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First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-formApr 04 2009We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant algebroid structures ... More

Quantization and the Issue of Time for Various Two-Dimensional Models of GravityAug 31 1993It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are ... More

Leibniz-Yang-Mills Gauge Theories and the 2-Higgs MechanismMar 18 2019Apr 08 2019A quadratic Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ],\kappa)$ gives rise to a canonical Yang-Mills type functional $S$ over every space-time manifold. The gauge fields consist of 1-forms $A$ taking values in $\mathbb{V}$ and 2-forms $B$ with values ... More

General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroidsJul 24 2014Jul 28 2014Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be ... More

Classical and Quantum Gravity in 1+1 Dimensions, Part II: The Universal CoveringsNov 30 1995Apr 26 1996A set of simple rules for constructing the maximal (e.g. analytic) extensions for any metric with a Killing field in an (effectively) two-dimensional spacetime is formulated. The application of these rules is extremely straightforward, as is demonstrated ... More

Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometriesApr 11 2019Consider an anchored bundle $(E,\rho)$, i.e. a vector bundle $E\to M$ equipped with a bundle map $\rho \colon E \to TM$ covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle ... More

Using EEG, SPECT, and Multivariate Resampling Methods to Differentiate Between Alzheimer's and other Cognitive ImpairmentsJun 29 2016The incidence of Alzheimer's disease (AD) and other forms of dementia is increasing in most western countries. For a precise and early diagnosis, several examination modalities exist, among them single-photon emission computed tomography (SPECT) and the ... More

Polarimetric Neutron Tomography of Magnetic Fields: Uniqueness of Solution and ReconstructionMar 25 2019We consider the problem of determination of a magnetic field from three dimensional polarimetric neutron tomography data. We see that this is an example of a non-Abelian ray transform and that the problem has a globally unique solution for smooth magnetic ... More

Polarimetric Neutron Tomography of Magnetic Fields: Uniqueness of Solution and ReconstructionMar 25 2019Mar 27 2019We consider the problem of determination of a magnetic field from three dimensional polarimetric neutron tomography data. We see that this is an example of a non-Abelian ray transform and that the problem has a globally unique solution for smooth magnetic ... More

Comment on Gravity and the Poincare GroupFeb 11 1993Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the above example ... More

Gravity from Lie algebroid morphismsOct 17 2003Inspired by the Poisson Sigma Model and its relation to 2d gravity, we consider models governing morphisms from TSigma to any Lie algebroid E, where Sigma is regarded as d-dimensional spacetime manifold. We address the question of minimal conditions to ... More

Dirac Quantization Gravity-Yang-Mills Systems in 1+1 DimensionsMar 21 1994In two dimensions a large class of gravitational systems including, e.g., $R^2$-gravity can be quantized exactly also when coupled dynamically to a Yang-Mills theory. Some previous considerations on the quantization of pure gravity theories are improved ... More

On the Consistency of the Deterministic Local Volatility Function Model ('implied tree')Jan 10 2000We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most general context ... More

Poisson Structure Induced Field Theories and Models of 1+1 Dimensional GravityNov 28 2000PhD thesis TU-Vienna, May 1994. Table of Contents: 1. Introduction, 2. Poisson Structure Induced Two Dimensional Field Theories, 3. Models of Gravity in 1+1 Dimensions

Achromatic Non-Interferometric Single Grating Neutron Phase ImagingMar 23 2019We demonstrate a simple single grating beam modulation technique, which enables the use of a highly intense neutron beam for phase imaging and thus spatially resolved structural correlation measurements in full analogy to quantum interference based methods. ... More

Gravity in Two Spacetime DimensionsNov 27 2000In this habilitation thesis we provide an introduction to gravitational models in two spacetime dimensions. Focus is put on exactly solvable models. We begin by introducing and motivating different possible gravitational actions, including those of generalized ... More

All Symmetries of Non-Einsteinian Gravity in $d =2$Jul 01 1992Nov 24 1992The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the Hamiltonian gauge ... More

Improvements for Vachaspati-Vilenkin-type Algorithms for Cosmic String and Disclination FormationAug 15 1996Aug 16 1996We derive various consistency requirements for Vachaspati-Vilenkin type Monte-Carlo simulations of cosmic string formation or disclination formation in liquid crystals. We argue for the use of a tetrakaidekahedral lattice in such simulations. We also ... More

Leibniz-Yang-Mills Gauge TheoriesMar 18 2019A quadratic Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ],\kappa)$ gives rise to a canonical Yang-Mills type functional $S$ over every space-time manifold. If the Leibniz bracket is antisymmetric, the quadratic Leibniz algebra reduces to a quadratic Lie ... More

Target-Superspace in 2d Dilatonic SupergravityJun 29 1999The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson Sigma Model, where the target space and its Poisson bracket are graded. The target space consists of a 1+1 superspace and the dilaton, which is the ... More

2d quantum dilaton gravity as/versus finite dimensional quantum mechanical systemsFeb 18 1997I present the ``Chern--Simons'' formulation of generalized 2d dilaton gravity, summarize its Hamiltonian quantization (reduced phase space and Dirac quantization) and briefly discuss the statistical mechanical entropy of 2d black holes. Focus is put on ... More

Non-abelian Gerbes and Enhanced Leibniz AlgebrasJun 30 2016We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only such as higher ... More

Algebroid Yang-Mills TheoriesJun 23 2004Nov 11 2004A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that ... More

Laue three dimensional neutron diffractionFeb 08 2019This article presents a measurement technique and data analysis tool to perform 3D grain distribution mapping and indexing of oligocrystalline samples using neutrons: Laue three-dimensional neutron diffraction (Laue3DND). The approach builds on forward ... More

Quantum dynamics in transverse-field Ising models from classical networksJul 20 2017Jan 23 2018The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field ... More

Poisson Geometry in Constrained SystemsDec 10 2001Feb 20 2002Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson manifolds associated ... More

Euclidian 2D Gravity with TorsionJul 03 1993Closing a gap in the literature on the subject, the local solutions of 2D-gravity with torsion are given for Euclidian signature. For the topology of a cylinder the system is quantized.

Gauging without Initial SymmetryMar 31 2014Apr 10 2014The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional Lie(G)-valued ... More

Improved Causal Discovery from Longitudinal Data Using a Mixture of DAGsJan 28 2019Many causal processes in biomedicine contain cycles and evolve. However, most causal discovery algorithms assume that the underlying causal process follows a single directed acyclic graph (DAG) that does not change over time. The algorithms can therefore ... More

Lie algebroids, gauge theories, and compatible geometrical structuresMar 14 2016Apr 12 2019The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular ... More

Discretisation of stochastic control problems for continuous time dynamics with delayFeb 17 2006As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow for delay in ... More

Diffeomorphisms Versus Non Abelian Gauge Transformations: An Example of 1+1 Dimensional GravityJan 21 1994We investigate the phase space of a typical model of 1+1 dimensional gravity (Jackiw-Teitelboim model with cylindrical topology) using its reformulation as a non abelian gauge theory based on the sl(2,R) algebra. Modifying the conventional approach we ... More

Poisson-Sigma-Models: A Generalization of 2-D Gravity Yang-Mills-SystemsNov 22 1994A new class of two dimensional integrable field theories, based on the mathematical notion of Poisson manifolds, and containing gravity-Yang-Mills systems as well as the G/G gauged Wess-Zumino Witten-model, are presented. The local solutions of the classical ... More

Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the CylinderJun 16 1994Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for the quantization ... More

Curving Yang-Mills-Higgs Gauge TheoriesOct 26 2015Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like ... More

Enhanced Leibniz Algebras: Structure Theorem and Induced Lie 2-AlgebraJan 04 2019An enhanced Leibniz algebra is an algebraic struture that arises in the context of particular higher gauge theories describing self-interacting gerbes. It consists of a Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ])$, a bilinear form on $\mathbb{V}$ with ... More

Three Dimensional Polarimetric Neutron Tomography of Magnetic FieldsApr 17 2017Feb 02 2018Through the use of Time-of-Flight Three Dimensional Polarimetric Neutron Tomography (ToF 3DPNT) we have for the first time successfully demonstrated a technique capable of measuring and reconstructing three dimensional magnetic field strengths and directions ... More

Poisson Structure Induced (Topological) Field TheoriesMay 17 1994A class of two dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang-Mills systems, is presented. Locally, the solutions of the classical equations of motion are given. A general scheme for the ... More

Dirac Sigma Models from GaugingNov 27 2013The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can ... More

Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary TopologyJul 30 1996Aug 13 1997All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is parametrized explicitly ... More

WZW-Poisson manifoldsApr 19 2001Oct 02 2001We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson Sigma model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The ... More

Universality and Critical Phenomena in String Defect StatisticsAug 15 1996The idea of biased symmetries to avoid or alleviate cosmological problems caused by the appearance of some topological defects is familiar in the context of domain walls, where the defect statistics lend themselves naturally to a percolation theory description, ... More

Statistical Properties of StringsOct 13 1994We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global $U(1)$ cosmic strings, or equivalently vortices in superfluid $^4$He. We use a new method which avoids the specification of boundary conditions ... More

Generalizing Geometry - Algebroids and Sigma ModelsApr 05 2010In this contribution we review some of the interplay between sigma models in theoretical physics and novel geometrical structures such as Lie (n-)algebroids. The first part of the article contains the mathematical background, the definition of various ... More

Integration of quadratic Lie algebroids to Riemannian Cartan-Lie groupoidsJan 02 2018Cartan-Lie algebroids, i.e. Lie algebroids equipped with a compatible connection, permit the definition of an adjoint representation, on the fiber as well as on the tangent of the base. We call (positive) quadratic Lie algebroids, Cartan-Lie algebroids ... More

A Global View of Kinks in 1+1 GravityJul 25 1997Following Finkelstein and Misner, kinks are non-trivial field configurations of a field theory, and different kink-numbers correspond to different disconnected components of the space of allowed field configurations for a given topology of the base manifold. ... More

Complete Classification of 1+1 Gravity SolutionsNov 25 1997A classification of the maximally extended solutions for 1+1 gravity models (comprising e.g. generalized dilaton gravity as well as models with non-trivial torsion) is presented. No restrictions are placed on the topology of the arising solutions, and ... More

Group Theoretical Quantization and the Example of a Phase Space S^1 x R^+Aug 27 1999Dec 13 1999The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the admissibility of group ... More

A Brief Introduction to Poisson Sigma-ModelsJul 04 1995The theory of Poisson-$\sigma$-models employs the mathematical notion of Poisson manifolds to formulate and analyze a large class of topological and almost topological two dimensional field theories. As special examples this class of field theories includes ... More

Canonical Quantization of Non-Einsteinian Gravity and the Problem of TimeNov 12 1992For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity like e.g.\ the ... More

Lie Algebroid Yang Mills with Matter FieldsAug 21 2009Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. ... More

Current Algebras and Differential GeometryOct 18 2004Mar 20 2005We show that symmetries and gauge symmetries of a large class of 2-dimensional sigma models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the sigma model. We compute ... More

Second Law of Black Hole Mechanics for all 2d Dilaton TheoriesSep 19 2000Sep 26 2000It is shown that all generalized two--dimensional dilaton theories with arbitrary matter content (with a curvature independent coupling to gravity) do not only obey a first law of black hole mechanics (which follows from Wald's general considerations, ... More

Generalized 2d dilaton gravity with matter fieldsMay 15 1998Jun 04 1998We extend the classical integrability of the CGHS model of 2d dilaton gravity [1] to a larger class of models, allowing the gravitational part of the action to depend more generally on the dilaton field and, simultaneously, adding fermion- and U(1)-gauge-fields ... More

Characteristic classes associated to Q-bundlesNov 26 2007A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections in the category ... More

Explicit Global Coordinates for Schwarzschild and Reissner-NordstroemJul 05 1995Mar 16 1996We construct coordinate systems that cover all of the Reissner-Nordstroem solution with m>|q| and m=|q|, respectively. This is possible by means of elementary analytical functions. The limit of vanishing charge q provides an alternative to Kruskal which, ... More

Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying ApproachAug 08 1995Aug 11 1997We provide a concise approach to generalized dilaton theories with and without torsion and coupling to Yang-Mills fields. Transformations on the space of fields are used to trivialize the field equations locally. In this way their solution becomes accessible ... More

Classical Solutions for Poisson Sigma Models on a Riemann surfaceApr 29 2003We determine the moduli space of classical solutions to the field equations of Poisson Sigma Models on arbitrary Riemann surfaces for Poisson structures with vanishing Poisson form class. This condition ensures the existence of a presymplectic form on ... More

Symplectic Cuts and Projection QuantizationDec 10 1999Jun 07 2000The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results established within ... More

Deep Multiple Kernel LearningOct 11 2013Deep learning methods have predominantly been applied to large artificial neural networks. Despite their state-of-the-art performance, these large networks typically do not generalize well to datasets with limited sample sizes. In this paper, we take ... More

Geometry on Lie algebroids I: compatible geometric structures on the baseMar 14 2016The object of our study is a Lie algebroid $A$ or a Cartan-Lie algebroid $(A,\nabla)$ (a Lie algebroid with a compatible connection) over a base manifold $M$ equipped with appropriately compatible geometrical structures. The main focus is on a Riemannian ... More

Transverse generalized metrics and 2d sigma modelsJan 25 2019We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections in purely Dirac-geometric ... More

The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge TheoriesDec 20 2018Dec 21 2018We show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a Leibniz algebra (with one of its induced quotient Lie algebras embedded into a rigid symmetry Lie algebra that provides ... More

Gamma-ray halos as a measure of intergalactic magnetic fields: a classical moment problemApr 27 2011The presence of weak intergalactic magnetic fields can be studied by their effect on electro-magnetic cascades induced by multi-TeV gamma-rays in the cosmic radiation background. Small deflections of secondary electrons and positrons as the cascade develops ... More

The Hubble diagram as a probe of mini-charged particlesApr 07 2009The luminosity-redshift relation of cosmological standard candles provides information about the relative energy composition of our Universe. In particular, the observation of type Ia supernovae up to redshift of z~2 indicate a universe which is dominated ... More

Exotic Neutrino Interactions in Cosmic RaysNov 29 2006The spectrum of extra-galactic cosmic rays (CRs) is expected to follow the Greisen-Zatsepin-Kuzmin (GZK) cutoff at about 5x10^10 GeV which results from energy losses of charged nuclei in the cosmic microwave background. So far the confrontation of this ... More

Strongly Interacting Astrophysical NeutrinosNov 16 2005The origin and chemical composition of ultra high energy cosmic rays is still an open question in astroparticle physics. The observed large-scale isotropy and also direct composition measurements can be interpreted as an extragalactic proton dominance ... More

On the possiblity of using vertically pointing Central Laser Facilities to calibrate the Cherenkov Telescope ArrayApr 22 2014A Central Laser Facility is a system composed of a laser placed at a certain distance from a light-detector array, emitting fast light pulses, typically in the vertical direction, with the aim to calibrate that array. During calibration runs, all detectors ... More

OPE-AlgebrasSep 03 2002Sep 20 2002In hep-th/0010293 Kapustin and Orlov introduce the notion of an OPE-algebra and propose that it formalizes conformal field theories in the same way as vertex algebras formalize chiral algebras, i.e. the subalgebras of holomorphic fields of conformal field ... More

The Harder-Narasimhan system in quantum groups and cohomology of quiver moduliApr 04 2002Methods of Harder and Narasimhan from the theory of moduli of vector bundles are applied to moduli of quiver representations. Using the Hall algebra approach to quantum groups, an analog of the Harder-Narasimhan recursion is constructed inside the quantized ... More

Gliders, Ether and TrianglesDec 01 2010This is a study of the about structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as example. It uses the formalism of "flexible time" to derive expressions that characterise triangles, gliders, and and periodic ... More

Toric Varieties as Spectra of Homogeneous Prime IdealsJun 06 2002Aug 06 2009We describe the construction of a class of toric varieties as spectra of homogeneous prime ideals.

Charge Relaxation in the Presence of Shot Noise in Coulomb Coupled Mesoscopic SystemsJun 25 1999In the presence of shot noise the charge on a mesoscopic conductor fluctuates. We are interested in the charge fluctuations which arise if the conductor is in the proximity of a gate to which it is coupled by long range Coulomb forces only. Specifically ... More

Charge densities and charge noise in mesoscopic conductorsDec 18 2001We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both ... More

Mass formulae for a class of nonrotating black holesMar 06 1997In the presence of a Killing symmetry, various self-gravitating field theories with massless scalars (moduli) and vector fields reduce to sigma-models, effectively coupled to 3-dimensional gravity. We argue that this particular structure of the Einstein-matter ... More

Transverse momentum of partons: from low to high pTNov 05 2008Transverse-momentum spectra in hard processes are typically described either in terms of intrinsic transverse momentum of partons, or in terms of perturbative radiation. The relation between these descriptions is discussed for the example of semi-inclusive ... More

Exclusive QCDJan 09 2001Jan 15 2001I give a brief introduction to the physics of generalized parton distributions and distribution amplitudes. I then report on the status of the calculation of radiative corrections for the exclusive processes where these quantities occur.

Synchrony-optimized Networks of Non-identical Kuramoto OscillatorsSep 26 2008In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling network to its ... More

Growth and Optimality in Network EvolutionMay 13 2011In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected old nodes. ... More

Physical limits to magnetogeneticsApr 05 2016Jul 04 2016This is an analysis of how magnetic fields affect biological molecules and cells. It was prompted by a series of prominent reports regarding magnetism in biological systems. The first claims to have identified a protein complex that acts like a compass ... More

The Density-Potential Mapping in Quantum DynamicsOct 18 2016This work studies in detail the possibility of defining a one-to-one mapping from charge densities as obtained by the time-dependent Schr\"odinger equation to external potentials. Such a mapping is provided by the Runge-Gross theorem and lies at the very ... More

Advancing Trace Recovery Evaluation - Applied Information Retrieval in a Software Engineering ContextFeb 24 2016Successful development of software systems involves efficient navigation among software artifacts. One state-of-practice approach to structure information is to establish trace links between artifacts, a practice that is also enforced by several development ... More

The Canonical 2-Gerbe of a Complex ManifoldJan 19 2016We present the construction of a holomorphic bundle 2-gerbe for each complex manifold, a higher analog of the canonical line bundle. It is a geometric representative of the second Beilinson-Chern class. Also, an Atiyah class for gerbes is introduced and ... More

Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticityApr 25 2016In isotropic strain gradient elasticity, we decompose the strain gradient tensor into its irreducible pieces under the n-dimensional orthogonal group O(n). Using the Young tableau method for traceless tensors, four irreducible pieces (n>2), which are ... More

Non-equilibrium interfacial tension during relaxationJun 17 2015Oct 06 2015The concept of a non-equilibrium interfacial tension, defined via the work required to deform the system such that the interfacial area is changed while the volume is conserved, is investigated theoretically in the context of the relaxation of an initial ... More

Sequential decoupling of negative-energy states in Douglas-Kroll-Hess theoryJan 23 2015Sep 25 2015Here, we review the historical development, current status, and prospects of Douglas--Kroll--Hess theory as a quantum chemical relativistic electrons-only theory.

Digit Polynomials and their application to integer factorizationJan 13 2015Dec 20 2015This paper presents the concept of digit polynomials, which leads to a deterministic and unconditional integer factorization algorithm with the runtime complexity $\mathcal{O}(N^{1/4+\epsilon})$. Strassen's well known factoring approach is a special case ... More

Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed LimitsAug 23 2016Sep 13 2016Quantum critical states exhibit strong quantum fluctuations and are therefore highly susceptible to perturbations. In this work we study the dynamical stability of such states against a sudden coupling to these strong fluctuations by quenching the order ... More

Purely electronic transport and localization in the Bose glassSep 11 2009Oct 26 2009We discuss transport and localization properties on the insulating side of the disorder dominated superconductor-insulator transition, described in terms of the dirty boson model. Analyzing the spectral properties of the interacting bosons in the absence ... More

A nonsingular solution of the edge dislocation in the gauge theory of dislocationsAug 19 2002Jan 28 2003A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and the solution ... More

Dislocation theory as a 3-dimensional translation gauge theoryJun 19 2000We consider the static elastoplastic theory of dislocations in an elastoplastic material. We use a Yang-Mills type Lagrangian (the teleparallel equivalent of Hilbert-Einstein Lagrangian) and some Lagrangians with anisotropic constitutive laws. The translational ... More

On the correspondence between a screw dislocation in gradient elasticity and a regularized vortexMay 28 2004Aug 17 2004We show the correspondence between a screw dislocation in gradient elasticity and a regularized vortex. The effective Burgers vector, nonsingular distortion and stress fields of a screw dislocation and the effective circulation, smoothed velocity and ... More

The static potential in QCD - a full Two-Loop CalculationFeb 04 1997Oct 17 1997A full analytic calculation of the two-loop diagrams contributing to the static potential in QCD is presented in detail. Using a renormalization group improvement, the ``three-loop'' potential in momentum space is thus derived and the third coefficient ... More

From Schritte and Wechsel to Coxeter GroupsJan 16 2019The PLR-moves of neo-Riemannian theory, when considered as reflections on the edges of an equilateral triangle, define the Coxeter group~$\widetilde S_3$. The elements are in a natural one-to-one correspondence with the triangles in the infinite Tonnetz. ... More

The Schulze Method of VotingMar 15 2018Dec 15 2018We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency, polynomial runtime). ... More

Algebraic Cobordism in mixed characteristicApr 09 2014We compute the geometric part of algebraic cobordism over Dedekind domains of mixed characteristic after inverting the positive residue characteristics and prove cases of a Conjecture of Voevodsky relating this geometric part to the Lazard ring for regular ... More

A transference principle for general groups and functional calculus on UMD spacesJul 24 2008We prove a transference principle for general (i.e., not necessarily bounded) strongly continuous groups on Banach spaces. If the Banach space has the UMD property, the transference principle leads to estimates for the functional calculus of the group ... More

A Gröbner basis proof of the flat extension theorem for moment matricesJan 28 2008Jan 19 2009This paper has been withdrawn by the author since $U$ in Lemma 2 is in general not a subspace.

Inversion of circular means and the wave equation on convex planar domainsJun 06 2012Jan 19 2013We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish back-projection type ... More

A reduction of integer factorization to modular tetrationJul 16 2017Feb 13 2018Let $a,k\in\mathbb{N}$. For the $k-1$-th iterate of the exponential function $x\mapsto a^x$, also known as tetration, we write \[ ^k a:=a^{a^{.^{.^{.^{a}}}}}. \] In this paper, we show how an efficient algorithm for tetration modulo natural numbers $N$ ... More