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Asymptotic behaviour of the Hodge Laplacian spectrum on graph-like manifoldsFeb 10 2015We consider a family of compact, oriented and connected Riemannian manifolds shrinking to a metric graph and describe the asymptotic behaviour of the eigenvalues of the Hodge Laplacian. We apply our results to produce manifolds with spectral gaps of arbitrarily ... More

Existence of spectral gaps, covering manifolds and residually finite groupsMar 03 2005Dec 10 2007In the present paper we consider Riemannian coverings $(X,g) \to (M,g)$ with residually finite covering group $\Gamma$ and compact base space $(M,g)$. In particular, we give two general procedures resulting in a family of deformed coverings $(X,g_\eps) ... More

First order operators and boundary triplesNov 14 2007Dec 06 2007The aim of the present paper is to introduce a first order approach to the abstract concept of boundary triples for Laplace operators. Our main application is the Laplace operator on a manifold with boundary; a case in which the ordinary concept of boundary ... More

First order approach and index theorems for discrete and metric graphsAug 28 2007Sep 03 2007The aim of the present paper is to introduce the notion of first order (supersymmetric) Dirac operators on discrete and metric (``quantum'') graphs. In order to cover all self-adjoint boundary conditions for the associated metric graph Laplacian, we develop ... More

Branched quantum wave guides with Dirichlet boundary conditions: the decoupling caseFeb 03 2005We consider a family of open sets $M_\epsilon$ which shrinks with respect to an appropriate parameter $\epsilon$ to a graph. Under the additional assumption that the vertex neighbourhoods are small we show that the appropriately shifted Dirichlet spectrum ... More

Abstract graph-like space and vector-valued metric graphsMar 30 2016In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum graphs or graph-like ... More

Spectral analysis of metric graphs and related spacesDec 10 2007Feb 15 2008The aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and explicitly allow ... More

Equilateral quantum graphs and boundary triplesDec 10 2007Jan 15 2008The aim of the present paper is to analyse the spectrum of Laplace and Dirac type operators on metric graphs. In particular, we show for equilateral graphs how the spectrum (up to exceptional eigenvalues) can be described by a natural generalisation of ... More

Spectral convergence of non-compact quasi-one-dimensional spacesDec 22 2005Jan 02 2006We consider a family of non-compact manifolds $X_\eps$ (``graph-like manifolds'') approaching a metric graph $X_0$ and establish convergence results of the related natural operators, namely the (Neumann) Laplacian $\laplacian {X_\eps}$ and the generalised ... More

Periodic Manifolds with Spectral GapsJul 14 2002We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding Laplacian has at least ... More

Eigenvalues in Spectral Gaps of a Perturbed Periodic ManifoldJul 14 2002We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the number of ... More

Boundary pairs associated with quadratic formsOct 17 2012May 04 2015We introduce an abstract framework for elliptic boundary value problems in a variational form. Given a non-negative quadratic form in a Hilbert space, a boundary pair consists of a bounded operator, the boundary operator, and an auxiliary Hilbert space, ... More

Path integrals and the essential self-adjointness of differential operators on noncompact manifoldsJun 28 2012Dec 07 2012We consider Schr\"odinger operators on possibly noncompact Riemannian manifolds, acting on sections in vector bundles, with locally square integrable potentials whose negative part is in the underlying Kato class. Using path integral methods, we prove ... More

Eigenvalue bracketing for discrete and metric graphsApr 07 2008We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph spectrum (also ... More

Convergence of resonances on thin branched quantum wave guidesFeb 21 2007We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family $X_\eps$ of branched quantum waveguides. Combining it with an exterior ... More

Quantum networks modelled by graphsJun 04 2007Dec 10 2007Quantum networks are often modelled using Schroedinger operators on metric graphs. To give meaning to such models one has to know how to interpret the boundary conditions which match the wave functions at the graph vertices. In this article we give a ... More

Convergence of spectra of graph-like thin manifoldsDec 10 2003Aug 16 2004We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph with ... More

On a generalisation of Krein's exampleOct 30 2017We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the ... More

Approximation of fractals by manifolds and other graph-like spacesFeb 08 2018We define a distance between energy forms on a graph-like metric measure space and on a discrete weighted graph using the concept of quasi-unitary equivalence. We apply this result to metric graphs and graph-like manifolds (e.g. a small neighbourhood ... More

Operator estimates for the crushed ice problemOct 09 2017Dec 26 2017Let $\Delta_{\Omega_\varepsilon}$ be the Dirichlet Laplacian in the domain $\Omega_\varepsilon:=\Omega\setminus\left(\cup_i D_{i \varepsilon}\right)$. Here $\Omega\subset\mathbb{R}^n$ and $\{D_{i \varepsilon}\}_{i}$ is a family of tiny identical holes ... More

A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifoldsMay 23 2012Sep 15 2012We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at ... More

Approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifoldsNov 22 2008We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann type Laplacian on such manifolds is amended by suitable potentials, the resulting Schr\"odinger operators can approximate ... More

Spectral Gaps for Periodic Elliptic Operators with High Contrast: an OverviewJul 16 2002We discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space $L_2(\R^m)$, for $m \ge 2$. We specifically consider situations where high contrast in the coefficients leads to weak coupling ... More

Generating spectral gaps by geometryJun 15 2004Jun 23 2005Motivated by the analysis of Schr\"odinger operators with periodic potentials we consider the following abstract situation: Let $\Delta_X$ be the Laplacian on a non-compact Riemannian covering manifold $X$ with a discrete isometric group $\Gamma$ acting ... More

On the spectra of carbon nano-structuresDec 07 2006Jan 19 2007An explicit derivation of dispersion relations and spectra for periodic Schr\"{o}dinger operators on carbon nano-structures (including graphen and all types of single-wall nano-tubes) is provided.

Anderson Localization for radial tree-like random quantum graphsNov 10 2006Jun 16 2008We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the RLM, the lengths ... More

Gaps in the differential forms spectrum on cyclic coveringsAug 29 2007Apr 18 2008We are interested in the spectrum of the Hodge-de Rham operator on a cyclic covering $X$ over a compact manifold $M$ of dimension $n+1$. Let $\Sigma$ be a hypersurface in $M$ which does not disconnect $M$ and such that $M-\Sigma$ is a fundamental domain ... More

On Open Scattering Channels for Manifolds with EndsFeb 02 2012Nov 15 2013In the framework of time-dependent geometric scattering theory, we study the existence and completeness of the wave operators for perturbations of the Riemannian metric for the Laplacian on a complete manifold of dimension $n$. The smallness condition ... More

Convergence of sectorial operators on varying Hilbert spaceJul 22 2010Nov 14 2012Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first results in this direction ... More

Continuity of the integrated density of states on random length metric graphsNov 27 2008Apr 25 2009We establish several properties of the integrated density of states for random quantum graphs: Under appropriate ergodicity and amenability assumptions, the integrated density of states can be defined using an exhaustion procedure by compact subgraphs. ... More

Spectral gaps and discrete magnetic LaplaciansOct 03 2017Aug 07 2018The aim of this article is to give a simple geometric condition that guarantees the existence of spectral gaps of the discrete Laplacian on periodic graphs. For proving this, we analyse the discrete magnetic Laplacian (DML) on the finite quotient and ... More

Exact Black-Hole Solution With Self-Interacting Scalar FieldFeb 03 1995Feb 22 1995Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair. The symmetric ... More

Continuity properties of the integrated density of states on manifoldsMay 08 2007We first analyze the integrated density of states (IDS) of periodic Schr\"odinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous ... More

Frustration index and Cheeger inequalities for discrete and continuous magnetic LaplaciansFeb 23 2015Aug 14 2015We discuss a Cheeger constant as a mixture of the frustration index and the expansion rate, and prove the related Cheeger inequalities and higher order Cheeger inequalities for graph Laplacians with cyclic signatures, discrete magnetic Laplacians on finite ... More

An infinite family of superintegrable deformations of the Coulomb potentialMar 26 2010May 11 2010We introduce a new family of Hamiltonians with a deformed Kepler- Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wave functions. ... More

General Nth order integrals of the motionJan 02 2015Feb 11 2015The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and the quantum cases are treated separately, emphasizing both the similarities ... More

QCD sum rules at finite density in the large-N_c limit: The coupling of the rho-nucleon system to the D_{13}(1520)Feb 13 2004QCD sum rules are studied for the vector-isovector current at finite baryon density in the limit of large number of colors N_c. For the condensate side it is shown that in this limit the four-quark condensate factorizes also for the finite density case. ... More

One Tree Suffices: A Simultaneous O(1)-Approximation for Single-Sink Buy-at-BulkApr 13 2010Aug 27 2010We study the single-sink buy-at-bulk problem with an unknown cost function. We wish to route flow from a set of demand nodes to a root node, where the cost of routing x total flow along an edge is proportional to f(x) for some concave, non-decreasing ... More

The simplex method is strongly polynomial for deterministic Markov decision processesAug 25 2012Jan 31 2013We prove that the simplex method with the highest gain/most-negative-reduced cost pivoting rule converges in strongly polynomial time for deterministic Markov decision processes (MDPs) regardless of the discount factor. For a deterministic MDP with n ... More

Explicit bracket in the exceptional simple Lie superalgebra cvect(0|3)_*Mar 18 1997This note is devoted to a more detailed description of one of the five simple exceptional Lie superalgebras of vector fields, cvect(0|3)_*, a subalgebra of vect(4|3). We derive differential equations for its elements, and solve these equations. Hence ... More

Vector Meson Decay of Baryon ResonancesMar 23 2001We investigate the coupling of vector mesons with nucleons to nucleon resonances in an isospin-selective VMD approach and explore the in-medium properties of vector mesons.

On some operator identities and representations of algebrasMay 26 1993Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.

Classification of linear differential operators with an invariant subspace of monomialsJul 21 1993A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.

Gate capacitance of back-gated nanowire field-effect transistorsJul 14 2006Gate capacitances of back-gated nanowire field-effect transistors (NW-FETs) are calculated by means of finite element methods and the results are compared with analytical results of the ``metallic cylinder on an infinite metal plate model''. Completely ... More

A note on closed isometric embeddingsMay 30 2008May 20 2016This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.

Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theoriesNov 30 2006May 11 2007We analyze the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein ... More

Noncommutative SolitonsMay 03 2006These lectures deal mainly with solitons in three-dimensional Moyal-deformed sigma models. The topics are: static and moving (multi-)solitons of the (integrable) Ward sigma model, with space-space and time-space noncommutativity, their scattering, moduli ... More

Background Independent Quantum Field Theory and the Cosmological Constant ProblemSep 03 2004Jan 28 2005We introduce the notion of background independent quantum field theory. The distinguishing feature of this theory is that the dynamics can be formulated without recourse to a background metric structure. We show in a simple model how the metric properties ... More

Relational Physics and Quantum SpaceApr 13 2004In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We then address this ... More

Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-timesMar 29 2004We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions. When applying standard coordinates to the complete rim ... More

Degeneracies and scaling relations in general power-law models for gravitational lensesFeb 20 2002The time delay in gravitational lenses can be used to derive the Hubble constant in a relatively simple way. The results of this method are less dependent on astrophysical assumptions than in many other methods. The most important uncertainty is related ... More

The Perspectives of Democratic Decision-Making in the Information SocietyMay 10 2016In order to structure the debate on the democratic potentials of digital information technology Hubertus Buchstein in 1996 created three ideal types, net optimism, net pessimism and net neutrality. In this study the viability of these positions is put ... More

Not on but ofDec 03 2012In physics we encounter particles in one of two ways. Either as fundamental constituents of the theory or as emergent excitations. These two ways differ by how the particle relates to the background. It either sits on the background, or it is an excitation ... More

Non-linear uplift Ansätze for the internal metric and the four-form field-strength of maximal supergravityFeb 10 2016Jun 15 2016The uplift of SO(8) gauged N=8 supergravity to 11-dimensional supergravity is well studied in the literature. It is given by consistent relations between the respective vector and scalar fields of both theories. For example, recent work provided non-linear ... More

On factorizations in perturbative quantum gravityFeb 28 2011Apr 25 2011Some features of Einstein gravity are most easily understood from string theory but are not manifest at the level of the usual Lagrangian formulation. One example is the factorization of gravity amplitudes into gauge theory amplitudes. Based on the recently ... More

Metrizability of spaces of homomorphisms between metric vector spacesMay 22 2009Nov 29 2014This note tries to give an answer to the following question: Is there a sufficiently rich class of metric vector spaces such that sufficiently large spaces of continuous linear maps between them are metrizable?

SUSY CP phases and asymmetries at collidersApr 21 2009In the Minimal Supersymmetric Standard Model, physical phases of complex parameters lead to CP violation. We show how triple products of particle momenta or spins can be used to construct asymmetries, that allow us to probe these CP phases. To give specific ... More

N=4 Mechanics, WDVV Equations and PolytopesNov 03 2008Nov 17 2008N=4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F. The ... More

Gravitational lensingSep 25 2007This is a short and biased review of gravitational lensing with emphasis on the radio and especially VLBI aspects. We briefly explain the basic idea and give a short sketch of the discovery of the first lens, before we more systematically discuss the ... More

Emergent Probabilities in Quantum MechanicsMar 22 2006The transition from the quantum to the classical is governed by randomizing devices (RD), i.e., dynamical systems that are very sensitive to the environment. We show that, in the presence of RDs, the usual arguments based on the linearity of quantum mechanics ... More

Classicality in Quantum MechanicsNov 07 2006In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality ... More

On the infinite-dimensional spin-2 symmetries in Kaluza-Klein theoriesNov 16 2005Jan 25 2006We consider the couplings of an infinite number of spin-2 fields to gravity appearing in Kaluza-Klein theories. They are constructed as the broken phase of a massless theory possessing an infinite-dimensional spin-2 symmetry. Focusing on a circle compactification ... More

Multifractality in a broad class of disordered systemsSep 21 2004We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles ... More

Invariants of 3-manifolds from representations of the framed-tangle categoryMar 03 2002A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.

The Gamma-Ray Properties of Unidentified EGRET SourcesFeb 28 2001Although the majority of gamma-ray sources still remain unidentified, we have various kinds of information to characterize the observational properties of unidentified EGRET sources. Despite astronomical properties like locations of individual sources ... More

The Self-Dual Critical N=2 StringJul 13 1996I review the covariant quantization of the closed fermionic string with (2,2) extended world-sheet supersymmetry on R^{2,2}. Results on n-point scattering amplitudes are presented, for tree- and one-loop world-sheets with arbitrary Maxwell instanton number. ... More

Integration Measure and Spectral Flow in the Critical N=2 StringDec 22 1995I present the moduli space of the (2+2)-dimensional critical closed fermionic string with two world-sheet supersymmetries. The integration of fermionic and Maxwell moduli in the presence of punctures yields the string measure for n-point amplitudes at ... More

Semiclassical Approach to Finite-N Matrix ModelsDec 17 1991Dec 18 1991We reformulate the zero-dimensional hermitean one-matrix model as a (nonlocal) collective field theory, for finite~$N$. The Jacobian arising by changing variables from matrix eigenvalues to their density distribution is treated {\it exactly\/}. The semiclassical ... More

A proof of Thorne's Hoop Conjecture for Einstein-Maxwell TheoryJul 18 2016Aug 18 2016We prove different variants of known singularity theorems and finally a statement in the spirit of Thorne's Hoop conjecture, concluding the existence of a region of finite lifetime that includes the outer trapped surface, and of a horizon. Conformal extensions ... More

Beyond information: A bit of meaningNov 06 2013Is our world just information? We argue that our current notion of information has one serious shortcoming: It is quite literally meaningless. We suggest a meaningful extension of the notion of information that is dynamic, internal, approximate, contains ... More

Instantons and Chern-Simons flows in 6, 7 and 8 dimensionsJan 30 2012Feb 23 2012The existence of K-instantons on a cylinder M^7 = R_tau x K/H over a homogeneous nearly K"ahler 6-manifold K/H requires a conformally parallel or a cocalibrated G_2-structure on M^7. The generalized anti-self-duality on M^7 implies a Chern-Simons flow ... More

Asymptotic flexibility of globally hyperbolic manifoldsOct 05 2011In this short note, a question of patching together globally hyperbolic manifolds is adressed which appeared in the context of the construction of Hadamard states.

The optimal constants in Khintchine's inequality for the case 2<p<3Jan 28 2016A mean step in Haagerup's proof for the optimal constants in Khintchine's inequality is to show integral inequalities of type $\int(g^s-f^s)\mathrm{d}\mu\geq 0$. F.L. Nazarov and A.N. Podkorytov made Haagerup's proof much more clearer for the case 0<p<2 ... More

On Asteroid EngineeringNov 23 2015I pose the question of maximal Newtonian surface gravity on a homogeneous body of a given mass and volume but with variable shape. In other words, given an amount of malleable material of uniform density, how should one shape it in order for a microscopic ... More

Reconciliation of RDF* and Property GraphsSep 11 2014Nov 13 2014Both the notion of Property Graphs (PG) and the Resource Description Framework (RDF) are commonly used models for representing graph-shaped data. While there exist some system-specific solutions to convert data from one model to the other, these solutions ... More

SPARQL for a Web of Linked Data: Semantics and Computability (Extended Version)Mar 07 2012Apr 06 2012The World Wide Web currently evolves into a Web of Linked Data where content providers publish and link data as they have done with hypertext for the last 20 years. While the declarative query language SPARQL is the de facto for querying a-priory defined ... More

Long baseline experiments with LOFARAug 25 2010I present first results of LOFAR observations with international baselines. An important cornerstone was the detection of the first long-baseline fringes. Their analysis turns out to be extremely useful to investigate and solve a number of technical issues ... More

Why things fallOct 23 2007May 20 2008In this paper we discuss Internal Relativity, a recent program to address the problem of quantum gravity. In our approach we change the relationship between spacetime and matter. Currently we view matter as propagating on spacetime. Einstein's equations ... More

A metric approach to Fréchet geometryDec 14 2006Jun 16 2007The aim of this article is to present the category of bounded Frechet manifolds in respect to which we will review the geometry of Frechet manifolds with a stronger accent on its metric aspect. An inverse function theorem in the sense of Nash and Moser ... More

Anomalous elasticity in nematic and smectic elastomer tubuleAug 12 2008We study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously-broken in-plane ... More

Early Universe Cosmology in Internal RelativityMay 23 2008We present a new approach to early universe cosmology. Inflation is replaced by a phase transition in which both matter and geometry are created simultaneously. We calculate the spectrum of metric perturbations and show that it is flat. We then argue ... More

Emergent General RelativityApr 18 2006We review different approaches to quantum gravity in which spacetime is emerging. We discuss in some detail the proposals by G. Volovik and S. Lloyd and show how they differ in the way they treat time. We further propose an approach to quantum gravity ... More

On The Origin Of Unidentified EGRET Gamma-Ray SourcesJun 15 2005The identification of celestial gamma-ray sources with astronomical objects or object classes has remained the initial and most fundamental key for understanding their physical nature. The observational characteristic of a gamma-ray emitter and the conditions ... More

Quasilinear Drift Of Cosmic Rays In Weak Turbulent Electromagnetic FieldsJan 13 2005A general quasilinear transport parameter for particle drift in arbitrary turbulence geometry is presented. The new drift coefficient is solely characterized by a nonresonant term and is evaluated for slab and two-dimensional turbulence geometry. The ... More

Quasinormal Modes, the Area Spectrum, and Black Hole EntropyNov 24 2002The results of canonical quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labelled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole ... More

From N=2 Fermionic Strings to Superstrings?Dec 31 1994I review the covariant quantization of the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. The BRST analysis yields massless bosonic and fermionic vertex operators in various ghost and picture number sectors, as well as ... More

A note on $H^* (\rm{Emb}_0 (M,N))$Jan 25 2002Jan 29 2002Aim of this note is to gain cohomological information about the infinite-dimensional manifold $\rm{Emb}_0 (M,N)$ of asymptotically fixed embeddings of M into N from the topology of the target manifold N. This paper has been withdrawn by the author due ... More

A natural symplectic form for every field theoryAug 21 2001Apr 15 2011The article has been withdrawn as its main result had already been known.

Continuum estimate of the heavy quark momentum diffusion coefficient $κ$Sep 12 2014Among quantities playing a central role in the theoretical interpretation of heavy ion collision experiments at RHIC and LHC are so-called transport coefficients. Out of those heavy quark diffusion coefficients play an important role e.g. for the analysis ... More

Global Existence and Uniqueness of Minimal Surfaces in Globally Hyperbolic ManifoldsOct 22 2002May 26 2004In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.

HorizonsNov 19 2011Aug 13 2015We define different notions of black holes, event horizons and Killing horizons for a general time-oriented manifold $(M,g)$ extending previous notions but without the assumption of asymptotical flatness. The notions of 'horizon' are always conformally ... More

Soliton surfaces associated with generalize symmetries of integrable equationsFeb 09 2011Mar 28 2011In this paper, based on the Fokas, Gel'fand et al approach [15,16], we provide a symmetry characterization of continuous deformations of soliton surfaces immersed in a Lie algebra using the formalism of generalized vector fields, their prolongation structure ... More

Soliton surfaces via zero-curvature representation of differential equationsNov 17 2011Sep 11 2012The main aim of this paper is to introduce a new version of the Fokas-Gel'fand formula for immersion of soliton surfaces in Lie algebras. The paper contains a detailed exposition of the technique for obtaining exact forms of 2D-surfaces associated with ... More

Surfaces immersed in Lie algebras associated with elliptic integralsJun 10 2011The main aim of this paper is to study soliton surfaces immersed in Lie algebras associated with ordinary differential equations (ODE's) for elliptic functions. That is, given a linear spectral problem for such an ODE in matrix Lax representation, we ... More

Analysis of $CP^{N-1}$ sigma models via projective structureOct 11 2010In this paper, we study rank-1 projector solutions to the completely integrable Euclidean $CP^{N-1}$ sigma model in two dimension and their associated surfaces immersed in the $su(N)$ Lie algebra. We reinterpret and generalize the proof of A.M. Din and ... More

Quantum Nash Equilibria and Quantum ComputingJul 03 2007In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes ... More

Coherent Photoproduction of Dileptons on Light Nuclei - a New Means to Learn about Vector MesonsMar 01 1999In the last years much work has been done to learn about the properties of the $\rho$-meson in nuclear matter. In a calculation of the in-medium spectralfunction of the $\rho$ we find that it is strongly modified by baryonic resonances, especially the ... More

Classical and Quantum Superintegrability with ApplicationsSep 10 2013A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals of motion ... More

Third-order superintegrable systems with potentials satisfying nonlinear equationsJan 02 2015The conditions for superintegrable systems in two-dimensional Euclidean space admitting separation of variables in an orthogonal coordinate system and a functionally independent third-order integral are studied. It is shown that only systems that separate ... More

Soliton surfaces and generalized symmetries of integrable systemsFeb 27 2013Nov 08 2013In this paper, we discuss some specific features of symmetries of integrable systems which can be used to contruct the Fokas-Gel'fand formula for the immersion of 2D-soliton surfaces, associated with such systems, in Lie algebras. We establish the sufficient ... More