Unexpected Results in the Chiral Limit with Staggered Fermions

A cluster algorithm is constructed and applied to study the chiral limit of the strongly coupled lattice Schwinger model involving staggered fermions. The algorithm is based on a novel loop representation of the model. Finite size scaling of the chiral susceptibility based on data from lattices of size up to $64\times 64$ indicates the absence of long range correlations at strong couplings. Assuming that there is no phase transition at a weaker coupling, the results imply that all mesons acquire a mass at non-zero lattice spacings. Although this does not violate any known physics, it is surprising since typically one expects a single pion to remain massless at non-zero lattice spacings in the staggered fermion formulation.Comment: 6 pages, 6 figures, espcrc2.sty format (Misprint in the caption of Figure 5 corrected

Propositional Dynamic Logic for Hyperproperties

Information security properties of reactive systems like non-interference often require relating different executions of the system to each other and following them simultaneously. Such hyperproperties can also be useful in other contexts, e.g., when analysing properties of distributed systems like linearizability. Since common logics like LTL, CTL, or the modal ?-calculus cannot express hyperproperties, the hyperlogics HyperLTL and HyperCTL^* were developed to cure this defect. However, these logics are not able to express arbitrary ?-regular properties. In this paper, we introduce HyperPDL-?, an adaptation of the Propositional Dynamic Logic of Fischer and Ladner for hyperproperties, in order to remove this limitation. Using an elegant automata-theoretic framework, we show that HyperPDL-? model checking is asymptotically not more expensive than HyperCTL^* model checking, despite its vastly increased expressive power. We further investigate fragments of HyperPDL-? with regard to satisfiability checking

Validation and quantification of cardiac parameters obtained by cine MR imaging in crustaceans

In future oceans, aquatic animals and marine ecosystems will have to cope with combined effects of ongoing warming and CO2 accumulation. This study investigated possible effects of ambient CO2 on the thermal tolerance window of the North Sea edible crab Cancer pagurus. To enhance ecological relevance, the temperature ramp was chosen to mimic daily temperature changes and allow for acclimation effects. Applied temperatures ranged from 12°C to 20°C with 2°C warming steps (within 2 hours). Temperature steps were held for 10 hours including 5 hours acclimation time and 5 h measurement time. Animals were exposed to present day normocapnia (ca. 480 μatm) and CO2 levels projected beyond 2100 (ca. 1400 μatm). Using a multi-parameter approach (measured/calculated parameters: metabolic rate, heart rate, cardiac stroke volume proxy, cardiac output proxy) enabling non-invasive recording of highly resolved and continuous data, it was investigated how aerobic metabolic rate and the cardiovascular system as key components of animal performance are modulated on a daily basis by changes in temperature and ambient CO2. As non-invasive measurements only allowed for detection of relative changes in cardiac stroke volume, an approach for non-invasive quantification using cine magnetic resonance imaging (MRI) is presented. This approach further revealed complex inner structures of the ventricle likely enhancing efficiency of the pumping mechanism. Despite high interindividual variability, exemplary analysis of the heart rate over time could reveal, that increasing amplitudes of rhythmic patterns (representing aerobic metabolism) in response to rising temperatures mostly depended on increases at the maximum level of performance, whereas minimum levels remained stable. Additionally, temperature-dependent changes from low to high frequencies could be observed. Beside these temperature-dependent effects, it could be shown, that CO2-concentrations around 1400 μatm can have light narcotic effects on the heart activity over time of C. pagurus. The diverse responses of the other parameters and no apparent CO2-dependent shifts in the performance response to temperature imply, that projected CO2 levels in the North Sea beyond the year 2100 do not narrow the thermal tolerance window of C. pagurus

Functional Differential Equations for the Free Energy and the Effective Energy in the Broken-Symmetry Phase of phi^4-Theory and Their Recursive Graphical Solution

Extending recent work on QED and the symmetric phase of the euclidean multicomponent scalar \phi^4-theory, we construct the vacuum diagrams of the free energy and the effective energy in the ordered phase of \phi^4-theory. By regarding them as functionals of the free correlation function and the interaction vertices, we graphically solve nonlinear functional differential equations, obtaining loop by loop all connected and one-particle irreducible vacuum diagrams with their proper weights.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/31

A Navigation Logic for Recursive Programs with Dynamic Thread Creation

Dynamic Pushdown Networks (DPNs) are a model for multithreaded programs with recursion and dynamic creation of threads. In this paper, we propose a temporal logic called NTL for reasoning about the call- and return- as well as thread creation behaviour of DPNs. Using tree automata techniques, we investigate the model checking problem for the novel logic and show that its complexity is not higher than that of LTL model checking against pushdown systems despite a more expressive logic and a more powerful system model. The same holds true for the satisfiability problem when compared to the satisfiability problem for a related logic for reasoning about the call- and return-behaviour of pushdown systems. Overall, this novel logic offers a promising approach for the verification of recursive programs with dynamic thread creation

Meson-meson scattering in the massive Schwinger model: a status report

We discuss the possibility of extracting phase shifts from finite volume energies for meson-meson scattering, where the mesons are fermion-antifermion bound states of the massive Schwinger model with SU(2) flavour symmetry. The existence of analytical strong coupling predictions for the mass spectrum and for the scattering phases makes it possible to test the reliability of numerical results