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Thermal contribution of unstable statesFeb 08 2019Within the framework of the Lee model, we analyze in detail the difference between the energy derivative of the phase shift and the standard spectral function of the unstable state. The fact that the model is exactly solvable allows us to demonstrate ... More

Polyakov loop fluctuations in SU(3) lattice gauge theory and an effective gluon potentialJul 23 2013We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctu- ations of the Polyakov loop, as well as, that of its absolute ... More

Probing Deconfinement with Polyakov Loop SusceptibilitiesJun 21 2013The susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop, are computed in SU(3) lattice gauge theory. We show that the ratios of these susceptibilities are excellent probes of the deconfinement transition, independent ... More

Restoration of tetragonal $C_4$ symmetry coexistent with filamentary superconductivity in the pressure induced intermediate phase in the iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$Jul 07 2015Jul 09 2015The hole doped Fe-based superconductors Ba$_{1-x}$A$_x$Fe$_2$As$_2$ (where A=Na or K) show a particular rich phase diagram. It was observed that an intermediate re-entrant tetragonal phase forms within the orthorhombic antiferromagnetically-ordered stripe-type ... More

Polyakov loop fluctuations and deconfinement in the limit of heavy quarksJun 16 2014We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows ... More

Confinement Models at Finite Temperature and DensityAug 27 2009Feb 12 2010In-medium chiral symmetry breaking in confining potential models of QCD is examined. Past attempts to analyse these models have been hampered by infrared divergences that appear at non-zero temperature. We argue that previous attempts to circumvent this ... More

Matching the Hagedorn mass spectrum with Lattice QCD resultsJul 23 2015Nov 06 2015Based on recent Lattice QCD (LQCD) results obtained at finite temperature, we discuss modeling of the hadronic phase of QCD in the framework of Hadron Resonance Gas (HRG) with discrete and continuous mass spectra. We focus on fluctuations of conserved ... More

Strangeness fluctuations from $K-π$ interactionsJul 15 2015Nov 06 2015Motivated by recent lattice QCD studies, we explore the effects of interactions on strangeness fluctuations in strongly interacting matter at finite temperature. We focus on S-wave $K\pi$ scattering and discuss the role of the $K_0^*(800)$ and $K^*(1430)$ ... More

Effects of $ρ$-meson width on pion distributions in heavy-ion collisionsAug 24 2016The influence of the finite width of $\rho$ meson on the pion momentum distribution is studied quantitatively in the framework of the S-matrix approach combined with a blast-wave model to describe particle emissions from an expanding fireball. We find ... More

On finding all positive integers $a,b$ such that $b\pm a$ and $ab$ are palindromicDec 20 2018Jan 13 2019It is proven that the only integer solutions $(a,b)$ such that $a+b$ and $ab$ are palindromic are $(2,5\cdot 10^k-3)$, $(3,24)$ and $(9,9)$, and in a similar fashion, $b-a$ and $ab$ are only palindromic at $(a,b)=(3,147\cdot 10^{4(k+1)}+5247\sum_{i=0}^k10^{4i})$, ... More

Interplay between antiferromagnetic order and spin polarization in ferromagnetic metal/electron-doped cuprate superconductor junctionsAug 24 2009Recently we proposed a theory of point-contact spectroscopy and argued that the splitting of zero-bias conductance peak (ZBCP) in electron-doped cuprate superconductor point-contact spectroscopy is due to the coexistence of antiferromagnetic (AF) and ... More

Zero-mode dynamics in supersymmetric Yang-Mills-Chern-Simons theoryDec 20 2012We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a spectrum of states ... More

Surface observables and the Weyl anomalyAug 27 1999I review the computation of the conformal anomaly of a Wilson surface observable in free two-form gauge theory in six dimensions.

Boundary conditions for GL-twisted N=4 SYMJun 20 2011Jul 04 2011We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a four-manifold of the form V = W \times R_+ or V = W \times I, where W is a Riemannian three-manifold. Different kinds of boundary conditions apply at infinity or at finite distance. ... More

The low-energy spectrum of (2,0) theory on T^5 x RSep 24 2008We consider the ADE-series of (2, 0) supersymmetric quantum theories on T^5 \times R, where the first factor is a flat spatial five-torus, and the second factor denotes time. The quantum states of such a theory \Phi are characterized by a discrete quantum ... More

Wilson-'t Hooft operators and the theta angleMar 24 2006We consider $(3+1)$-dimensional $SU(N)/\mathbb Z_N$ Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle $\theta\to\theta+2\pi$, a 't Hooft operator $T(\gamma)$ ... More

The partition bundle of type A_{N-1} (2, 0) theoryDec 20 2010Dec 27 2010Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss ... More

Automorphic properties of (2, 0) theory on T6Nov 30 2009We consider ADE-type (2, 0) theory on a family of flat six-tori endowed with flat Sp(4) connections coupled to the R-symmetry. Our main objects of interest are the components of the `partition vector' of the theory. These constitute an element of a certain ... More

BPS states in (2,0) theory on R x T5Jan 07 2009We consider $(2, 0)$ theory on a space-time of the form $R \times T^5$, where the first factor denotes time, and the second factor is a flat spatial five-torus. In addition to their energy, quantum states are characterized by their spatial momentum, 't ... More

Mirror symmetry for the Kazama-Suzuki modelsFeb 21 1994Apr 13 1994We study the $N = 2$ coset models in their formulation as supersymmetric gauged Wess-Zumino-Witten models. A model based on the coset $G/H$ is invariant under a symmetry group isomorphic to $\Z_{k+Q}$, where $k$ is the level of the model and $Q$ is the ... More

A class of six-dimensional conformal field theoriesJun 29 2000Dec 06 2000We describe a class of six-dimensional conformal field theories that have some properties in common with and possibly are related to a subsector of the tensionless string theories. The latter theories can for example give rise to four-dimensional $N = ... More

Commutation relations for surface operators in six-dimensional (2, 0) theoryDec 08 2000The A_{N - 1} (2, 0) superconformal theory has an observable associated with every two-cycle in six dimensions. We make a natural guess for the commutation relations of these operators, which reduces to the commutation relations of Wilson and 't Hooft ... More

BPS-spectra in four dimensions from M-theoryNov 11 1997I review my work together with Piljin Yi on the spectrum of BPS-saturated states in N = 2 supersymmetric Yang-Mills theories. In an M-theory description, such states are realized as certain two-brane configurations. We first show how the central charge ... More

Moduli of PT-Semistable Objects INov 25 2010We show boundedness for PT-semistable objects of any Chern classes on a smooth projective three-fold $X$. Then we show that the stack of objects in the heart $\langle \Coh_{\leq 1}(X), \Coh_{\geq 2}(X)[1] \rangle$ satisfies a version of the valuative ... More

A note on rainbow matchings in properly edge-coloured graphsAug 26 2011A rainbow matching in an edge-coloured graph is a matching such that its edges have distinct colours. We show that every properly edge-coloured graph $G$ with $|G| \ge (9\delta(G) -5)/2$ has a rainbow matching of size $\delta(G)$, improving a result of ... More

Polynomial Bridgeland Stable Objects and Reflexive SheavesDec 19 2011Aug 01 2012On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of PT-stable objects ... More

Moduli of PT-semistable objects IINov 29 2010May 04 2011We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ ... More

Properly coloured Hamiltonian cycles in edge-coloured complete graphsDec 30 2012Oct 14 2014Let $K_n^c$ be an edge-coloured complete graph on $n$ vertices. Let $\Delta_{\rm mon}(K_n^c)$ denote the largest number of edges of the same colour incident with a vertex of $K_n^c$. A properly coloured cycle is a cycle such that no two adjacent edges ... More

A Perturbation Inequality for the Schatten-$p$ Quasi-Norm and Its Applications to Low-Rank Matrix RecoverySep 03 2012Jun 27 2014In this paper, we establish the following perturbation result concerning the singular values of a matrix: Let $A,B \in \mathbb{R}^{m\times n}$ be given matrices, and let $f:\mathbb{R}_+\rightarrow\mathbb{R}_+$ be a concave function satisfying $f(0)=0$. ... More

Uniqueness Theorem for non-compact mean curvature flow with possibly unbounded curvaturesSep 01 2017Feb 03 2019In this paper, we discuss uniqueness and backward uniqueness for mean curvature flow of non-compact manifolds. We use an energy argument to prove two uniqueness theorems for mean curvature flow with possibly unbounded curvatures. These generalize the ... More

Zero-energy states of N = 4 SYM on T^3: S-duality and the mapping class groupFeb 05 2008We continue our studies of the low-energy spectrum of N=4 super-Yang-Mills theory on a spatial three-torus. In two previous papers, we computed the spectrum of normalizable zero-energy states for all choices of gauge group and all values of the electric ... More

Weyl anomaly for Wilson surfacesMay 22 1999We consider a free two-form in six dimensions and calculate the conformal anomaly associated with a Wilson surface observable.

Growth estimates on positive solutions of the equation $Δu + K u^{{n + 2}\over {n - 2}} = 0$ in ${\R}^n$Feb 01 2000We construct unbounded positive $C^2$-solutions of the equation $\Delta u + K u^{(n + 2)/(n - 2)} = 0$ in ${\R}^n$ (equipped with Euclidean metric $g_o$) such that $K$ is bounded between two positive numbers in ${\R}^n$, the conformal metric $g = u^{4/(n ... More

On the $L^{n\over 2}$-norm of Scalar CurvatureAug 03 1995Comparisons on $L^{n\over 2}$-norms of scalar curvatures between Riemannian metrics and standard metrics are obtained. The metrics are restricted to conformal classes or under certain curvature conditions.

A universal constant for dark matter-baryon interplayFeb 11 2019Recent studies point out that there exists some rough scaling relations for dark matter and some tight connections between dark matter and baryons. However, most of the relations and tight connections can only be found in galaxies, but not in galaxy clusters. ... More

Construction of Blow-up Sequence for the Conformal Scalar Curvature Equation on S^n. I, II, and AppendixOct 06 2011Using the Lyapunov-Schmidt reduction method, we describe how to use annular domains to construct (scalar curvature) functions on S^n, (n > 5), so that each one of them enables the conformal scalar curvature equation to have a blowing-up sequence of positive ... More

Diversity and Origin of 2:1 Orbital Resonances in Extrasolar Planetary SystemsJan 21 2004May 07 2004(Abridged) A diversity of 2:1 resonance configurations can be expected in extrasolar planetary systems, and their geometry can provide information about the origin of the resonances. Assembly during planet formation by the differential migration of planets ... More

A short representation of the six-dimensional (2, 0) algebraApr 20 2001We construct a BPS-saturated representation of the six-dimensional (2, 0) algebra with a certain non-zero value of the `central' charge. This representation is naturally carried by strings with internal degrees of freedom rather than by point particles. ... More

The light spectrum near the Argyres-Douglas pointJun 07 1999We consider N = 2 super Yang-Mills theory with SU(2) gauge group and a single quark hypermultiplet in the fundamental representation. For a specific value of the quark bare mass and at a certain point in the moduli space of vacua, the central charges ... More

The Holographic Weyl anomalyJun 11 1998Jun 17 1998We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. ... More

Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-dualityMar 19 2007Jun 10 2007We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions ... More

Uniqueness of Positive Solutions of the Conformal Scalar Curvature Equation and Applications to Conformal TransformationsOct 25 1996We study uniqueness of positive solutions to the conformal scalar curvature equation on complete Riemannian manifolds with constant negative scalar curvature. We apply the results to show that conformal transformations on certain complete Riemannian manifolds ... More

Nonnegative Trigonometric Polynomials and Sturms TheoremJul 02 2015Jul 03 2015In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. The algorithm proves to be an indispensable tool in establishing some recent ... More

Rotationally Symmetric F-harmonic Maps EquationsMay 27 1996We study a second order differential equation corresponding to rotationally symmetric $F$-harmonic maps between certain noncompact manifolds. We show unique continuation and Liouville's type theorems for positive solutions. Asymptotic properties and the ... More

Excluded Volume Effects in Gene StretchingJun 17 2002We investigate the effects excluded volume on the stretching of a single DNA in solution. We find that for small force F, the extension h is not linear in F but proportion to F^{\chi}, with \chi=(1-\nu)/\nu, where \nu is the well-known universal correlation ... More

A New Family of Nonnegative Sine PolynomialsJul 28 2016We present a new family of sine polynomials that are nonnegative for all $x$ in $[0,\pi]$. We also characterize all nonnegative sine polynomials of degree 3 and all nonnegative cosine polynomials of degree 2.

The flat Grothendieck-Riemann-Roch theorem without adiabatic techniquesMar 15 2012May 31 2016In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation ... More

Compact Hermitian manifolds with quasi-negative curvatureOct 17 2018Nov 14 2018In this work, we show that along a particular choice of Hermitian curvature flow, the non-positivity of Chern-Ricci curvature will be preserved if the initial metric has non-positive bisectional curvature. As an application, we show that the canonical ... More

Rotationally Symmetric $p$-harmonic mapsApr 23 1996We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive entire solutions. ... More

Four-dimensional BPS-spectra via M-theoryJul 30 1997Aug 13 1997We consider the realization of four-dimensional theories with N = 2 supersymmetry as M-theory configurations including a five-brane. Our emphasis is on the spectrum of massive states, that are realized as two-branes ending on the five-brane. We start ... More

Nonnegative Trigonometric Polynomials, Sturms Theorem, and Symbolic ComputationFeb 27 2014Apr 26 2016In this paper, we explain a procedure based on a classical result of Sturm that can be used to determine rigorously whether a given trigonometric polynomial is nonnegative in a certain interval or not. Many examples are given. This technique has been ... More

Spinors and the AdS/CFT correspondenceMar 30 1998Apr 03 1998We consider a free massive spinor field in Euclidean Anti-de Sitter space. The usual Dirac action in bulk is supplemented by a certain boundary term. The boundary conditions of the field are parametrized by a spinor on the boundary, subject to a projection. ... More

A condensed proof of the differential Grothendieck-Riemann-Roch theoremNov 23 2011Jul 18 2012We give a direct proof that the Freed-Lott differential analytic index is well defined and a condensed proof of the differential Grothendieck-Riemann-Roch theorem. As a byproduct we also obtain a direct proof that the R/Z analytic index is well defined ... More

The differential analytic index in Simons-Sullivan differential K-theoryOct 02 2011Apr 09 2012We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential ... More

Homology Decompositions of the Loops on 1-Stunted Borel Constructions of C_2-ActionsJan 05 2013Carlsson's construction is a simplicial group whose geometric realization is the loop space of the 1-stunted reduced Borel construction. Our main results are: i) Given a pointed simplicial set acted upon by the discrete cyclic group C_2 of order 2, if ... More

Asymptotic properties of energy of harmonic maps on asymptotically hyperbolic manifoldsOct 30 1996Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant if the total ... More

Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groupsJun 19 2007The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and electric 't Hooft fluxes. At weak coupling, the ... More

Holography and the Weyl anomalyDec 03 1998We review our calculation of the Weyl anomaly for d-dimensional conformal field theories that have a description in terms of a (d + 1)-dimensional gravity theory.

A tight scaling relation of dark matter in galaxy clustersMar 18 2014Recent studies in different types of galaxies reveal that the product of the central density and the core radius ($\rho_cr_c$) is a constant. However, some empirical studies involving galaxy clusters suggest that the product $\rho_cr_c$ depends weakly ... More

Scaling relations of the slightly self-interacting cold dark matter in galaxies and clustersMay 20 2013Recent observations in galaxies and clusters indicate dark matter density profiles exhibit core-like structures which contradict to the numerical simulation results of collisionless cold dark matter. The idea of self-interacting cold dark matter (SICDM) ... More

Electron-positron pair production near the Galactic Centre and the 511 keV emission lineNov 25 2015Recent observations indicate that a high production rate of positrons (strong 511 keV line) and a significant amount of excess GeV gamma-ray exist in our Galactic bulge. The latter issue can be explained by $\sim 40$ GeV dark matter annihilation through ... More

Shaping the relation between the mass of supermassive black holes and the velocity dispersion of galactic bulgesJan 28 2013I use the fact that the radiation emitted by the accretion disk of supermassive black hole can heat up the surrounding gas in the protogalaxy to achieve hydrostatic equilibrium during the galaxy formation. The correlation between the black hole mass M_BH ... More

On $δ'$-like potential scattering on star graphsJul 02 2010We discuss the potential scattering on the noncompact star graph. The Schr\"{o}dinger operator with the short-range potential localizing in a neighborhood of the graph vertex is considered. We study the asymptotic behavior the corresponding scattering ... More

Misere Hackenbush FlowersDec 24 2012Jan 07 2013We show that any disjunctive sum of Hackenbush Flowers $G$ has as evil twin $G^* \in {G, G+*}$ such that the outcomes of $G$ under normal and mis\`ere play are the same as the outcomes of $G^*$ under mis\`ere and normal play respectively. We also show ... More

The Ziegler spectrum of the D-infinity plane singularityNov 30 2016We will describe the Cohen--Macaulay part of the Ziegler spectrum of the D-infinity plane singularity S and calculate the nilpotency index of the radical of the category of finitely generated Cohen--Macaulay S-modules.

Codegree Turán density of complete $r$-uniform hypergraphsJan 04 2018Let $r\ge 3$. Given an $r$-graph $H$, the minimum codegree $\delta_{r-1}(H)$ is the largest integer $t$ such that every $(r-1)$-subset of $V(H)$ is contained in at least $t$ edges of $H$. Given an $r$-graph $F$, the codegree Tur\'an density $\gamma(F)$ ... More

Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spacesOct 21 2015In H\"ormander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or Neumann boundary conditions. We prove that the operators corresponding to these ... More

3-manifold diagrams and NP vs $\#$PNov 21 2014In computational complexity, a significant amount of useful theory is built on a foundation of widely-believed conjectures about the separation of complexity classes, the most famous of which is P $\neq$ NP. In this work, we examine the consequences of ... More

Some Bounds on the Rainbow Connection Number of 3-, 4- and 5-connected GraphsDec 24 2012The rainbow connection number, $rc(G)$, of a connected graph $G$ is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same. We show that for $\kappa ... More

Homogeneous and nonlinear generalized master equations accounting for initial correlationsDec 13 2015To take initial correlations into account, a method, based on the time-independent projection operator technique, that allows converting the conventional linear inhomogeneous (containing a source caused by initial correlations) time-convolution generalized ... More

Exact closed equation for reduced equilibrium distribution functions of the many-particle systemJul 21 2013An exact closed equation for s - particle equilibrium distribution function (s<N) of the system of N>>1 interacting particles is obtained. This integra-differential {\beta} - convolution equation ({\beta}=1/k_{B}T) follows from the Bloch equation for ... More

$\ell$-degree Turán densityOct 21 2012Oct 14 2014Let $H_n$ be a $k$-graph on $n$ vertices. For $0 \le \ell <k$ and an $\ell$-subset $T$ of $V(H_n)$, define the degree $\deg(T)$ of $T$ to be the number of $(k-\ell)$-subsets~$S$ such that $S \cup T$ is an edge in~$H_n$. Let the minimum $\ell$-degree of ... More

Convergence Vague (IA) - Suites de Vecteurs AléatoiresNov 11 2016This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary foundation that paves ... More

Duality Spectral Sequences for Weierstrass Fibrations and ApplicationsJun 06 2017We study duality spectral sequences for Weierstrass fibrations. Using these spectral sequences, we show that on a K-trivial Weierstrass threefold over a K-numerically trivial surface, any line bundle of nonzero fiber degree is taken by a Fourier-Mukai ... More

Hidden correlations in indivisible qudits as a resource for quantum technologies on examples of superconducting circuitsDec 28 2015We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and Araki--Lieb inequality, which characterize hidden quantum correlations ... More

The maps of matrices and portrait maps of density operators of composite and noncomposite systemsApr 14 2014We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. ... More

Tomographic entropic inequalities in the probability representation of quantum mechanicsAug 28 2012A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the state tomograms ... More

Canonical transforms, quantumness and probability representation of quantum mechanicsMar 01 2011The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or density matrix. ... More

Entanglement and other quantum correlations of a single qudit state as a resource for quantum technologiesSep 15 2014The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong subadditivity ... More

Quantum strong subadditivity condition for systems without subsystemsDec 25 2013The strong subadditivity condition for the density matrix of a quantum system, which does not contain subsystems, is derived using the qudit-portrait method. An example of the qudit state in the seven-dimensional Hilbert space corresponding to spin j ... More

Unparticles and Holographic Renormalization GroupMar 03 2009Jun 28 2009We revisit the unparticle interactions and propagators from the AdS-CFT point of view, and we show how the contact terms and their renormalization group flow appear in the context of the holographic renormalization. We study both vector unparticles and ... More

Hierarchy in Sampling Gaussian-correlated BosonsAug 12 2016Boson Sampling represents a class of physical processes potentially intractable for classical devices to simulate. The Gaussian extension of Boson Sampling remains a computationally hard problem, where the input state is a product of uncorrelated Gaussian ... More

Representation spaces for central extensions and almost commuting unitary matricesFeb 18 2015Jul 09 2016Let $\Gamma$ denote a central extension of the form $1\to \mathbb{Z}^r\to\Gamma\to \mathbb{Z}^n\to 1$. In this paper we describe the topology of the spaces of homomorphisms $\text{Hom}(\Gamma, U(m))$ and the associated moduli spaces $\text{Rep}(\Gamma, ... More

Conformal scalar curvature equation on S^n: functions with two close critical points (twin pseudo-peaks)Jan 23 2017By using the Lyapunov-Schmidt reduction method without perturbation, we consider existence results for the conformal scalar curvature on S^n (n greater or equal to 3) when the prescribed function (after being projected to R^n) has two close critical points, ... More

Difference Nevanlinna theories with vanishing and infinite periodsOct 09 2015Mar 13 2017By extending the idea of a difference operator with a fixed step to varying-steps difference operators, we have established a difference Nevanlinna theory for meromorphic functions with the steps tending to zero (vanishing period) and a difference Nevanlinna ... More

Dynamic scaling theory of the forced translocation of a semi-flexible polymer through a nanoporeSep 10 2015We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force ... More

Spin correlation functions and quasiparticle decayAug 21 2016We study one-dimensional anisotropic XXZ spin-$\frac12$ model with ferromagnetic sign of the coupling and $z-z$ exchange constant $J_z = \Delta J$, where $\Delta < 1$, and $J$ is the coupling within XY spin plane. We calculate damping of low-energy excitations ... More

Thermal transport in disordered one-dimensional spin chainsSep 03 2015We study one-dimensional anisotropic XY-Heisenberg spin-$\frac{1}{2}$ chain with weak random fields $h_i^z S^z_i$ by means of Jordan-Wigner transformation to spinless Luttinger liquid with disorder and bosonization technique. First we investigate phase ... More

Zeno-anti-Zeno crossover via external fields in a one-dimensional coupled-cavity waveguideOct 09 2010Nov 03 2010We have studied a hybrid system of a one-dimensional coupled-cavity waveguide with a two-level system inside, which subject to a external periodical field. Using the extended Hilbert space formalism, the time-dependent Hamiltonian is reduced into an equivalent ... More

Alternative commutation relations, star products and tomographyDec 19 2001Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are discussed. The ... More

Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie--Weiss modelJul 25 2009Apr 12 2011Let $(W,W')$ be an exchangeable pair. Assume that \[E(W-W'|W)=g(W)+r(W),\] where $g(W)$ is a dominated term and $r(W)$ is negligible. Let $G(t)=\int_0^tg(s)\,ds$ and define $p(t)=c_1e^{-c_0G(t)}$, where $c_0$ is a properly chosen constant and $c_1=1/\int_{-\infty}^{\infty}e^{-c_0G(t)}\,dt$. ... More

Nevanlinna theory of the Askey-Wilson divided difference operatorFeb 08 2015Apr 21 2016This paper establishes a version of Nevanlinna theory based on Askey-Wilson divided difference operator for meromorphic functions of finite logarithmic order in the complex plane $\mathbb{C}$. A second main theorem that we have derived allows us to define ... More

Absorbing-state phase transitions on percolating latticesJan 14 2009Apr 27 2009We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation ... More

Sturm Theorem and a Refinement of Vietoris Inequality for Cosine PolynomialsJun 03 2014In a recent work, the authors established a refinement of the well-known 1958 result of Vietoris on nonnegative cosine polynomials. In four places of the proof, use was made of the classical Sturm Theorem on determining the number of real roots of an ... More

Nonlocality threshold for entanglement under general dephasing evolutions: A case studyAug 10 2015Jan 15 2016Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, ... More

A Blowup Problem of Reaction Diffusion Equation Related to the Diffusion Induced Blowup PhenomenonJul 31 2003This work studies nonnegative solutions for the Cauchy, Neumann, and Dirichlet problems of a logistic type reaction-diffusion equation. The finite time blowup results for nonnegative solutions under various restrictions on the coefficients of this equation ... More

Find Subtrees of Specified Weight and Cycles of Specified Length in Linear TimeFeb 18 2019We introduce a variant of DFS which finds subtrees of specified weight in linear time, by which, as observed by Mohr, cycles of specified length in planar hamiltonian graphs can be found. We show, for example, that every planar hamiltonian graph $G$ with ... More

Hidden Quantum Correlations in Single Qudit SystemsJul 22 2015We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.) random variables ... More

Inequalities for nonnegative numbers and information propertiesJul 03 2013We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize ... More

Hidden Bell correlations in the four-level atomJan 22 2016We extend the Bell inequality known for two qubits to the four-level atom, including an artificial atom realized by the superconducting circuit, and qudit with j=3/2. We formulate the extended inequality as the inequality valid for an arbitrary Hermitian ... More