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Normal Vectors on Modified Hopf Manifolds of Delay Differential EquationsMar 13 2019This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled "Robust optimization of delay ... More

A method for the optimization of nonlinear systems with delays that guarantees stability and robustnessMar 13 2019We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we ensure stability ... More

Bounding Search Space Size via (Hyper)tree DecompositionsJun 13 2012This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to exploit determinism ... More

Partial Hölder continuity for Q-valued energy minimizing mapsFeb 11 2014We consider multivalued maps between $\Omega \subset \mathbb{R}^N$ open ($N \ge 2$) and a smooth, compact Riemannian manifold $\mathcal{N}$ locally minimizing the Dirichlet energy. An interior partial H\"older regularity result in the spirit of R. Schoen ... More

On the integral kernels of derivatives of the Ornstein-Uhlenbeck semigroupSep 18 2015This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein-Uhlenbeck semigroup $e^{tL}$. Our approach is to expand the Mehler kernel into Hermite polynomials and applying the powers $L^N$ of the ... More

Non-leptonic D0, D+, and Ds Branching FractionsFeb 15 2010Non-leptonic charm decays provide insights into both electro-weak and strong dynamics. This includes the study of long-distance hadronic effects, the approximate symmetries of strong interactions, and precision tests of the Standard Model. In these proceedings ... More

Electromagnetics from a quasistatic perspectiveJun 13 2006Quasistatics is introduced so that it fits smoothly into the standard textbook presentation of electrodynamics. The usual path from statics to general electrodynamics is rather short and surprisingly simple. A closer look reveals however that it is not ... More

Most Frequent Itemset OptimizationApr 16 2019In this paper we are dealing with the frequent itemset mining. We concentrate on the special case that we only want to identify the most frequent itemset of length N. To do that, we present a pattern on how to consider this search as an optimization problem. ... More

Efficient ray tracing on 3D regular grids for fast generation of digitally reconstructed radiographs in iterative tomographic reconstruction techniquesSep 04 2016Cone beam projection is an essential and particularly time consuming part of any iterative tomographic reconstruction algorithm. On current graphics hardware especially the amount and pattern of memory accesses is a limiting factor when read-only textures ... More

Computing partial transposes and related entanglement functionsSep 01 2016Nov 07 2016The partial transpose (PT) is an important function for entanglement testing and quantification and also for the study of geometrical aspects of the quantum state space. In this article, considering general bipartite and multipartite discrete systems, ... More

Fortran code for generating random probability vectors, unitaries, and quantum statesDec 16 2015Mar 14 2016The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards ... More

The Maccone-Pati uncertainty relationMay 25 2017Jun 07 2017The existence of incompatible observables constitutes one of the most prominent characteristics of quantum mechanics (QM) and can be revealed and formalized through uncertainty relations. The Heisenberg-Robertson-Schr\"odinger uncertainty relation (HRSUR) ... More

On the use of shot noise for photon countingJan 14 2015Feb 24 2015Lieu et al. (2015) have recently claimed that it is possible to substantially improve the sensitivity of radio astronomical observations. In essence, their proposal is to make use of the intensity of the photon shot noise as a measure of the photon arrival ... More

Resolving multi-proxy transitive vote delegationDec 11 2014Solving a delegation graph for transitive votes is already a non-trivial task for many programmers. When extending the current main paradigm, where each voter can only appoint a single transitive delegation, to a system where each vote can be separated ... More

Characteristic (Fedosov-)class of a twist constructed by Drinfel'dMar 15 2019In a seminal paper Drinfel'd explained how to associate to every classical r-matrix for a Lie algebra $\lie g$ a twisting element based on $\mathcal{U}(\lie g)[[\hbar]]$, or equivalently a left invariant star product of the corresponding symplectic structure ... More

Cylindrical lattice paths and the Loehr-Warrington 10^n conjectureSep 22 2005Sep 30 2005The following special case of a conjecture by Loehr and Warrington was proved recently by Ekhad, Vatter, and Zeilberger: There are 10^n zero-sum words of length 5n in the alphabet {+3,-2} such that no zero-sum consecutive subword that starts with +3 may ... More

Classification of certain cellular classes of chain complexesJan 25 2008Let (R, m) be a local commutative ring. Suppose that m is principal and that m^2 = 0. We give a complete description of the cellular lattice of perfect chain complexes of modules over this ring.

Most Frequent Itemset OptimizationApr 16 2019Apr 17 2019In this paper we are dealing with the frequent itemset mining. We concentrate on the special case that we only want to identify the most frequent itemset of length N. To do that, we present a pattern on how to consider this search as an optimization problem. ... More

From geometry to geology: An invitation to mathematical pluralism through the phenomenon of independenceSep 01 2016This paper explores how a pluralist view can arise in a natural way out of the day-to-day practice of modern set theory. By contrast, the widely accepted orthodox view is that there is an ultimate universe of sets $V$, and it is in this universe that ... More

The Ground AxiomSep 02 2006A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set-forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class-forcing extension which satisfies it. The ... More

On the Structure of Double ComplexesDec 03 2018We provide a proof of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags and show how it makes questions about the associated cohomology groups and spectral sequences easy to understand. This may ... More

Jahn-Teller systems from a cavity QED perspectiveApr 28 2008Sep 23 2008Jahn-Teller systems and the Jahn-Teller effect are discussed in terms of cavity QED models. By expressing the field modes in a quadrature representation, it is shown that certain setups of a two-level system interacting with a bimodal cavity is described ... More

Diode for Bose-Einstein condensatesMay 13 2011Nov 18 2011Given a quantum state at some instant of time t, the underlying system Hamiltonian can not only predict how the state will evolve, but also the history of the state prior to t. Thereby, in order to have a directed motion, like in a diode, some sort of ... More

Harmonic morphisms and eigenfamilies on the exceptional Lie group G2Aug 31 2013We construct harmonic morphisms on the compact simple Lie group G2. The construction uses eigenfamilies in a representation theoretic scheme.

Equivariant birational geometry of quintic del Pezzo surfaceAug 16 2018In this paper we prove that there are exactly two $G$-minimal surfaces which are $G$-birational to the quintic del Pezzo surface, where $G \cong C_5 \rtimes C_4$. These surfaces are the quintic del Pezzo surface itself and the surface $\mathbb{P}^1 \times ... More

Cohomology of moduli spaces of curves of genus three via point countsNov 27 2006Jun 05 2007In this article we consider the moduli space of smooth $n$-pointed non-hyperelliptic curves of genus 3. In the pursuit of cohomological information about this space, we make $\mathbb{S}_n$-equivariant counts of its numbers of points defined over finite ... More

On the well-posedness of Bayesian inverse problemsFeb 26 2019The subject of this article is the introduction of a weaker concept of well-posedness of Bayesian inverse problems. The conventional concept of (`Lipschitz') well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice, ... More

On the sign-imbalance of skew partition shapesJul 16 2005Sep 18 2006Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan ... More

Bi-Lipschitz parts of quasisymmetric mappingsAug 02 2013Feb 27 2015A natural quantity that measures how well a map $f:\mathbb{R}^{d}\rightarrow \mathbb{R}^{D}$ is approximated by an affine transformation is \[\omega_{f}(x,r)=\inf_{A}\left(\frac{1}{|B(x,r)|}\int_{B(x,r)}\left(\frac{|f-A|}{|A'|r}\right)^{2}\right)^{\frac{1}{2}},\] ... More

Making multigraphs simple by a sequence of double edge swapsApr 15 2019A double edge swap is an operation on (undirected) loopy multigraphs (multiple edges and multiple loops are allowed) that replaces two edges $(v_1,v_2)$ and $(v_3,v_4)$ by $(v_2,v_3)$ and $(v_4,v_1)$. The swap is admissible if $(v_1,v_2)$ and $(v_3,v_4)$ ... More

Expected length of a product of random reflectionsNov 24 2010We present a simple formula for the expected number of inversions in a permutation of size $n$ obtained by applying $t$ random (not necessarily adjacent) transpositions to the identity permutation. More general, for any finite irreducible Coxeter group ... More

Boundary regularity of Dirichlet minimizing Q-valued functionsFeb 11 2014We consider the H\"older continuity for the Dirichlet problem at the boundary. Almgren introduced the multivalued; Q-valued functions for studying regularity of minimal surfaces in higher codimension. The H\"older continuity in the interior for Dirichlet ... More

A new method for constructing Anosov Lie algebrasDec 10 2013Jan 12 2015It is conjectured that every manifold admitting an Anosov diffeomorphism is, up to homeomorphism, finitely covered by a nilmanifold. Motivated by this conjecture, an important problem is to determine which nilmanifolds admit an Anosov diffeomorphism. ... More

A note on the Gaussian maximal functionsNov 20 2013Jul 08 2014This note presents a proof that the non-tangential maximal function of the Ornstein-Uhlenbeck semigroup is bounded almost surely by the Gaussian Hardy-Littlewood maximal function. In particular this entails improvement on a result by Pineda and Urbina ... More

A fibrational study of realizability toposesMar 14 2014This is the author's PhD thesis. It is a contribution to categorical logic, in particular to the theory of realizability toposes. While the tools of categorical logic have proven very successful in analyzing and organizing proof theoretic realizability ... More

Complete classification of 2-ramified power seriesJan 14 2016Mar 21 2016In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding lower ramification ... More

Clean positive operator valued measures for qubits and similar casesMar 14 2006Mar 22 2007In a recent paper, Buscemi and al. defined a notion of clean positive operator valued measures (POVMs). We here characterize which POVMs are clean in some class that we call quasi-qubit POVMs, namely POVMs whose elements are all rank-one or full-rank. ... More

Reduction of Statistical Power Per Event Due to Upper Lifetime Cuts in Lifetime MeasurementsFeb 25 2005Feb 09 2007A cut on the maximum lifetime in a lifetime fit not only reduces the number of events, but also, in some circumstances dramatically, decreases the statistical significance of each event. The upper impact parameter cut in the hadronic B trigger at CDF, ... More

The cover pebbling theoremOct 06 2004For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a cover pebbling ... More

Realizability Toposes from SpecificationsApr 24 2015We investigate a framework of Krivine realizability with I/O effects, and present a method of associating realizability models to specifications on the I/O behavior of processes, by using adequate interpretations of the central concepts of `pole' and ... More

Learning a Predictive Model for Music Using PULSESep 26 2017Predictive models for music are studied by researchers of algorithmic composition, the cognitive sciences and machine learning. They serve as base models for composition, can simulate human prediction and provide a multidisciplinary application domain ... More

Computing coherence vectors and correlation matrices, with application to quantum discord quantificationMar 16 2016Jun 30 2016Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a ... More

The Kraus representation for the dynamics of open quantum systemsOct 30 2015May 11 2016The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a general and ... More

Non-monotonicity of trace distance under tensor productsMar 10 2015Aug 21 2015The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible ... More

The Double Complex of a Blow-upAug 08 2018We compute the double complex of smooth complex-valued differential forms on projective bundles over and blow-ups of compact complex manifolds up to a suitable notion of quasi-isomorphism. This simultaneously yields formulas for 'all' cohomologies naturally ... More

Tangents, rectifiability, and corkscrew domainsMay 15 2015Dec 28 2016In a recent paper, Cs\"ornyei and Wilson prove that curves in Euclidean space of $\sigma$-finite length have tangents on a set of positive $\mathscr{H}^{1}$-measure. They also show that a higher dimensional analogue of this result is not possible without ... More

Hausdorff dimension of wiggly metric spacesMar 29 2013Jan 27 2014For a compact connected set $X\subseteq \ell^{\infty}$, we define a quantity $\beta'(x,r)$ that measures how close $X$ may be approximated in a ball $B(x,r)$ by a geodesic curve. We then show there is $c>0$ so that if $\beta'(x,r)>\beta>0$ for all $x\in ... More

Semi-uniform domains and the $A_{\infty}$ property for harmonic measureNov 08 2017Aug 28 2018We study the properties of harmonic measure in semi-uniform domains. Aikawa and Hirata showed in \cite{AH08} that, for John domains satisfying the capacity density condition (CDC), the doubling property for harmonic measure is equivalent to the domain ... More

Dimension drop for harmonic measure on Ahlfors regular boundariesNov 09 2018Dec 17 2018We show that given a domain $\Omega\subseteq \mathbb{R}^{d+1}$ with uniformly non-flat Ahlfors $s$-regular boundary and $s\geq d$, the dimension of its harmonic measure is strictly less than $s$.

A nonrelativistic quantum field theory with point interactions in three dimensionsApr 23 2018May 17 2019We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction between the two types ... More

Convergence of nodal sets in the adiabatic limitMay 08 2014Nov 09 2014We study the nodal sets of non-degenerate eigenfunctions of the Laplacian on fibre bundles $\pi{:}\, M\to B$ in the adiabatic limit. This limit consists in considering a family $G_\varepsilon$ of Riemannian metrics, that are close to Riemannian submersions, ... More

An Exact Formula to Describe the Amplification Process in a Photomultiplier TubeJun 08 2004An analytical function is derived that exactly describes the amplification process due to a series of discrete, Poisson-like amplifications like those in a photo multiplier tube (PMT). A numerical recipe is provided that implements this function as a ... More

B Physics at CDFJun 07 2004Due to the large b-bbar cross section at 1.96 TeV p-pbar collisions, the Tevatron is currently the most copious source of B hadrons. Recent detector upgrades for Run II have made these more accessible, allowing for a wide range of B and CP violation physics ... More

The Complexity of Simple Stochastic GamesApr 20 2007In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.

Graded Betti numbers and $h$-vectors of level modulesDec 04 2006Dec 04 2006We study $h$-vectors and graded Betti numbers of level modules up to multiplication by a rational number. Assuming a conjecture on the possible graded Betti numbers of Cohen-Macaulay modules we get a description of the possible $h$-vectors of level modules ... More

Gaussian fluctuations of eigenvalues in the GUEJan 08 2004Apr 04 2007Under certain conditions on k we calculate the limit distribution of the k:th largest eigenvalue, x_k, of the Gaussian Unitary Ensemble (GUE). More specifically, if n is the dimension of a random matrix from the GUE and k is such that both k and n-k tends ... More

Pluricomplex charge at weak singularitiesOct 31 2005Let $u$ be a plurisubharmonic function, defined on a neighbourhood of a point $x,$ such that the complex Monge-Amp\`ere operator is well-defined on $u.$ Suppose also that $u$ has a weak singularity, in the sense that the Lelong number of $u$ at $x$ vanish. ... More

NIL-affine crystallographic actions of virtually polycyclic groupsOct 26 2018A classical result by K.B. Lee states that every group morphism between almost crystallographic groups is induced by an affine map on the nilpotent Lie group whereon these groups by definition act. It is the main technique for studying morphisms between ... More

A note on the structure of underlying Lie algebrasJan 29 2019Every Lie algebra over a field $E$ gives rise to new Lie algebras over any subfield $F \subseteq E$ by restricting the scalar multiplication. This paper studies the structure of these underlying Lie algebra in relation to the structure of the original ... More

Cross ratios on boundaries of symmetric spaces and Euclidean buildingsJan 31 2017Jul 11 2018We generalize the natural cross ratio on the ideal boundary of a rank one symmetric spaces, or even $\mathrm{CAT}(-1)$ space, to higher rank symmetric spaces and (non-locally compact) Euclidean buildings - we obtain vector valued cross ratios defined ... More

Characterization of 2-ramified power seriesJan 14 2016Apr 20 2017In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding lower ramification ... More

Improper poisson line process as sirsn in any dimensionMar 13 2015Sep 29 2016Aldous has introduced a notion of scale-invariant random spatial network (SIRSN) as a mathematical formalization of road networks. Intuitively, those are random processes that assign a route between each pair of points in Euclidean space, while being ... More

Random Sampling of Quantum States: A Survey of MethodsFeb 12 2015Oct 30 2015The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating ... More

On the values of unipotent characters of finite Chevalley groups of type $E_6$ in characteristic 3Jan 18 2019Let $G$ be a finite Chevalley group. We are concerned with computing the values of the unipotent characters of $G$ by making use of Lusztig's theory of character sheaves. In this framework, one has to find the transformation between several bases for ... More

How many T-tessellations on $k$ lines? Existence of associated Gibbs measures on bounded convex domainsDec 10 2010Apr 23 2014The paper bounds the number of tessellations with T-shaped vertices on a fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms retrieve them, proving injectivity. This yields existence of a completely random T-tessellation, as ... More

Anomalous decoherence and absence of thermalization in a photonic many-body systemMar 04 2011The intention of this work is twofold, first to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons, and second to study various outcomes deriving from inherent or external decoherence. A qubit induces ... More

Travelling to exotic places with cavity QED systemsAug 12 2009Recent theoretical schemes for utilizing cavity QED models as quantum simulators are reviewed. By considering a quadrature representation for the fields, it is shown how Jahn-Teller models, effective Abelian or non-Abelian gauge potentials, transverse ... More

Analog of the spin-orbit induced anomalous Hall effect with quantized radiationMay 18 2009May 27 2010We demonstrate how the term describing interaction between a single two-level atom and two cavity field modes may attain a Rashba form. As an outcome, cavity QED provides a testbed for studies of phenomena reminiscent of the spin-orbit induced anomalous ... More

On the rotating wave approximation in the adiabatic limitAug 09 2012I revisit a longstanding question in quantum optics; When is the rotating wave approximation justified? In terms of the Jaynes-Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system ... More

The Ground Axiom (GA)Sep 10 2006Feb 21 2007A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class forcing extension which satisfies it. The ... More

Idiomatic and Reproducible Software Builds using Containers for Reliable ComputingFeb 09 2017Containers as the unit of application delivery are the 'next big thing' in the software development world. They enable developers to create an executable image containing an application bundled with all its dependencies which a user can run inside a controlled ... More

Computing partial transposes and related entanglement functionsSep 01 2016The partial transpose (PT) is an important function for entanglement testing and quantification and also for the study of geometrical aspects of the quantum state space. In this article, considering general bipartite and multipartite discrete systems, ... More

Measuring CP violation in 3- and 4-body decaysDec 17 2013Multibody charm decays have a rich phenomenology and potentially unique sensitivity to CP violation. In these proceedings we discuss recent results, challenges and prospects in searches for CP violation in three and four body charm decays.

Fast rate estimation of an unitary operation in SU(d)Mar 13 2006Feb 05 2007We give an explicit procedure based on entangled input states for estimating a $SU(d)$ operation $U$ with rate of convergence $1/N^2$ when sending $N$ particles through the device. We prove that this rate is optimal. We also evaluate the constant $C$ ... More

Heavy Flavour Lifetimes and Lifetime DifferencesJun 26 2003Oct 28 2003We give an overview of heavy flavour lifetime measurements, focusing on recent results from the Tevatron and the B factories.

Tangents, rectifiability, and corkscrew domainsMay 15 2015Dec 27 2015In a recent paper, Cs\"ornyei and Wilson prove that curves in Euclidean space of $\sigma$-finite length have tangents on a set of positive $\mathscr{H}^{1}$-measure. They also show that a higher dimensional analogue of this result is not possible without ... More

A Characterization of Realizability ToposesApr 28 2014Realizability toposes over partial combinatory algebras (PCAs) were introduced in 1980 by Hyland, Johnstone, and Pitts, and they are important in categorical logic as models of non-classical logics and type systems. Except for the trivial case of $\mathbf{Set}$, ... More

Strings as sigma models and in the tensionless limitMay 16 2007This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models. The tensionless limit is used to find a IIB supergravity background generated by a tensionless string. Quantization of the ... More

T-duality and Generalized Complex GeometryDec 05 2006Mar 26 2007We find the explicit T-duality transformation in the phase space formulation of the N=(1,1) sigma model. We also show that the T-duality transformation is a symplectomorphism and it is an element of O(d,d). Further, we find the explicit T-duality transformation ... More

Multi-loop amplitudes in maximally supersymmetric pure spinor field theorySep 29 2010This paper provides a more detailed background to the results of arXiv:1004.2692 concerning properties of multi-loop amplitudes in a pure spinor formulation of field theories with maximal supersymmetry. This involves the development of a first quantised ... More

A complete description of the antipodal set of most symmetric spaces of compact typeMar 29 2016It is known that the antipodal set of a Riemannian symmetric space of compact type $G/ K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we ... More

A note on reduced and von Neumann algebraic free wreath productsNov 18 2014In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix quantum group. Based on recent result on their corepresentation ... More

Computer Algebra for MicrohydrodynamicsAug 19 2017I describe a method for computer algebra that helps with laborious calculations typically encountered in theoretical microhydrodynamics. The program mimics how humans calculate by matching patterns and making replacements according to the rules of algebra ... More

Elicitability and its Application in Risk ManagementJul 30 2017Elicitability is a property of $\mathbb{R}^k$-valued functionals defined on a set of distribution functions. These functionals represent statistical properties of a distribution, for instance its mean, variance, or median. They are called elicitable if ... More

Computing partial traces and reduced density matricesJan 27 2016Aug 23 2016Taking partial traces for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this article, we present a thorough description of this function and analyze the number of ... More

Generating pseudo-random discrete probability distributionsFeb 07 2015Jul 01 2015The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in quantum information ... More

Circuit QED scheme for realization of the Lipkin-Meshkov-Glick modelApr 28 2010Jun 17 2010We propose a scheme in which the Lipkin-Meshkov-Glick model is realized within a circuit QED system. An array of N superconducting qubits interacts with a driven cavity mode. In the dispersive regime, the cavity mode is adiabatically eliminated generating ... More

Scheme for generating entangled states of two field modes in a cavityAug 11 2005Apr 15 2006This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes-Cummings model. For some particular field states, coherent and squeezed ... More

Wave packet methods in cavity QEDNov 15 2007The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled harmonic oscillators, ... More

Curvature conditions for complex-valued harmonic morphismsFeb 20 2014Oct 31 2014We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental ... More

A nonrelativistic quantum field theory with point interactions in three dimensionsApr 23 2018Oct 01 2018We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction between the two types ... More

A complete description of the antipodal set of most symmetric spaces of compact typeMar 29 2016Jan 25 2017It is known that the antipodal set of a Riemannian symmetric space of compact type $G / K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we ... More

On the holonomy groups of Weyl manifoldsOct 15 2014Jun 12 2015We classify the possible local holonomy groups of Weyl connections. The Berger-Simons theorem and the Merkulov-Schwachh\"ofer classification of holonomy groups of irreducible torsion-free connections leaves us with the remaining case, where the Weyl connection ... More

On the sign-imbalance of partition shapesSep 15 2003Sep 30 2005Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2^[n/2]. We present ... More

Non-existence of a Wente's $L^\infty$ estimate for the Neumann problemJul 10 2017Dec 19 2017We provide a counterexample of Wente's inequality in the context of Neumann boundary conditions. We will also show that Wente's estimates fails for general boundary conditions of Robin type.

Monte Carlo Simulations of Higgs-Fermion SystemsApr 08 1992To gain understanding of the Higgs-fermion sector of the standard model, we study the one-component $Z_2$ symmetric and the four-component O(4) symmetric scalar models coupled to staggered fermions using the hybrid Monte Carlo algorithm. We map out the ... More

Analytic Performance Model of a Main-Memory Index StructureSep 05 2016Efficient evaluation of multi-dimensional range queries in a main-memory database is an important, but difficult task. State-of-the-art techniques rely on optimised sequential scans or tree-based structures. For range queries with small result sets, sequential ... More

Mean-field quantum dynamics with magnetic fieldsFeb 06 2012Jul 15 2012We consider a system of $N$ bosons in three dimensions interacting through a mean-field Coulomb potential in an external magnetic field. For initially factorized states we show that the one-particle density matrix associated with the solution of the $N$-body ... More

Characterization of 2-ramified power seriesJan 14 2016Nov 27 2016In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding lower ramification ... More

Distribution of Mutual Information in Multipartite StatesAug 21 2013Feb 13 2014Using the relative entropy of total correlation, we derive an expression relating the mutual information of $n$-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by ... More