4,138 research outputs found
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 0 states of the actinides
= 0 states have been investigated in the actinide nucleus
Pu up to an excitation energy of 3 MeV with a high-resolution (p,t)
experiment at = 24 MeV. To test the recently proposed = 0
double-octupole structure, the phenomenological approach of the
spdf-interacting boson model has been chosen. In addition, the total 0
strength distribution and the 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 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 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
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