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Point-ellipse and some other exotic configurationsMar 14 2019In this paper we introduce point-ellipse configurations and point-conic configurations. We study some of their basic properties and describe two interesting families of balanced point-ellipse, respectively point-conic $6$-configurations. The construction ... More

The Sierpiński product of graphsApr 08 2019In this paper we introduce a product-like operation that generalizes the construction of generalized Sierpi\'nski graphs. Let $G,H$ be graphs and let $f: V(G) \to V(H)$ be a function. Then the Sierpi\'nski product of $G$ and $H$ with respect to $f$ is ... More

Combinatorial configurations, quasiline arrangements, and systems of curves on surfacesOct 09 2014It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this paper we provide ... More

On domains of noncommutative rational functionsAug 08 2016In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities ... More

Matrix coefficient realization theory of noncommutative rational functionsMay 27 2015Apr 21 2018Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressions on tuples of matrices. This interpretation extends their traditional ... More

Stable noncommutative polynomials and their determinantal representationsJul 16 2018Jan 29 2019A noncommutative polynomial is stable if it is nonsingular on all tuples of matrices whose imaginary parts are positive definite. In this paper a characterization of stable polynomials is given in terms of strongly stable linear matrix pencils, i.e., ... More

Integral identities and bounds for scattering calculations in the Dirac formalismOct 27 1998Integral identities that hold between ``desired'' and ``comparison'' solutions of the radial Dirac equations for scattering precesses are considered. Applications of these identities are discussed, particularly the determination of bounds to variational ... More

On domains of noncommutative rational functionsAug 08 2016Nov 17 2016In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities ... More

A variational calculation of particle-antiparticle bound states in the scalar Yukawa modelAug 05 1999Aug 05 1999We consider particle-antiparticle bound states in the scalar Yukawa (Wick-Cutkosky) model. The variational method in the Hamiltonian formalism of quantum field theory is employed. A reformulation of the model is studied, in which covariant Green's functions ... More

Free loci of matrix pencils and domains of noncommutative rational functionsDec 08 2015Sep 27 2016Consider a monic linear pencil $L(x) = I - A_1x_1 - \cdots - A_gx_g$ whose coefficients $A_j$ are $d \times d$ matrices. It is naturally evaluated at $g$-tuples of matrices $X$ using the Kronecker tensor product, which gives rise to its free locus $Z(L) ... More

Some exact solutions of reduced scalar Yukawa theoryJul 02 1998The scalar Yukawa model, in which a complex scalar field interact via a real scalar field, is reduced by using covariant Green functions. It is shown that exact few-particle eigenstates of the truncated QFT Hamiltonian can be obtained in the Feshbach-Villars ... More

Higgs particles interacting via a scalar Dark Matter fieldJun 19 2016We study a system of two Higgs bound state, interacting via a real scalar Dark Matter mediating field, without imposing $Z_2$ symmetry on the DM sector of the postulated Lagrangian. The variational method in the Hamiltonian formalism of QFT is used to ... More

Exact two-particle eigenstates in partially reduced QEDApr 02 2002Nov 18 2010We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be obtained in the canonical ... More

Exact spinor-scalar bound states in a QFT with scalar interactionsDec 21 2000We study two-particle systems in a model quantum field theory, in which scalar particles and spinor particles interact via a mediating scalar field. The Lagrangian of the model is reformulated by using covariant Green's functions to solve for the mediating ... More

Free loci of matrix pencils and domains of noncommutative rational functionsDec 08 2015Sep 24 2017Consider a monic linear pencil $L(x) = I - A_1x_1 - \cdots - A_gx_g$ whose coefficients $A_j$ are $d \times d$ matrices. It is naturally evaluated at $g$-tuples of matrices $X$ using the Kronecker tensor product, which gives rise to its free locus $Z(L) ... More

Exact solutions and triviality of lambda (phi^*phi)^2 theory in the Feshbach-Villars formulationApr 15 1997The complex scalar quantum field theory with a lambda (phi^*phi)^2 interaction is considered in the Feshbach-Villars formulation. It is shown that exact few-particle eigenstates of the QFT Hamiltonian can be obtained. The resulting relativistic few-body ... More

Universal Scaling of the Conductivity at the Superfluid-Insulator Phase TransitionSep 26 2005The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally ... More

Relativistic Three-Fermion Wave Equations in Reformulated QED and Relativistic Effects in Muonium MinusJun 20 2007The variational method, within the Hamiltonian formalism of reformulated QED is used to determine relativistic wave equations for a system of three fermions of arbitrary mass interacting electromagnetically. The interaction kernels of the equations are, ... More

Analysis of inter-quark interactions in classical chromodynamicsDec 15 2011The QCD gluon equation of motion is solved approximately by means of the Green function. This solution is used to reformulate the Lagrangian of QCD such that the gluon propagator appears directly in the interaction terms of the Lagrangian. The nature ... More

Confinement interaction in nonlinear generalizations of the Wick-Cutkosky modelOct 23 2009Nov 18 2010We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky model. Using an iterative approach and eliminating the mediating field by means of the covariant Green function we arrive at a Lagrangian density containing many-point time-nonlocal ... More

Effect of Virtual Pairs on the Inter-quark PotentialSep 10 2013We use the variational method, in a reformulated Hamiltonian formalism of QCD, to derive the wave equation for a heavy quark-antiquark system using a trial state that contains a component with a virtual light quark pair. We examine the quark-antiquark ... More

Higgs particles interacting via a scalar Dark Matter fieldJun 19 2016Nov 04 2016We study a system of two Higgs bound state, interacting via a real scalar Dark Matter mediating field, without imposing $Z_2$ symmetry on the DM sector of the postulated Lagrangian. The variational method in the Hamiltonian formalism of QFT is used to ... More

Inter-particle potentials in a scalar QFT with a Higgs-like mediating fieldApr 25 2011May 15 2012We study the inter-particle potentials for few-particle systems in a scalar theory with a non-linear mediating field of the Higgs type. We use the variational method, in a reformulated Hamiltonian formalism of QFT, to derive relativistic three and four ... More

Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QEDMar 27 2003Jan 02 2004We present a variational method for deriving relativistic two-fermion wave equations in a Hamiltonian formulation of QED. A reformulation of QED is performed, in which covariant Green functions are used to solve for the electromagnetic field in terms ... More

Multipartite rational functionsSep 10 2015Consider a tensor product of free algebras over a field $k$, the so-called multipartite free algebra $A=k \langle X^{(1)}\rangle\otimes\cdots\otimes k\langle X^{(G)}\rangle$. It is well-known that $A$ is a domain, but not a fir nor even a Sylvester domain. ... More

STM measurement of single spin relaxation time in superconductorsApr 26 2001Localized spin states in conventional superconductors at low temperatures are expected to have long decoherence time due to the strong suppression of spin relaxation channels. We propose a scanning tunneling microscopy (STM) experiment allowing the direct ... More

Positive trace polynomials and the universal Procesi-Schacher conjectureFeb 06 2017May 19 2018Positivstellensatz is a fundamental result in real algebraic geometry providing algebraic certificates for positivity of polynomials on semialgebraic sets. In this article Positivstellens\"atze for trace polynomials positive on semialgebraic sets of $n\times ... More

Geometry of free loci and factorization of noncommutative polynomialsAug 17 2017Apr 02 2018The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if $Z_n(f)$ is eventually irreducible. ... More

Regular and positive noncommutative rational functionsMay 10 2016Call a noncommutative rational function $r$ regular if it has no singularities, i.e., $r(X)$ is defined for all tuples of self-adjoint matrices $X$. In this article regular noncommutative rational functions $r$ are characterized via the properties of ... More

Null- and Positivstellensätze for rationally resolvable idealsApr 29 2015Hilbert's Nullstellensatz characterizes polynomials that vanish on the vanishing set of an ideal in C[x]. In the free algebra C<X> the vanishing set of a two-sided ideal I is defined in a dimension-free way using images in finite-dimensional representations ... More

Regular and positive noncommutative rational functionsMay 10 2016Dec 23 2016Call a noncommutative rational function $r$ regular if it has no singularities, i.e., $r(X)$ is defined for all tuples of self-adjoint matrices $X$. In this article regular noncommutative rational functions $r$ are characterized via the properties of ... More

Variational Two Fermion Wave Equations in QED: Muonium Like SystemsNov 10 2003We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-state variational ... More

Multipartite rational functionsSep 10 2015Sep 13 2018Consider a tensor product of free algebras over a field $k$, the so-called multipartite free algebra $A=k \langle X^{(1)}\rangle\otimes\cdots\otimes k\langle X^{(G)}\rangle$. It is well-known that $A$ is a domain, but not a fir nor even a Sylvester domain. ... More

Null- and Positivstellensätze for rationally resolvable idealsApr 29 2015Apr 11 2017Hilbert's Nullstellensatz characterizes polynomials that vanish on the vanishing set of an ideal in C[x]. In the free algebra C<X> the vanishing set of a two-sided ideal I is defined in a dimension-free way using images in finite-dimensional representations ... More

CCD based phase resolved stroboscopic photometry of pulsarsMar 17 2003A stroboscope designed to observe pulsars in the optical spectrum is presented. The absolute phase of the stroboscope is synchronized to better than 2.5 microseconds with the known radio ephemerides for a given pulsar. The absolute timing is provided ... More

Josephson scanning tunneling microscopySep 20 2000We propose a set of scanning tunneling microscopy experiments in which the surface of superconductor is scanned by a superconducting tip. Potential capabilities of such experimental setup are discussed. Most important anticipated results of such an experiment ... More

Application of the Eckart frame to soft matter: rotation of star polymers under shear flowJul 28 2017The Eckart co-rotating frame is used to analyze the dynamics of star polymers under shear flow, either in melt or solution and with different types of bonds. This formalism is compared with the standard approach used in many previous studies on polymer ... More

A quantum Monte Carlo algorithm for softcore boson systemsJan 22 2003An efficient Quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin quantum number. ... More

Skolem-Noether algebrasJun 27 2017An algebra $S$ is called a Skolem-Noether algebra (SN algebra for short) if for every central simple algebra $R$, every homomorphism $R\to R\otimes S$ extends to an inner automorphism of $R\otimes S$. One of the important properties of such an algebra ... More

Hyperfine Structure and Zeeman Splitting in Two-Fermion Bound-State SystemsJan 28 2007A relativistic wave equation for bound states of two fermions with arbitrary masses which are exposed to a magnetic field is derived from quantum electrodynamics. The interaction kernels are based upon the generalized invariant M-matrices for inter-fermion ... More

Relativistic wave equations of n-body systems of fermions and antifermions of various masses in quantum electrodynamicsSep 20 2013The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels of these equations ... More

Non-linear mechanical response of the Red Blood CellOct 17 2007We measure the dynamical mechanical properties of human red blood cells. Single cell response is measured with optical tweezers. We investigate both the stress relaxation following a fast deformation, and the effect of varying the strain rate. We find ... More

Binding of holons and spinons in the one-dimensional anisotropic t-J modelFeb 08 2007Jun 29 2007We study the binding of a holon and a spinon in the one-dimensional anisotropic t-J model using a Bethe-Salpeter equation approach, exact diagonalization, and density matrix renormalization group methods on chains of up to 128 sites. We find that holon-spinon ... More

Optical trapping of colloids at a liquid-liquid interfaceMar 23 2017We demonstrate the realization of (laterally) optically bounded colloidal structures on a liquid-liquid interface of an emulsion droplet. We use DNA tethers to graft the particles to the droplet surface, effectively confining them to a quasi-2D plane ... More

Real-time monitoring of complex moduli from micro-rheologyOct 06 2010Nov 09 2010We describe an approach to online analysis of micro-rheology data using a multi-scale time-correlation method. The method is particularly suited to process high-volume data streams and compress the relevant information in real time. Using this, we can ... More

Bound-State Variational Wave Equation For Fermion Systems In QEDApr 10 2006We present a formulation of the Hamiltonian variational method for QED which enables the derivation of relativistic few-fermion wave equation that can account, at least in principle, for interactions to any order of the coupling constant. We derive a ... More

Bianalytic free maps between spectrahedra and spectraballsApr 25 2018Dec 01 2018Linear matrix inequalities (LMIs) are ubiquitous in real algebraic geometry, semidefinite programming, control theory and signal processing. LMIs with (dimension free) matrix unknowns, called free LMIs, are central to the theories of completely positive ... More

Spinon-holon interactions in an anisotropic t-J chain: a comprehensive studyMay 22 2007Sep 10 2007We consider a generalization of the one-dimensional t-J model with anisotropic spin-spin interactions. We show that the anisotropy leads to an effective attractive interaction between the spinon and holon excitations, resulting in a localized bound state. ... More

2D colloidal condensation driven by substrate elasticityNov 05 2010May 12 2011This paper has been withdrawn by the authors.

Relativistic corrections to the Zeeman splitting of hyperfine structure levels in two-fermion bound-state systemsMay 26 2008A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to the g-factor ... More

Mechanical effects in quantum dots in magnetic and electric fieldsJan 10 2001The mechanical effects in finite two-dimensional electron systems (quantum dots or droplets) in a strong perpendicular magnetic field are studied. It is shown that, due to asymmetry of the cyclotron dynamics, an additional in-plane electric field causes ... More

Stochastic model of dispersive multi-step polarization switching in ferroelectrics due to spatial electric field distributionApr 26 2019A stochastic model for polarization switching in tetragonal ferroelectric ceramics is introduced, which includes sequential 90{\deg}- and parallel 180{\deg}-switching processes and accounts for the dispersion of characteristic switching times due to a ... More

Minimal two-sphere model of the generation of fluid flow at low Reynolds numbersOct 19 2009May 31 2010Locomotion and generation of flow at low Reynolds number are subject to severe limitations due to the irrelevance of inertia: the "scallop theorem" requires that the system have at least two degrees of freedom, which move in non-reciprocal fashion, i.e. ... More

QMC Calculation of the Electronic Binding Energy in a C60 MoleculeNov 16 2004Electronic energies are calculated for a Hubbard model on the $C_{60}$ molecule using projector quantum Monte Carlo (QMC). Calculations are performed to accuracy high enough to determine the pair binding energy for two electrons added to neutral $C_{60}$. ... More

Imaginary chemical potential quantum Monte Carlo for Hubbard moleculesDec 22 2004Dec 23 2004We generalize the imaginary chemical potential quantum Monte Carlo (QMC) method proposed by Dagotto et al. [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations ... More

Multistep kinetic self-assembly of DNA-coated colloidsFeb 22 2013Self-assembly is traditionally described as the process through which an initially disordered system relaxes towards an equilibrium ordered phase only driven by local interactions between its building blocks. However, This definition is too restrictive. ... More

Enhancement of the electrocaloric cooling by electric field reversal: simulation and experimentMar 25 2016Jul 11 2016An improved thermodynamic cycle is proposed, where the cooling effect of an electrocaloric refrigerant is enhanced by applying a reversed electric field. In contrast to conventional adiabatic heating or cooling by on-off cycles of the external electric ... More

Hydrodynamically synchronized states in active colloidal arraysOct 07 2011Oct 10 2011Colloidal particles moving in a fluid interact via the induced velocity field. The collective dynamic state for a class of actively forced colloids, driven by harmonic potentials via a rule that couples forces to configurations, to perform small oscillations ... More

Volume and porosity thermal regulation in lipid mesophases by coupling mobile ligands to soft membranesJul 21 2014Jan 09 2015Short DNA linkers are increasingly being exploited for driving specific self-assembly of Brownian objects. DNA-functionalised colloids can assemble into ordered or amorphous materials with tailored morphology. Recently, the same approach has been applied ... More

Long-range interactions and phase defects in chains of fluid-coupled oscillatorsJun 02 2016Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient ... More

Interactions between colloids induced by a soft cross-linked polymer substrateJun 20 2011Using video-microscopy imaging we demonstrate the existence of a short-ranged equilibrium attraction between heavy silica colloids diffusing on soft surfaces of cross-linked polymer gels. The inter-colloid potential can be tuned by changing the gel stiffness ... More

Analyzing Hypersensitive AI: Instability in Corporate-Scale Machine LearningJul 17 2018Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied to large datasets. ... More

Orbital-dependent electron dynamics in Fe-pnictide superconductorsNov 15 2017May 04 2018We report on orbital-dependent quasiparticle dynamics in EuFe$_2$As$_2$, a parent compound of Fe-based superconductors and a novel way to experimentally identify this behavior, using time- and angle-resolved photoelectron spectroscopy across the spin ... More