganites

A realistic modeling of manganites should include the Coulomb repulsion between $e_g$ electrons, the Hund's rule coupling to $t_{2g}$ spins, and Jahn-Teller phonons. Solving such a model by dynamical mean field theory, we report large magnetoresistances and spectra in good agreement with experiments. The physics of the unusual, insulating-like paramagnetic phase is determined by correlated electrons which are-due to strong correlations-easily trapped as Jahn-Teller polarons.Comment: 4 pages, 3 figure

Bayesian Modelling of Inseparable Space-Time Variation in Disease Risk

This paper proposes a unified framework for a Bayesian analysis of incidence or mortality data in space and time. We introduce four different types of prior distributions for space $\times$ time interaction in extension of a model with only main effects. Each type implies a certain degree of prior dependence for the interaction parameters, and corresponds to the product of one of the two spatial with one of the two temporal main effects. The methodology is illustrated by an analysis of Ohio lung cancer data 1968-88 via Markov chain Monte Carlo simulation. We compare the fit and the complexity of several models with different types of interaction by means of quantities related to the posterior deviance. Our results confirm an epidemiological hypothesis about the temporal development of the association between urbanization and risk factors for cancer

Two-Level Rectilinear Steiner Trees

Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$) and a top-level tree $T_{top}$ connecting the trees $T_1, ..., T_k$. The goal is to minimize the total length of all trees. This problem arises naturally in the design of low-power physical implementations of parity functions on a computer chip. For bounded $k$ we present a polynomial time approximation scheme (PTAS) that is based on Arora's PTAS for rectilinear Steiner trees after lifting each partition into an extra dimension. For the general case we propose an algorithm that predetermines a connection point for each $T_i$ and $T_{top}$ ($i=1,...,k$). Then, we apply any approximation algorithm for minimum rectilinear Steiner trees in the plane to compute each $T_i$ and $T_{top}$ independently. This gives us a $2.37$-factor approximation with a running time of $\mathcal{O}(|P|\log|P|)$ suitable for fast practical computations. The approximation factor reduces to $1.63$ by applying Arora's approximation scheme in the plane

Higgs stability-bound and fermionic dark matter

Higgs-portal interactions of fermionic dark matter -- in contrast to fermions coupled via Yukawa interactions -- can have a stabilizing effect on the standard-model Higgs potential. A non-perturbative renormalization-group analysis reveals that, similar to higher-order operators in the Higgs potential itself, the fermionic portal coupling can increase the metastability scale by only about one order of magnitude. Furthermore, this regime of very weakly coupled dark matter is in conflict with relic-density constraints. Conversely, fermionic dark matter with the right relic abundance requires either a low cutoff scale of the effective field theory or a strongly interacting scalar sector. This results in a triviality problem in the scalar sector which persists at the non-perturbative level. The corresponding breakdown of the effective field theory suggests a larger dark sector to be present not too far above the dark-fermion mass-scale.Comment: 12 pages; 3 figure