Results for "Erik Zupanič"

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Quasicrystals and Unit-Cell TwinningMar 03 2015The structure and the corresponding electron diffraction patterns of quasicrystals are explained by unit-cell twinning. The twinning operation is applied to the primitive golden rhombohedra, obtained by a slight deformation of a parent cubic close-packed ... More
Emission of twin jets from a driven matter-wave soliton in a quasi-one-dimensional geometryMay 24 2019The modulation of the interaction between the atoms in a matter-wave soliton in a quasi-one-dimensional optical trap triggers an emission of correlated atom jets. We characterize the dependence of jet properties on the frequency, amplitude and length ... More
Nanostructured and Modulated Low-Dimensional SystemsMar 26 2013Charge density wave (CDW) ordering in NbSe3 and the structurally related quasi one-dimensional compounds is reconsidered. Since the modulated ground state is characterized by unstable nano-domains, the structural information obtained from diffraction ... More
Cesium bright matter-wave solitons and soliton trainsFeb 08 2019A setup for studying bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is studied. Formation of soliton ... More
Cesium bright matter-wave solitons and soliton trainsFeb 08 2019Mar 05 2019A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains ... More
Correlated Configurational States and a Quantum Charge Liquid in Layered Metallic DichalcogenidesJan 08 2019Two-dimensional metallic dichalcogenides display diverse charge ordering phenomena, but the mechanisms for the formation of low-temperature commensurate order have proven surprisingly controversial. Fermi surface instabilities, the electron-phonon interaction, ... More
Configurational Electronic States in Layered Metallic DichalcogenidesJan 08 2019Mar 06 2019Mesoscopic irregularly ordered and even amorphous self-assembled electronic structures were recently reported in two-dimensional metallic dichalcogenides (TMDs), created and manipulated with short light pulses or by charge injection. Apart from promising ... More
Test of renormalization predictions for universal finite-size scaling functionsNov 02 1999We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular epsilon-expansion, where ... More
Black Hole Evaporation and ComplementarityMar 17 1995About twenty years ago Hawking made the remarkable suggestion that the black hole evaporation process will inevitably lead to a fundamental loss of quantum coherence. The mechanism by which the quantum radiation is emitted appears to be insensitive to ... More
Torsion and electron motion in Quantum Dots with crystal lattice dislocationsNov 25 1997The motion of a conducting electron in a quantum dot with one or several dislocations in the underlying crystal lattice is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of torsion are ... More
Endomorphisms of quantized Weyl algebrasJul 15 2010Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized ... More
Comment on "Geometric phases for mixed states during cyclic evolutions"Apr 30 2004Jul 08 2004It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent.
Isometric Embeddability of SnowflakesSep 21 2015We show that a snowflake of a metric space with positive Hausdorff dimension does not admit an isometric embedding into euclidean space.
Astrometry 1960-80: from Hamburg to HipparcosAug 08 2014Astrometry, the most ancient branch of astronomy, was facing extinction during much of the 20th century in the competition with astrophysics. The revival of astrometry came with the European astrometry satellite Hipparcos, approved by ESA in 1980 and ... More
A stabilized nonconforming finite element method for the elliptic Cauchy problemJun 17 2014In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data on the estimates ... More
A Primer on Energy ConditionsApr 30 2014An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be ... More
Feynman integrals via hyperlogarithmsJun 30 2014This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future directions. ... More
The Double Eulerian Polynomial and Inversion TablesJan 22 2014We show that the pair (des, ides) of statistics on the set of permu- tations has the same distribution as the pair (asc, row) of statistics on the set of inversion tables, proving a conjecture of Visontai. The common generating function of these pairs ... More
A Simple Proof of the Marker-Steinhorn Theorem for Expansions of Ordered Abelian GroupsSep 23 2013We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.
Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integralsMar 13 2014We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we discuss various ... More
Performance and Optimization Abstractions for Large Scale Heterogeneous Systems in the Cactus/Chemora FrameworkAug 06 2013We describe a set of lower-level abstractions to improve performance on modern large scale heterogeneous systems. These provide portable access to system- and hardware-dependent features, automatically apply dynamic optimizations at run time, and target ... More
Using Monte Carlo to optimize variable cutsDec 20 2007Dec 20 2007A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.
Low Threshold Bootstrap Percolation on the Hamming TorusJul 09 2014Jun 09 2015This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More
SIR dynamics in random networks with heterogeneous connectivityMay 15 2007Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by showing how the ... More
SIR dynamics in structured populations with heterogeneous connectivityAug 22 2005Dec 20 2005Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by describing the ... More
On the analytic computation of massless propagators in dimensional regularizationMay 09 2013Mar 20 2014We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including order $\varepsilon^4$ ... More
Recursive prescription for logarithmic jet rate coefficientsMay 27 2013Feb 11 2014We derive a recursion relation for the analytic leading logarithmic coefficients of a final state gluon cascade. We demonstrate the potential of our method by analytically computing the rate coefficients for the emission of up to 80 gluons in both the ... More
Rapidity Dependence of Elliptic Flow at RHICJan 04 2006The measured elliptic flow (v2) of identified particles as a function of pT and centrality at RHIC suggests the created medium in Au+Au collisions achieves early local thermal equilibrium that is followed by hydrodynamic expansion. It is not known if ... More
Continuity in the Alexiewicz normJun 21 2006If $f$ is a Henstock--Kurzweil integrable function on the real line, the Alexiewicz norm of $f$ is $\|f\|=\sup_I|\int_I f|$ where the supremum is taken over all intervals $I\subset\R$. Define the translation $\tau_x$ by $\tau_xf(y)=f(y-x)$. Then $\|\tau_xf-f\|$ ... More
Necessary and sufficient conditions for differentiating under the integral signJan 02 2001We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every derivative. The ... More
What Is a Black Hole?Aug 04 2018Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically ... More
Tournament limits: Degree distributions, score functions and self-conversenessNov 29 2016Motivated by known results for finite tournaments, we define and study the score functions of tournament kernels and the degree distributions of tournament limits. Our main theorem completely characterises those distributions that appear as the degree ... More
Non-geometric backgrounds in string theoryNov 27 2018Dec 13 2018This review provides an introduction to non-geometric backgrounds in string theory. Starting from a discussion of T-duality, geometric and non-geometric torus-fibrations are reviewed, generalised geometry and its relation to non-geometric backgrounds ... More
The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction FactorsJan 19 2019The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. ... More
Some divergent trigonometric integralsJan 02 2001Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly) famous mathematician ... More
On invertibility preserving linear maps, simultaneous triangularization and Property LFeb 18 1997Let F be a linear unital map of a unital matrix algebra A over the complex numbers into the complex n by n matrices. Then F induces a linear unital map Fk of the k by k matrices over A into the complex nk by nk matrices by the action of F on each entry ... More
Exo-Jupiters and Saturns from two Gaia-like missionsAug 19 2014Detection and orbit determination for thousands of planets with periods up to about 40 years would be obtained by astrometry from two Gaia-like missions, results which cannot be obtained by any other mission, planned or proposed. A billion stars of all ... More
On Young tableau involutions and patterns in permutationsAug 01 2009This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to permutations ... More
Finite von Neumann algebra factors with property GammaOct 13 2000Oct 14 2000Techniques introduced by G. Pisier in his proof that finite von Neumann factors with property gamma have length at most 5 are modified to prove that the length is 3. It is proved that if such a factor is a complemented subspace of some larger C*-algebra ... More
Bootstrap percolation on the Hamming torus with threshold 2Jul 09 2014Nov 01 2017This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More
Principally polarized abelian surfaces with surjective galois representations on l-torsionDec 14 2012Nov 15 2013Given a rational variety $V$ defined over $K$, we consider a principally polarized abelian variety $A$ of dimension $g$ defined over $V$. For each prime l we then consider the galois representation on the $l$-torsion of $A_t$, where $t$ is a $K$-rational ... More
Classification of pairs of rotations in finite-dimensional Euclidean spaceFeb 20 2008A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous conjugation with orthogonal ... More
Local Moufang setsJun 15 2017All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang sets in a way ... More
On weakly D-differentiable operatorsMar 29 2013Mar 11 2015For an unbounded self-adjoint operator D on a Hilbert space H and a bounded operator a on H we say that a is weakly D-differentiable if for any pair of vectors x, y in H the function <exp(itD) a exp(-itD)x, y> is differentiable at t =0. We find several ... More
Hall-Littlewood polynomials and vector bundles on the Hilbert schemeDec 28 2012Let $E$ be the bundle defined by applying a polynomial representation of $GL_n$ to the tautological bundle on the Hilbert scheme of $n$ points in the complex plane. By a result of Haiman, the Cech cohomology groups $H^i(E)$ vanish for all $i>0$. It follows ... More
The regulated primitive integralNov 15 2009A function on the real line is called regulated if it has a left limit and a right limit at each point. If $f$ is a Schwartz distribution on the real line such that $f=F'$ (distributional or weak derivative) for a regulated function $F$ then the regulated ... More
Generalized integrands and bond portfolios: Pitfalls and counter examplesSep 12 2009Jan 05 2011We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their ... More
Detection of a Hypercharge Axion in ATLASMay 28 2001This Master of Science thesis treats the hypercharge axion, which is a hypothetical pseudo-scalar particle with electroweak interactions. First, the theoretical context and the motivations for this study are discussed. In short, the hypercharge axion ... More
Tomography of random social networksSep 15 2005We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at a distance ... More
Limit points of the iterative scaling procedureJul 23 2012The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many cases, for example ... More
Path correlations in a randomly oriented complete bipartite graphFeb 08 2011In a randomly oriented graph containing vertices $x$ and $y$, denote by $\{x\to y\}$ the event that there is a directed path from $x$ to $y$. We study the correlation between the events $\{x\to y\}$ and $\{y\to z\}$ for a (large) oriented complete bipartite ... More
Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz PotentialSep 27 2010The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" ... More
Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or VerticesMar 15 2012The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation ... More
Outbursts of WZ Sge stars/TOADs: a phenomenological comparison with soft X-ray transientsDec 01 1998The outbursts of WZ Sge stars (or TOADs), are compared to those seen in the (soft) X-ray transients. Both types of outbursts exhibit strong similarities: large amplitudes, long recurrence times, occurrence of superhumps, and of rebrightenings or reflares ... More
Towards 4U 1630-47: a black-hole soft X-ray transient odysseyJul 27 1998Aug 12 19984U 1630-47 is a black-hole X-ray transient with one of the shortest recurrence times. Despite its regular outburst behaviour little is known about this source. Only recently has attention to this system increased. I discuss there the basic known (X-ray) ... More
Askey-Wilson polynomials and the quantum SU(2) group: survey and applicationsJul 25 1994Generalised matrix elements of the irreducible representations of the quantum $SU(2)$ group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to ... More
One-parameter orthogonality relations for basic hypergeometric seriesMay 27 2003The second order hypergeometric q-difference operator is studied for the value c=-q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l^2(Z). The operator has deficiency indices ... More
The observers' view of (very) long X-ray bursts: they are super!Oct 15 2003In many X-ray point sources on the sky, the X-ray emission arises because hydrogen and/or helium is accreted onto a neutron star from a nearby donor star. When this matter settles on the neutron star surface, it will undergo nuclear fusion. For a large ... More
Bootstrap percolation on the Hamming torus with threshold 2Jul 09 2014Oct 15 2016This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More
A decomposition of the Schur block product on matrices of operatorsNov 08 2018Given two $m \times n $ matrices $A = (a_{ij})$ and $B=(b_{ij}) $ with entries in $B(H)$ for some Hilbert space $H,$ the Schur block product is the $m \times n$ matrix $ A\square B := (a_{ij}b_{ij}).$ There exists an $m \times n$ matrix $S = (s_{ij})$ ... More
Quantal interferometry with dissipative internal motionJun 02 2004Nov 16 2004In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds ... More
Estimates of Henstock--Kurzweil Poisson integralsJun 18 2004If $f$ is a real-valued function on $[-\pi,\pi]$ that is Henstock--Kurzweil integrable, let $u_r(\theta)$ be its Poisson integral. It is shown that $\|u_r\|_p=o(1/(1-r))$ as $r\to 1$ and this estimate is sharp for $1\leq p\leq\infty$. If $\mu$ is a finite ... More
Hölder estimates for viscosity solutions of equations of fractional $p$-Laplace typeMay 26 2014Jun 24 2014We prove H\"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \text{PV} \int_{\mathbb{R}^n}\frac{|u(x)-u(x+y)|^{p-2}(u(x)-u(x+y))}{|y|^{n+sp}}\, dy =0, $$ ... More
Static overscreening and nonlinear response in the Hubbard ModelMay 29 2001We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of course, down ... More
Jigsaw Percolation on Erdos-Renyi Random GraphsMar 21 2015Mar 28 2015We extend the jigsaw percolation model to analyze graphs where both underlying people and puzzle graphs are Erd\H{o}s-R\'enyi random graphs. Let $p_{\text{ppl}}$ and $p_{\text{puz}}$ denote the probability that an edge exists in the respective people ... More
Block matching algorithm based on Harmony Search optimization for motion estimationJun 17 2014Motion estimation is one of the major problems in developing video coding applications. Among all motion estimation approaches, Block-matching (BM) algorithms are the most popular methods due to their effectiveness and simplicity for both software and ... More
Astrometry for DynamicsAug 14 2014In May 2013, I responded with the present paper to ESA's call for White Papers for the definition of Large missions. This was half a year before the launch of ESA's large astrometry mission Gaia. The present proposal for a Gaia successor mission is similar ... More
Estimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integralJun 18 2004When a real-valued function of one variable is approximated by its $n^{th}$ degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are Henstock--Kurzweil integrable. When ... More
Bounds on the Mordell--Weil rank of elliptic curves over imaginary quadratic number fields with class number 1Nov 19 2018We generalize the lemmas of Thomas Kretschmer to arbitrary number fields, and apply them with a 2-descent argument to obtain bounds for families of elliptic curves over certain imaginary quadratic number fields with class number 1. One such family occurs ... More
On work and heat in time-dependent strong couplingMay 22 2017This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known the system then obeys an equation, which in the bulk and ... More
Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugationMar 12 2007Jun 08 2007The exceptional Lie group G_2 acts on the set of real symmetric 7x7-matrices by conjugation. We solve the normal form problem for this group action. In view of earlier results, this gives rise to a classification of all finite-dimensional real flexible ... More
Equity Allocation and Portfolio Selection in Insurance: A simplified Portfolio ModelJul 22 1999A quadratic discrete time probabilistic model, for optimal portfolio selection in (re-)insurance is studied. For positive values of underwriting levels, the expected value of the accumulated result is optimized, under constraints on its variance and on ... More
Isotopes of Hurwitz algebrasDec 08 2010Aug 10 2018We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of isotopes of ... More
Fourier series with the continuous primitive integralMay 27 2011Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of distributions is denoted $\alext$ and is a Banach space under the Alexiewicz ... More
Rapidly growing Fourier integralsJan 02 2001The Riemann-Lebesgue Lemma says that the Fourier transform of an absolutely integrable function on the real line tends to zero as the transform parameter tends to infinity. When the integral is allowed to converge conditionally, the transform can have ... More
Higher Weak Derivatives and Reflexive Algebras of OperatorsApr 14 2015Jul 09 2015Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function < exp(itD)x exp(-itD) a, b> is n-times differentiable. We give several ... More
Robust error estimates for stabilized finite element approximations of the two dimensional Navier-Stokes equations with application to implicit large eddy simulationMar 08 2013Apr 12 2013We consider error estimates in weak parametrised norms for stabilized finite element approximations of the two-dimensional Navier-Stokes' equations. These weak norms can be related to the norms of certain filtered quantities, where the parameter of the ... More
Error estimates for shock capturing finite element approximations of the one dimensional Burgers' equationNov 04 2011May 07 2014We propose an error analysis in weak norms of a shock capturing finite element method for the Burgers' equation. The estimates can be related to estimates of certain filtered quantities and are robust in the inviscid limit. Using a total variation apriori ... More
Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of SetsJan 30 2012Bishop's informal set theory is briefly discussed and compared to Lawvere's Elementary Theory of the Category of Sets (ETCS). We then present a constructive and predicative version of ETCS, whose standard model is based on the constructive type theory ... More
Upper and Lower Bounds on Zero-Sum Generalized Schur NumbersAug 11 2018Let $S_{\mathfrak{z}}(k,r)$ be the least positive integer such that for any $r$-coloring $\chi : \{1,2,\dots,S_{\mathfrak{z}}(k,r)\} \longrightarrow \{1, 2, \dots, r\}$, there is a sequence $x_1, x_2, \dots, x_k$ such that $\sum_{i=1}^{k-1} x_i = x_k$, ... More
Understanding AI Data Repositories with Automatic Query GenerationApr 20 2018We describe a set of techniques to generate queries automatically based on one or more ingested, input corpuses. These queries require no a priori domain knowledge, and hence no human domain experts. Thus, these auto-generated queries help address the ... More
A unified picture of strong coupling stochastic thermodynamics and time reversalsDec 21 2017Jan 02 2018Strong-coupling statistical thermodynamics is formulated as Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics, defined as the ... More
Del Pezzo Surfaces in Weighted Projective SpacesJan 23 2013Nov 15 2016We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.
Categories with families and first-order logic with dependent sortsMay 05 2016Jul 07 2019First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories ... More
Addition formula for 2-parameter family of Askey-Wilson polynomialsDec 07 1994For a two parameter family of Askey-Wilson polynomials, that can be regarded as basic analogues of the Legendre polynomials, an addition formula is derived. The addition formula is a two-parameter extension of Koornwinder's addition formula for the little ... More
A global view of quantum computation with noisy componentsJun 30 2016The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories ... More
On RG-flow and the Cosmological ConstantDec 07 1999Dec 13 1999The AdS/CFT correspondence implies that the effective action of certain strongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation of 5d gravity. Using an analogy with the relativistic point particle, I construct a low energy effective ... More
Global Aspects of Electric-Magnetic DualityJun 01 1995Jun 06 1995We show that the partition function of free Maxwell theory on a generic Euclidean four-manifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one partition function ... More
Ordinary differential equations with only entire solutionsJun 06 1997We prove necessary and sufficient conditions for a system $\dot z_i=z_ip_i(z)$ ($p_i$ a polynomial) to have only entire analytic functions as solutions.
A quantum cloning bound and application to quantum key distributionMar 20 2013Aug 14 2013We introduce a quantum cloning bound which we apply to a straightforward and relatively direct security proof of the prepare-and-measure Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol against collective attacks. The approach we propose ... More
On geometric phases for quantum trajectoriesAug 30 2006A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by using Uhlmann's ... More
Experimentally testable geometric phase of sequences of Everett's relative quantum statesMar 09 2009May 25 2009Everett's concept of relative state is used to introduce a geometric phase that depends nontrivially on entanglement in a pure quantum state. We show that this phase can be measured in multiparticle interferometry. A correlation-dependent generalization ... More
Geometric phase in weak measurementsApr 06 2006Sep 27 2006Pancharatnam's geometric phase is associated with the phase of a complex-valued weak value arising in a certain type of weak measurement in pre- and post-selected quantum ensembles. This makes it possible to test the nontransitive nature of the relative ... More
Geometric phases in quantum informationMar 16 2015Oct 07 2015The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by focusing on three ... More
Nonadiabatic holonomic single-qubit gates in off-resonant $Λ$ systemsNov 03 2015We generalize nonadiabatic holonomic quantum computation in a resonant $\Lambda$ configuration proposed in [New J. Phys. 14 (2012) 103035] to the case of off-resonant driving lasers. We show that any single-qubit holonomic gate can be realized by separately ... More
Stabilised finite element methods for ill-posed problems with conditional stabilityDec 09 2015In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific Computing, and ... More
The Baltic Meetings 1957 to 1967Dec 07 2015The Baltic meetings of astronomers from Northern Germany and Scandinavia began in 1957 and gathered up to 70 participants. Reports of the presentations are available from all meetings, providing an overview of the interests of astronomers in this part ... More
Young astronomer in Denmark 1946 to 1958Dec 07 2015This is a personal account of how I became an astronomer. Fascinated by the stars and planets in the dark sky over Lolland, an island 100 km south of Copenhagen, the interest in astronomy was growing. Encouraged by my teachers, I polished mirrors and ... More
Asymptotic degree distribution of a duplication-deletion random graph modelAug 19 2014We study a discrete-time duplication-deletion random graph model and analyse its asymptotic degree distribution. The random graphs consists of disjoint cliques. In each time step either a new vertex is brought in with probability $0<p<1$ and attached ... More
Classical Black Holes Are HotAug 16 2014Nov 09 2014In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy ... More