A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

A variable neurodegenerative phenotype with polymerase gamma mutation

mtDNA replication and repair, causes mitochondrial diseases including autosomal dominant progressive external ophthalmoplegia (PEO),1 childhood hepato-encephalopathy (Alpers– Huttenlocher syndrome), adult-onset spinocerebellar ataxia, and sensory nerve degeneration with dysarthria and ophthalmoparesis (SANDO)

Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model

We discuss a representation of the Z(3) Gauge-Higgs lattice field theory at finite density in terms of dual variables, i.e., loops of flux and surfaces. In the dual representation the complex action problem of the conventional formulation is resolved and Monte Carlo simulations at arbitrary chemical potential become possible. A suitable algorithm based on plaquette occupation numbers and link-fluxes is introduced and we analyze the model at zero temperature and finite density both in the weak and strong coupling phases. We show that at zero temperature the model has different first order phase transitions as a function of the chemical potential both for the weak and strong coupling phases. The exploratory study demonstrates that alternative degrees of freedom may successfully be used for Monte Carlo simulations in several systems with gauge and matter fields.Comment: Typos corrected and some statements refined. Final version to appear in Phys. Rev.

Improving Lifelong Learning by Fostering Students' Learning Strategies at University

The foundation of how students usually learn is laid early in their academic lives. However, many or even most students do not primarily rely on those learning strategies that are most favorable from a scientific point of view. To change students' learning behavior when they start their university education, we developed a computer-based adaptive learning environment to train favorable learning strategies and change students' habits using them. This learning environment pursues three main goals: acquiring declarative and conditional knowledge about learning strategies, consolidating that knowledge, and applying these learning strategies in practice. In this report, we describe four experimental studies conducted to optimize this learning environment (n = 336). With those studies, we improved the learning environment with respect to how motivating it is, investigated an efficient way to consolidate knowledge, and explored how to facilitate the formation of effective implementation intentions for applying learning strategies and changing learning habits. Our strategy-training module is implemented in the curriculum for freshman students at the Department of Psychology, University of Freiburg (Germany). Around 120 students take part in our program every year. An open version of this training intervention is freely available to everyone

Possible experimental signature of octupole correlations in the 02+^+_2 states of the actinides

$J^{\pi}$= 0$^+$ states have been investigated in the actinide nucleus ${}^{240}$Pu up to an excitation energy of 3 MeV with a high-resolution (p,t) experiment at $E_{p}$= 24 MeV. To test the recently proposed $J^{\pi}$= 0$^+_2$ double-octupole structure, the phenomenological approach of the spdf-interacting boson model has been chosen. In addition, the total 0$^+$ strength distribution and the $0^+$ strength fragmentation have been compared to the model predictions as well as to the previously studied (p,t) reactions in the actinides. The results suggest that the structure of the 0$^+_2$ states in the actinides might be more complex than the usually discussed pairing isomers. Instead, the octupole degree of freedom might contribute significantly. The signature of two close-lying 0$^+$ states below the 2-quasiparticle energy is presented as a possible manifestation of strong octupole correlations in the structure of the 0$^+_2$ states in the actinides.Comment: 6 pages, 5 figures, published in Phys. Rev. C 88, 041303(R) (2013

Zeta functions of quantum graphs

In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of the star. We then extend the technique to allow any matching conditions at the center for which the Laplace operator is self-adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions. In the process it is convenient to work with new forms for the secular equation of a quantum graph that extend the well known secular equation of the Neumann star graph. In the second half of the article we apply the zeta function to obtain new results for the spectral determinant, vacuum energy and heat kernel coefficients of quantum graphs. These have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature.Comment: 32 pages, typos corrected, references adde

Wootters' distance revisited: a new distinguishability criterium

The notion of distinguishability between quantum states has shown to be fundamental in the frame of quantum information theory. In this paper we present a new distinguishability criterium by using a information theoretic quantity: the Jensen-Shannon divergence (JSD). This quantity has several interesting properties, both from a conceptual and a formal point of view. Previous to define this distinguishability criterium, we review some of the most frequently used distances defined over quantum mechanics' Hilbert space. In this point our main claim is that the JSD can be taken as a unifying distance between quantum states.Comment: 15 pages, 3 figures, changed content, added reference for last sectio