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Lattice-induced photon scattering in an optical lattice clockFeb 08 2018We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several ten seconds. Rayleigh scattering does not cause significant decoherence of the atomic ... More

Study of the Born-Oppenheimer Approximation for Mass-Scaling of Cold Collision PropertiesJun 15 2007Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a molecular beam. ... More

Absolute frequency measurement of the magnesium intercombination transition $^1S_0 \to ^3P_1$Nov 30 2007We report on a frequency measurement of the $(3s^2)^1S_0\to(3s3p)^3P_1$ clock transition of $^{24}$Mg on a thermal atomic beam. The intercombination transition has been referenced to a portable primary Cs frequency standard with the help of a femtosecond ... More

On the relation between uncertainties of weighted frequency averages and the various types of Allan deviationsApr 02 2015Apr 27 2015The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability of an oscillatory ... More

Wavelength dependent ac-Stark shift of the 1S0 - 3P1 transition at 657 nm in CaJun 04 2004We have measured the ac-Stark shift of the 4s2 1S0 - 4s4p 3P1 line in 40Ca for perturbing laser wavelengths between 780 nm and 1064 nm with a time domain Ramsey-Borde atom interferometer. We found a zero crossing of the shift for the mS = 0 - mP = 0 transition ... More

Long range transport of ultra cold atoms in a far-detuned 1D optical latticeApr 16 2012We present a novel method to transport ultra cold atoms in a focused optical lattice over macroscopic distances of many Rayleigh ranges. With this method ultra cold atoms were transported over 5 cm in 250 ms without significant atom loss or heating. By ... More

High accuracy correction of blackbody radiation shift in an optical lattice clockAug 14 2012Oct 29 2012We have determined the frequency shift that blackbody radiation is inducing on the $5s^2$ $^1$S$_0$ -- $5s5p$ $^3$P$_0$ clock transition in strontium. Previously its uncertainty limited the uncertainty of strontium lattice clocks to $1\times10^{-16}$. ... More

Delivering pulsed and phase stable light to atoms of an optical clockAug 18 2011Feb 10 2012In optical clocks, transitions of ions or neutral atoms are interrogated using pulsed ultra-narrow laser fields. Systematic phase chirps of the laser or changes of the optical path length during the measurement cause a shift of the frequency seen by the ... More

Geodesy and metrology with a transportable optical clockMay 11 2017The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability and uncertainty, are already being used to test physical theories and herald a revision of ... More

8E-17 fractional laser frequency instability with a long room-temperature cavityFeb 09 2015Mar 31 2015We present a laser system based on a 48 cm long optical glass resonator. The large size requires a sophisticated thermal control and optimized mounting design. A self balancing mounting was essential to reliably reach sensitivities to acceleration of ... More

Potassium ground state scattering parameters and Born-Oppenheimer potentials from molecular spectroscopyApr 18 2008We present precision measurements with MHz uncertainty of the energy gap between asymptotic and well bound levels in the electronic ground state X $^1\Sigma_{\mathrm{g}}^+$ of the $^{39}$K$_2$ molecule. The molecules are prepared in a highly collimated ... More

Ultra-stable laser with average fractional frequency drift rate below $5\times10^{-19}/\mathrm{s}$May 07 2014Cryogenic single-crystal optical cavities have the potential to provide highest dimensional stability. We have investigated the long-term performance of an ultra-stable laser system which is stabilized to a single-crystal silicon cavity operated at 124 ... More

Demonstration of a Transportable 1 Hz-Linewidth LaserOct 13 2010May 18 2011We present the setup and test of a transportable clock laser at 698 nm for a strontium lattice clock. A master-slave diode laser system is stabilized to a rigidly mounted optical reference cavity. The setup was transported by truck over 400 km from Braunschweig ... More

Noise and instability of an optical lattice clockJul 17 2015Nov 03 2015We present an analysis of the different types of noise from the detection and interrogation laser in our strontium lattice clock. We develop a noise model showing that in our setup quantum projection noise--limited detection is possible if more than 130~atoms ... More

A compact and efficient strontium oven for laser-cooling experimentsSep 25 2012Here we describe a compact and efficient strontium oven well suited for laser-cooling experiments. Novel design solutions allowed us to produce a collimated strontium atomic beam with a flux of 1.0\times10^13 s^-1 cm^-2 at the oven temperature of 450 ... More

Tackling the blackbody shift in a strontium optical lattice clockSep 10 2010A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87-Sr: firstly, by a measurement of the dc Stark shift of the clock transition ... More

A strontium lattice clock with $3 \times 10^{-17}$ inaccuracy and its frequencyDec 12 2013Aug 15 2014We have measured the absolute frequency of the optical lattice clock based on $^{87}$Sr at PTB with an uncertainty of $3.9\times 10^{-16}$ using two caesium fountain clocks. This is close to the accuracy of today's best realizations of the SI second. ... More

On spatial and temporal multilevel dynamics and scaling effects in epileptic seizuresMar 30 2011Jul 29 2011Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of ... More

Thermal Quantum Fields without Cut-offs in 1+1 Space-time DimensionsMar 26 2004We construct interacting quantum fields in 1+1 dimensional Minkowski space, representing neutral scalar bosons at positive temperature. Our work is based on prior work by Klein and Landau and Hoegh-Krohn

Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear SystemsMar 11 2015In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and discuss further ... More

Differential Characters and Geometric ChainsMar 26 2013Apr 09 2013We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit ... More

Staggered domain wall fermionsSep 16 2016We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared ... More

On the relativistic KMS condition for the P(φ)_2 modelSep 29 2006The relativistic KMS condition introduced by Bros and Buchholz provides a link between quantum statistical mechanics and quantum field theory. We show that for the $P(\phi)_2$ model at positive temperature, the two point function for fields satisfies ... More

Friction force: from mechanics to thermodynamicsNov 17 2009Jul 01 2010We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws ... More

Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger modelFeb 26 2016Jul 05 2016We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, ... More

Thermal Quantum Fields with Spatially Cut-off Interactions in 1+1 Space-time DimensionsJul 25 2003We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Hoegh-Krohn. Generalized path ... More

0.75 atoms improve the clock signal of 10,000 atomsMay 25 2016Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas ... More

Removable presymplectic singularities and the local splitting of Dirac structuresOct 20 2014Oct 27 2015We call a singularity of a presymplectic form $\omega$ removable in its graph if its graph extends to a smooth Dirac structure over the singularity. An example for this is the symplectic form of a magnetic monopole. A criterion for the removability of ... More

MPL - a program for computations with iterated integrals on moduli spaces of curves of genus zeroOct 14 2015We introduce the computer program MPL for computations with homotopy invariant iterated integrals on moduli spaces $\mathcal{M}_{0,n}$ of curves of genus 0 with $n$ ordered marked points. The program is an implementation of the algorithms presented in ... More

Predicting zero reductions in Gröbner basis computationsApr 01 2014Since Buchberger's initial algorithm for computing Gr\"obner bases in 1965 many attempts have been taken to detect zero reductions in advance. Buchberger's Product and Chain criteria may be known the most, especially in the installaton of Gebauer and ... More

Discrete Complex Structure on Surfel SurfacesFeb 12 2008This paper defines a theory of conformal parametrization of digital surfaces made of surfels equipped with a normal vector. The main idea is to locally project each surfel to the tangent plane, therefore deforming its aspect-ratio. It is a generalization ... More

No information or horizon paradoxes for Th. SmithsMay 04 2015'Th'e 'S'tatistical 'm'echanician 'i'n 'th'e 's'treet (our Th. Smiths) must be surprised upon hearing popular versions of some of today's most discussed paradoxes in astronomy and cosmology. In fact, rather standard reminders of the meaning of thermal ... More

Many-body theory of degenerate systems: A simple exampleDec 05 2003The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold degenerate level. The complete hierarchy is derived ... More

Renormalization of QED in an external fieldFeb 08 2002The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these equations are ... More

Quantum field theory of degenerate systemsJul 22 2003To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf algebraic techniques ... More

Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part IIFeb 25 2000In the second part of this series we apply the ``string-inspired'' technique to the calculation of one-loop amplitudes involving both vectors and axialvectors, as well as a general constant electromagnetic background field. The vector-axialvector two-point ... More

Cataclysmic Variables in Globular ClustersDec 05 2011Feb 10 2012Every massive globular cluster (GC) is expected to harbour a significant population of cataclysmic variables (CVs). In this review, I first explain why GC CVs matter astrophysically, how many and what types are theoretically predicted to exist and what ... More

Far-Ultraviolet Surveys of Globular Clusters: Hunting for the Products of Stellar Collisions and Near MissesJul 02 2004Globular clusters are gravitationally bound stellar systems containing on the order of 100,000 stars. Due to the high stellar densities in the cores of these clusters, close encounters and even physical collisions between stars are inevitable. These dynamical ... More

On the Calculation of QED Amplitudes in a Constant FieldJul 08 1998It is explained how first-quantized worldline path integrals can be used as an efficient alternative to Feynman diagrams in the calculation of QED amplitudes and effective actions. The examples include the one-loop photon splitting amplitude, the two-loop ... More

Embedded spheres and 4-manifolds with spin coveringsOct 27 2001A strategy for constructing an embedded sphere in a 4-manifold realizing a given homology class which has been successfully applied in the past is to represent the class as a first step stably by an embedded sphere, i.e. after adding products of 2-spheres, ... More

On the Stability of Contention Resolution Diversity Slotted ALOHAMar 21 2012In this paper a Time Division Multiple Access (TDMA) based Random Access (RA) channel with Successive Interference Cancellation (SIC) is considered for a finite user population and reliable retransmission mechanism on the basis of Contention Resolution ... More

$α$-minimal Banach spacesApr 18 2011A Banach space with a Schauder basis is said to be $\alpha$-minimal for some countable ordinal $\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\alpha$. We prove a dichotomy that characterises ... More

An exact Ramsey principle for block sequencesJul 14 2008We prove an exact, i.e., formulated without $\Delta$-expansions, Ramsey principle for infinite block sequences in vector spaces over countable fields, where the two sides of the dichotomic principle are represented by respectively winning strategies in ... More

Isotropy of Angular Frequencies and Weak Chimeras With Broken SymmetryDec 04 2015Oct 28 2016The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here we generalize the definition weak chimera to a more general class of equivariant dynamical systems by characterizing ... More

A note on the coincidence of the projective and conformal Weyl tensorsJan 23 2013This article examines the coincidence of the projective and conformal Weyl tensors associated to a given connection D. The connection may be a general Weyl connection associated to a conformal class of metrics [g]. The main result for n>3 is that the ... More

On bijections between 231-avoiding permutations and Dyck pathsMar 26 2008Oct 02 2009We construct a bijection between 231-avoiding permutations and Dyck paths that sends the sum of the major index and the inverse major index of a 231-avoiding permutation to the major index of the corresponding Dyck path. Furthermore, we relate this bijection ... More

Perturbative Symmetries on Noncommutative SpacesFeb 12 2004Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is reviewed in ... More

The Reeh-Schlieder property for ground statesJan 24 2000Feb 10 2000Recently it has been shown that the Reeh-Schlieder property w.r.t. thermal equilibrium states is a direct consequence of locality, additivity and the relativistic KMS condition. Here we extend this result to ground states.

Cluster Estimates for Modular StructuresApr 02 1998Apr 07 1999The basic ingredients of Tomita-Takesaki modular theory are used to establish cluster estimates. Applications to thermal quantum field theory are discussed.

Magnetoelectric bistabilities in ferromagnetic resonant tunneling structuresJul 28 2008The conditions for the occurrence of pronounced magnetoelectric bistabilities in the resonant tunneling through a ferromagnetic quantum well are theoretically investigated. The bistability appears due to the mutual feedback of the carriers Coulomb interaction ... More

The p-torsion subgroup scheme of an elliptic curveApr 08 2009Jul 12 2011Let $k$ be a field of positive characteristic $p$. Question: Does every twisted form of $\mu_p$ over $k$ occur as subgroup scheme of an elliptic curve over $k$? We show that this is true for most finite fields, for local fields and for fields of characteristic ... More

Quickly proving the Andrásfai-Erdős-Sós-TheoremDec 11 2012Mar 20 2016Given an integer $r\gs 2$, an important theorem first proved by B. Andr\'asfai, P. Erd\H{o}s, and V. T. S\'os states that any $K_{r+1}$--free graph on $n$ vertices whose minimum degree is greater than $(3r-4)n/(3r-1)$ is $r$--colourable, and determines ... More

Ricci curvature bounds for warped productsSep 06 2012Nov 09 2013We prove generalized lower Ricci curvature bounds for warped products over complete Finsler manifolds. On the one hand our result covers a theorem of Bacher and Sturm concerning euclidean and spherical cones. On the other hand it can be seen in analogy ... More

Obata's rigidity theorem for metric measure spacesOct 20 2014Apr 13 2015We prove Obata's rigidity theorem for metric measure spaces that satisfy a Riemannian curvature-dimension condition. Additionally, we show that a lower bound $K$ for the generalized Hessian of a sufficiently regular function $u$ holds if and only if $u$ ... More

Nominal Unification RevisitedDec 22 2010Nominal unification calculates substitutions that make terms involving binders equal modulo alpha-equivalence. Although nominal unification can be seen as equivalent to Miller's higher-order pattern unification, it has properties, such as the use of first-order ... More

Orthogonal bundles over curves in characteristic twoNov 11 2008Dec 09 2008Let X be a smooth projective curve of genus g \geq 2 defined over a field of characteristic two. We give examples of stable orthogonal bundles with unstable underlying vector bundles and use them to give counterexamples to Behrend's conjecture on the ... More

Evaluations of some determinants of matrices related to the Pascal triangleNov 30 2001We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence $a_{i,j}=a_{i-1,j}+a_{i,j-1}$, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Th\'eorie ... More

Localization and Semibounded Energy - A Weak Unique Continuation TheoremOct 15 1999Let D be a self-adjoint differential operator of Dirac type acting on sections in a vector bundle over a closed Riemannian manifold M. Let H be a closed D-invariant subspace of the Hilbert space of square integrable sections. Suppose D restricted to H ... More

On a sequence involving the prime numbersApr 17 2015In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

Discrete Riemann surfaces, linear and non-linearFeb 11 20083 pages presentation of the theory of discrete conformal parameterization using circle patterns or its linearized theory. Principal results and ideas.

Auxiliary matrices on both sides of the equatorAug 12 2004Aug 17 2004The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity ... More

Lie algebraic structures in integrable models, affine Toda field theoryAug 25 2000Sep 01 2000The most prominent class of integrable quantum field theories in 1+1 dimensions is affine Toda theory. Distinguished by a rich underlying Lie algebraic structure these models have in recent years attracted much attention not only as test laboratories ... More

A Q-operator for the quantum transfer matrixOct 12 2006Oct 24 2006Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the finite temperature ... More

The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phaseOct 03 2014Oct 02 2015We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well as powers of ... More

Exact asymptotics of the freezing transition of a logarithmically correlated random energy modelMay 12 2011Aug 26 2011We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model ... More

Primitive cohomology and the tube mappingNov 26 2007Feb 21 2009Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain "tube classes," constructed from the monodromy of the family of smooth hyperplane sections on X. The proof makes use ... More

LHC Phenomenology of the Three-Site Higgsless ModelNov 08 2010We investigate the potential of the LHC for discovering the heavy vector and fermion resonances present in the Three-Site Higgsless Model. To this end, the model was implemented into the WHIZARD parton-level Monte Carlo eventgenerator. The results of ... More

On quasi-normal modes, area quantization and Bohr correspondence principleMar 18 2015Mar 30 2015In Int. Journ. Mod. Phys. D 14, 181 (2005), the author Khriplovich verbatim claims that "the correspondence principle does not dictate any relation between the asymptotics of quasinormal modes and the spectrum of quantized black holes" and that "this ... More

Bohr-like black holesMar 11 2015The idea that black holes (BHs) result in highly excited states representing both the "hydrogen atom" and the "quasi-thermal emission" in quantum gravity is today an intuitive but general conviction. In this paper it will be shown that such an intuitive ... More

Gravitational Waves Astronomy: a cornerstone for gravitational theoriesJun 28 2010Realizing a gravitational wave (GW) astronomy in next years is a great challenge for the scientific community. By giving a significant amount of new information, GWs will be a cornerstone for a better understanding of gravitational physics. In this paper ... More

An oscillating Universe from the linearized R^{2} theory of gravityFeb 18 2008Feb 19 2008An oscillating Universe which arises from the linearized R^{2} theory of gravity is discussed, showing that some observative evidences like the cosmological redshift and the Hubble law are in agreement with the model. In this context Dark Energy is seen ... More

Massive gravitational waves from the R^2 theory of gravity: production and response of interferometersNov 30 2007We show that from the R^{2} high order gravity theory it is possible to produce, in the linearized approch, particles which can be seen like massive modes of gravitational waves (GWs). The presence of the mass generates a longitudinal force in addition ... More

The Virgo - MiniGRAIL cross correlation for the detection of scalar gravitational wavesJun 26 2007Jul 05 2007After a review of the frequency - dependent angular pattern of interferometers in the TT gauge for scalar gravitational waves (SGWs), which has been recently analysed by Capozziello and Corda, in this letter the result is used to study the cross correlation ... More

Extension of the frequency-range of interferometers for the ''magnetic'' components of gravitational waves?Oct 31 2006Mar 26 2007Recently, with an enlighting treatment, Baskaran and Grishchuk have shown the presence and importance of the so-called ``magnetic'' components of gravitational waves (GWs), which have to be taken into account in the context of the total response functions ... More

Quasi-normal modes: the "electrons" of black holes as "gravitational atoms"? Implications for the black hole information puzzleFeb 26 2015Mar 31 2015Some recent important results on black hole (BH) quantum physics concerning the BH effective state and the natural correspondence between Hawking radiation and BH quasi-normal modes (QNMs) are reviewed, clarified and refined. Such a correspondence permits ... More

Quantum transitions of minimum energy for Hawking quanta in highly excited black holes: problems for loop quantum gravity?Dec 03 2012Dec 12 2013By analysing some recent results by Yoon, which arise from loop quantum gravity and from the assumption of the locality of photon emission in a black hole, we argue that they are not consistent with our recent semi-classical results for highly excited ... More

Effective temperature, Hawking radiation and quasinormal modesMay 17 2012Parikh and Wilczek have shown that Hawking radiation's spectrum cannot be strictly thermal. Such a non-strictly thermal character implies that the spectrum is also not strictly continuous and thus generates a natural correspondence between Hawking radiation ... More

General relativity and OPERA ExperimentJan 21 2012Nov 08 2012In his paper "A very simple solution to the OPERA neutrino velocity problem" the author J. Manuel Garcia-Islas claims to have very easily solved and explained within the general theory of relativity that OPERA's neutrinos are not traveling faster than ... More

A clarification on a common misconception about interferometric detectors of gravitational wavesMar 24 2011The aims of this letter are two. First, to show the angular gauge-invariance on the response of interferometers to gravitational waves (GWs). In this process, after resuming for completeness results on the Transverse-Traceless (TT) gauge, where, in general, ... More

Presentation of the Second Big Challenge Symposium - The Big Challenge of Cosmological Understanding: Gravitation, Dark Matter and Dark Energy. Towards New ScenariosJul 23 2010This Symposium is devoted to the Memory of Lev Kofman, June-17-1957-November-12-2009. The accelerated expansion of the Universe, which is today observed, shows that cosmological dynamics is dominated by the so-called Dark Energy field which provides a ... More

Will gravitational waves confirm Einstein's General Relativity?Jul 13 2009Jul 21 2009Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this proceeding paper ... More

Consistent Dyson summation of Higgs propagators in nonlinear parameterizations revisitedJul 05 2004Dec 10 2004As we demonstrate in a process independent way, in a nonlinear parameterization of the scalar sector of the standard model the Dyson summation of the Higgs self energy can be performed without violating the Ward Identities. This implies also the Goldstone ... More

Higgsless fermion masses and unitarityFeb 11 2004Apr 20 2004We discuss the consistency of fermion mass generation by boundary conditions and brane localized terms in higher dimensional Higgsless models of gauge symmetry breaking. The sum rules imposed by tree-level unitarity and Ward Identities are applied to ... More

Twistor-inspired construction of massive quark amplitudesSep 09 2008Oct 30 2008The analog of the Cachazo-Svrvcek-Witten rules for scattering amplitudes with massive quarks is derived following an approach previously employed for amplitudes with massive scalars. A prescription for the external wave-functions is given that leads to ... More

From Tree Unitarity to Top Quark Physics in 5D Higgsless ModelsSep 26 2005In five dimensional models of Higgsless electroweak symmetry breaking, tree level unitarity in gauge boson scattering is restored by the exchange of gauge boson Kaluza-Klein modes instead of a Higgs boson. Unitarity of scattering amplitudes involving ... More

Bornological quantum groupsNov 08 2005We introduce and study the concept of a bornological quantum group. This generalizes the theory of algebraic quantum groups in the sense of van Daele from the algebraic setting to the framework of bornological vector spaces. Working with bornological ... More

Bayesian photometric redshifts with empirical training setsApr 22 2009We combine in a single framework the two complementary benefits of chi^2-template fits and empirical training sets used e.g. in neural nets: chi^2 is more reliable when its probability density functions (PDFs) are inspected for multiple peaks, while empirical ... More

The congruence of Wolstenholme and generalized binomial coefficients related to Lucas sequencesSep 30 2014Using generalized binomial coefficients with respect to fundamental Lucas sequences we establish congruences that generalize the classical congruence of Wolstenholme and other related stronger congruences.

Theory status of four-fermion production at e-e+ collidersDec 17 2015The status of predictions for four-fermion production at e-e+ colliders is reviewed with an emphasis on the developments after the LEP2 era and an outlook to the challenges posed by the precision program at future colliders.

Hadronic fluctuations and correlations at nonzero chemical potentialOct 22 2009We present a lattice study of fluctuations and correlations among the conserved charges baryon number and strangeness in (2+1)-flavor QCD. The lattice calculations are based on a Taylor expansion of the pressure. Results are presented at zero and nonzero ... More

Rank four vector bundles without theta divisor over a curve of genus twoApr 18 2008We show that the locus of stable rank four vector bundles without theta divisor over a smooth projective curve of genus two is in canonical bijection with the set of theta-characteristics. We give several descriptions of these bundles and compute the ... More

Algebraic quantum theoryApr 08 2004The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on ... More

When is the underlying space of an orbifold a topological manifold?Jul 18 2013We answer the question posed by Davis: "When is the underlying space of an orbifold a topological manifold". It amounts to the classification of finite groups acting linearly on a Euclidean vector space such that the quotient space is homeomorphic to ... More

Warning signs for wave speed transitions of noisy Fisher-KPP invasion frontsDec 03 2012Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The approach is based ... More

Normal Hyperbolicity and Unbounded Critical ManifoldsApr 04 2012Aug 01 2013This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. In particular, this paper answers an open question posed by Guckenheimer and Scheper [SIAM J. Appl. Dyn. Syst. 10-1 (2011), pp. 92-128] ... More

Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoidsJun 17 2011Jan 09 2012Numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory. Continuation techniques have been employed in all branches of the natural sciences as well as in engineering ... More

Introduction to Potential Theory via ApplicationsApr 29 2008We introduce the basic concepts related to subharmonic functions and potentials, mainly for the case of the complex plane and prove the Riesz decomposition theorem. Beyond the elementary facts of the theory we deviate slightly from the usual path of exposition ... More

The Curse of InstabilityMay 16 2015High-dimensional computational challenges are frequently explained via the curse of dimensionality, i.e., increasing the number of dimensions leads to exponentially growing computational complexity. In this commentary, we argue that thinking on a different ... More

Scaling of Saddle-Node Bifurcations: Degeneracies and Rapid Quantitative ChangesJul 09 2008Jan 27 2012The scaling of the time delay near a "bottleneck" of a generic saddle-node bifurcation is well-known to be given by an inverse square-root law. We extend the analysis to several non-generic cases for smooth vector fields. We proceed to investigate $C^0$ ... More

Equivariant smoothing of piecewise linear manifoldsJul 09 2015We prove that every piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly. This solves a challenge posed by ... More