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Three loop heavy quark form factors and their asymptotic behaviorJun 13 2019A summary of the calculation of the color-planar and complete light quark contributions to the massive three-loop form factors is presented. Here a novel calculation method for the Feynman integrals is used, solving general uni-variate first order factorizable ... More
Perturbative analysis of the colored Alexander polynomial and KP soliton $τ$-functionsJun 13 2019In this paper we elaborate on the statement given in arXiv:1805.02761. Mainly, we study the relation between the colored Alexander polynomial and the famous KP hierarchy. We explain and prove this relation by exploring the fact that the dispersion equations ... More
On bulk deviations for the local behavior of random interlacementsJun 13 2019We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the average value of some suitable non-decreasing local function ... More
Static Spherically Symmetric Einstein-aether models: Integrability and the Modified Tolman-Oppenheimer-Volkoff approachJun 13 2019We study the evolution of the dynamics and the existence of analytic solutions for the field equations in the Einstein-aether theory for a static spherically symmetric spacetime. In particular, we investigate if the gravitational field equations in the ... More
Towards Gaussian states for loop quantum gravityJun 13 2019An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a vacuum in which ... More
Spectrum absolute continuity in a twisted Dirichlet-Neumann waveguideJun 13 2019Quantum waveguide with the shape of planar infinite straight strip and combined Dirichlet and Neumann boundary conditions on the opposite half-lines of the boundary is considered. The absence of the point as well as of the singular continuous spectrum ... More
Localization in Gaussian disordered systems at low temperatureJun 13 2019For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain (i) a version of "complete" path localization ... More
Emergent Gauge Symmetries and Quantum OperationsJun 13 2019The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, ... More
N-dimensional Heisenberg's uncertainty principle for fractional Fourier transformJun 13 2019A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional fractional Fourier ... More
Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmionsJun 12 2019Magnetic skyrmions have been the subject of extensive experimental studies in ferromagnetic thin films and multilayers, revealing a diversity in their size, stability and internal structure. While the orthodox skyrmion theory focuses on the Dzyaloshinskii-Moryia ... More
Homogenization results for a coupled system of reaction-diffusion equationsJun 12 2019The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying several metabolic ... More
A generating integral for the matrix elements of the Coulomb Green's function with the Coulomb wave functionsJun 12 2019We analytically evaluate the generating integral $K_{nl}(\beta,\beta') = \int_{0}^{\infty}\int_{0}^{\infty} e^{-\beta r - \beta' r'}G_{nl} r^{q} r'^{q'} dr dr'$ and integral moments $J_{nl}(\beta, r') = \int_{0}^{\infty} dr' G_{nl}(r,r') r'^{q} e^{-\beta ... More
Next-to$^k$ leading log expansions by chord diagramsJun 12 2019Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter. The leading logs are given by the main diagonal of this expansion, i.e. the subseries where the coupling and the scale parameter appear ... More
On the absolutely continuous spectrum of generalized indefinite strings IIJun 12 2019We continue to investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two more model examples of generalized indefinite ... More
Variational symmetries and Lagrangian multiformsJun 12 2019By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether's theorem to show that every variational symmetry of a Lagrangian has a corresponding a Lagrangian multiform. In doing so, we provide a systematic method ... More
On the structure of quantum vertex algebrasJun 12 2019A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a braided state-field correspondence which satisfies associativity and braided ... More
Activated Random Walks on $\mathbb{Z}^d$Jun 12 2019Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main models is that ... More
Geometric approach to quantum theoryJun 12 2019We formulate quantum theory taking as a starting point the cone of states.
On the quantum Geroch groupJun 11 2019The Geroch group is an infinite dimensional transitive group of symmetries of cylindrically symmetric gravitational waves which acts by non-canonical transformations on the phase space of these waves. The unique Poisson bracket on the Geroch group which ... More
On the balance problem for two rotating and charged black holesJun 11 2019It is an interesting open problem whether two non-extremal rotating and electrically charged black holes can be in physical equilibrium, which might be possible due to a balance between the gravitational attraction and the spin-spin and electrical repulsions. ... More
Electromagnetic fields on Kerr spacetime, Hertz potentials and Lorentz gaugeJun 11 2019We review two procedures for constructing the vector potential of the electromagnetic field on Kerr spacetime, namely, the classic method of Cohen & Kegeles, yielding $A^\mu$ in a radiation gauge, and the newer method of Frolov et al., yielding $A^\mu$ ... More
Quantization of dynamical symplectic reductionJun 11 2019A long-standing problem in quantum gravity and cosmology is the quantization of systems in which evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented, together with new structures ... More
Evolution speed of open quantum dynamicsJun 11 2019The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of the state. ... More
Asymptotic analysis of exit time for dynamical systems with a single well potentialJun 11 2019We study the exit time from a bounded multi-dimensional domain $\Omega$ of the stochastic process $\mathbf{Y}_\varepsilon=\mathbf{Y}_\varepsilon(t,a)$, $t\geqslant 0$, $a\in \mathcal{A}$, governed by the overdamped Langevin dynamics \begin{equation*} ... More
Generalized Langevin equations for systems with local interactionsJun 11 2019We present a new method to approximate the Mori-Zwanzig (MZ) memory integral in generalized Langevin equations (GLEs) describing the evolution of observables in high-dimensional nonlinear systems with local interactions. Building upon the Faber operator ... More
Solution of all quartic matrix modelsJun 11 2019We consider the quartic analogue of the Kontsevich model, which is defined by a measure $\exp(-N\,\mathrm{Tr}(E\Phi^2+(\lambda/4)\Phi^4)) d\Phi$ on Hermitean $N \times N$-matrices, where $E$ is any positive matrix and $\lambda$ a scalar. We prove that ... More
On the explicit constructions of certain unitary $t$-designsJun 11 2019Unitary $t$-designs are `good' finite subsets of the unitary group $U(d)$ that approximate the whole unitary group $U(d)$ well. Unitary $t$-designs have been applied in randomized benchmarking, tomography, quantum cryptography and many other areas of ... More
When random walkers help solving intriguing integralsJun 11 2019We revisit a family of integrals that delude intuition, and that recently appeared in mathematical literature in connection with computer algebra package verification. We show that the remarkable properties displayed by these integrals become transparent ... More
Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEsJun 11 2019We investigate the relation between pluri-Lagrangian hierarchies of $2$-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings in [Petrera, ... More
On a series of Darboux integrable discrete equations on the square latticeJun 11 2019We present a series of Darboux integrable discrete equations on the square lattice. Equations of the series are numbered with natural numbers $M$. All the equations have a first integral of the first order in one of directions of the two-dimensional lattice. ... More
Generalized Product Formulas and Quantum ControlJun 11 2019We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of situations, ... More
On the quest for generalized Hamiltonian descriptions of $3D$-flows generated by curl of a vector potentialJun 11 2019We study Hamiltonian analysis of three-dimensional advection flow $\mathbf{\dot{x}}=\mathbf{v}({\bf x})$ of incompressible nature $\nabla \cdot {\bf v} ={\bf 0}$ assuming that dynamics is generated by the curl of a vector potential $\mathbf{v} = \nabla ... More
Direct Characterization of Spectral Stability of Small Amplitude Periodic Waves in Scalar Hamiltonian Problems Via Dispersion RelationJun 11 2019Various approaches to studying the stability of solutions of nonlinear PDEs lead to explicit formulae determining the stability or instability of the wave for a wide range of classes of equations. However, these are typically specialized to a particular ... More
Schwinger-Dyson and loop equations for a product of square Ginibre random matricesJun 11 2019In this paper, we study the product of two complex Ginibre matrices and the loop equations satisfied by their resolvents (i.e. the Stieltjes transform of the correlation functions). We obtain using Schwinger-Dyson equation (SDE) techniques the general ... More
Gait modeling and optimization for the perturbed Stokes regimeJun 11 2019Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the "Stokesian" (viscous; ... More
Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principleJun 11 2019We consider the Anderson model with Bernoulli potential on $\mathbb{Z}^{3}$, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. The proof follows the framework by Bourgain--Kenig and Ding--Smart. ... More
A Novel Discrete Theory of a Screw Dislocation in the BCC Crystal LatticeJun 11 2019In this paper, we proposed a novel method using the elementary number theory to investigate the discrete nature of the screw dislocations in crystal lattices, simple cubic (SC) lattice and body centered cubic (BCC) lattice, by developing the algebraic ... More
On singular Frobenius for linear differential equations of second and third order, part 1: ordinary differential equationsJun 10 2019We study second order and third order linear differential equations with analytic coefficients under the viewpoint of finding formal solutions and studying their convergence. We address some untouched aspects of Frobenius methods for second order as the ... More
Full counting statistics of energy transfers in inhomogeneous nonequilibrium states of (1+1)D CFTJun 10 2019Employing the conformal welding technique, we find an exact expression for the Full Counting Statistics of energy transfers in a class of inhomogeneous nonequilibrium states of a (1+1)-dimensional unitary Conformal Field Theory. The expression involves ... More
Twisted characters and holomorphic symmetriesJun 10 2019We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly ... More
Disentangling the Generalized Double Semion ModelJun 10 2019We analyze the class of Generalized Double Semion (GDS) models in arbitrary dimensions from the point of view of lattice Hamiltonians. We show that on a $d$-dimensional spatial manifold $M$ the dual of the GDS is equivalent, up to constant depth local ... More
Equilibrium states in Thermal Field Theory and in Algebraic Quantum Field TheoryJun 10 2019In this paper we compare the construction of equilibrium states at finite temperature for self-interacting massive scalar quantum field theories on Minkowski spacetime proposed by Fredenhagen and Lindner with results obtained in ordinary thermal field ... More
On Mean Field Limit and Quantitative Estimates with a Large Class of Singular Kernels: Application to the Patlak-Keller-Segel ModelJun 10 2019In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (2018) and references therein] to treat more general kernels in mean field ... More
Stochastic PDE limit of the dynamic ASEPJun 10 2019We study a stochastic PDE limit of the height function of the dynamic asymmetric simple exclusion process (dynamic ASEP). A degeneration of the stochastic Interaction Round-a-Face (IRF) model of arXiv:1701.05239, dynamic ASEP has a jump parameter $q\in ... More
Heat kernel: proper time method, Fock-Schwinger gauge, path integral representation, and Wilson lineJun 10 2019The proper time method plays an important role in modern mathematics and physics. It includes many approaches, each of which has its pros and cons. This work is devoted to the description of one model case, which reflects the subtleties of construction ... More
Morse theory for the Yang-Mills energy function near flat connectionsJun 10 2019A result (Corollary 4.3) in an article by Uhlenbeck (1985) asserts that the $W^{1,p}$-distance between the gauge-equivalence class of a connection $A$ and the moduli subspace of flat connections $M(P)$ on a principal $G$-bundle $P$ over a closed Riemannian ... More
Noncommutative minimal embeddings and morphisms of pseudo-Riemannian calculiJun 10 2019In analogy with classical submanifold theory, we introduce morphisms of real metric calculi together with noncommutative embeddings. We show that basic concepts, such as the second fundamental form and the Weingarten map, translate into the noncommutative ... More
Gravitational perturbations as $T\bar{T}$-deformations in 2D dilaton gravity systemsJun 10 2019We consider gravitational perturbations of 2D dilaton gravity systems and show that these can be recast into $T\bar{T}$-deformations (at least) under certain conditions, where $T$ means the energy-momentum tensor of the matter field coupled to a dilaton ... More
Trigonal Toda lattice EquationJun 10 2019In this article, we give the trigonal Toda lattice equation, $$ -\frac{1}{2}\frac{d^3}{du^3} q_{\ell}(u) = e^{q_{\ell+1}(u)} +e^{q_{\ell+\zeta_3}(u)} +e^{q_{\ell-1-\zeta_3}(u)}-3e^{q_\ell(u)}, $$ for a lattice points $\ell \in \mathbb{Z}[\zeta_3]$ of ... More
Non-boundedness of the number of nodal domains of a sum of eigenfunctionsJun 09 2019Generalizing Courant's nodal domain theorem, the ``Extended Courant property'' is the statement that a linear combination of the first $n$ eigenfunctions has at most $n$ nodal domains. In the first part of the paper, we prove that the Extended Courant ... More
A Lorentz-Covariant Interacting Electron-Photon System in One Space DimensionJun 09 2019A Lorenz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac's formalism of multi-time wave functions, ... More
A uniqueness result on detecting a prey in a spider orb-webJun 09 2019We consider the inverse problem of localizing a prey hitting a spider orb-web from dynamic measurements taken near the center of the web, where the spider is supposed to stay. The actual discrete orb-web, formed by a finite number of radial and circumferential ... More
Extreme Eigenvalue Distributions of Jacobi Ensembles: New Exact Representations, Asymptotics and Finite Size CorrectionsJun 09 2019Let $\mathbf{W}_1$ and $\mathbf{W}_2$ be independent $n\times n$ complex central Wishart matrices with $m_1$ and $m_2$ degrees of freedom respectively. This paper is concerned with the extreme eigenvalue distributions of double-Wishart matrices $(\mathbf{W}_1+\mathbf{W}_2)^{-1}\mathbf{W}_1$, ... More
On a thermodynamic framework for developing boundary conditions for Korteweg fluidsJun 08 2019We provide a derivation of several classes of boundary conditions for fluids of Korteweg-type using a simple and transparent thermodynamic approach that automatically guarentees that the derived boundary conditions are compatible with the second law of ... More
Lifschitz tail for alloy-type models driven by the fractional LaplacianJun 08 2019We establish precise asymptotics near zero of the integrated density of states for the random Schr\"{o}dinger operators $(-\Delta)^{\alpha/2} + V^{\omega}$ in $L^2(\mathbb R^d)$ for the full range of $\alpha\in(0,2]$ and a fairly large class of random ... More
On the Differentiation Lemma and the Reynolds Transport Theorem for Manifolds with CornersJun 07 2019We state and prove generalizations of the Differentiation Lemma and the Reynolds Transport Theorem in the general setting of smooth manifolds with corners (e.g. cuboids, spheres, $\mathbb{R}^n$, simplices). Several examples of manifolds with corners are ... More
Bethe vectors for orthogonal integrable modelsJun 07 2019We consider quantum integrable models associated with $\mathfrak{so}_3$ algebra. We describe Bethe vectors of these models in terms of the current generators of the $\mathcal{D}Y(\mathfrak{so}_3)$ algebra. To implement this approach we use isomorphism ... More
Hohenberg-Kohn theorems for interactions, spin and temperatureJun 07 2019We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any ground state contain the information of the interactions ... More
The equilibrium dynamics of the XX chain revisitedJun 07 2019The equilibrium dynamics of the spin-1/2 XX chain is re-examined within a recently developed formalism based on the quantum transfer matrix and a thermal form factor expansion. The transversal correlation function is evaluated in real time and space. ... More
Invariant tori, action-angle variables and phase space structure of the Rajeev-Ranken modelJun 07 2019We study the classical Rajeev-Ranken model, a Hamiltonian system with three degrees of freedom describing nonlinear continuous waves in a 1+1-dimensional nilpotent scalar field theory pseudodual to the SU(2) principal chiral model. While it loosely resembles ... More
Chirality in the planeJun 07 2019It is well-known that many three-dimensional chiral material models become non-chiral when reduced to two dimensions. Chiral properties of the two-dimensional model can then be restored by adding appropriate two-dimensional chiral terms. In this paper ... More
Quantization of Hydrodynamics: Rotating Superfluid and Gravitational AnomalyJun 07 2019We present a consistent scheme of quantization of chiral flows (flows with extensive vorticity) in ideal hydrodynamics in two dimensions. Chiral flows occur in rotating superfluid, rotating turbulence and also in electronic systems in the magnetic field ... More
On beautiful analytic structure of the S-matrixJun 07 2019For an exponentially decaying potential, analytic structure of the $s$-wave S-matrix can be determined up to the slightest detail, including position of all its poles and their residui. Beautiful hidden structures can be revealed by its domain colouring. ... More
The positive geometry for $φ^{p}$ interactionsJun 07 2019Starting with the seminal work of Arkani-Hamed et al arXiv:1711.09102, in arXiv:1811.05904, the "Amplituhedron program" was extended to analyzing (planar) amplitudes in massless $\phi^{4}$ theory. In this paper we show that the program can be further ... More
The Boltzmann equation with an external force on the torus: Incompressible Navier-Stokes-Fourier hydrodynamical limitJun 07 2019We study the Boltzmann equation with external forces, not necessarily deriving from a potential, in the incompressible Navier-Stokes perturbative regime. On the torus, we establish local-in-time, for any time, Cauchy theories that are independent of the ... More
Relaxed highest-weight modules II: classifications for affine vertex algebrasJun 07 2019This is the second of a series of articles devoted to the study of relaxed highest-weight modules over affine vertex algebras and W-algebras. The first studied the simple "rank-$1$" affine vertex superalgebras $L_k(\mathfrak{sl}_2)$ and $L_k(\mathfrak{osp}(1\vert2))$, ... More
Classification and Construction of Topological Phases of Quantum MatterJun 07 2019We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting gapped quantum many-body systems that exhibit topological ... More
On the dynamics of a Hamilton-Poisson systemJun 06 2019The dynamics of a three-dimensional Hamilton-Poisson system is closely related to its constants of motion, the energy or Hamiltonian function $H$ and a Casimir $C$ of the corresponding Lie algebra. The orbits of the system are included in the intersection ... More
Phase diagram of helicoids in Chiral Liquid CrystalsJun 06 2019Jun 10 2019Cholesteric Liquid Crystals (CLCs), in presence of an external uniform electric field and confined between two parallel planes with strong homeotropic anchoring conditions, are found to admit different types of helicoidal solutions with disclinations. ... More
Bargmann-Fock percolation is noise sensitiveJun 06 2019We show that planar Bargmann-Fock percolation is noise sensitive under the Ornstein-Ulhenbeck process. The proof is based on the randomized algorithm approach introduced by Schramm and Steif and gives quantitative polynomial bounds on the noise sensitivity ... More
Double phase transonic flow problems with variable growth: nonlinear patterns and stationary wavesJun 06 2019In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is driven by the Baouendi-Grushin operator with variable coefficient. This ... More
Hyperbolic spin Ruijsenaars-Schneider model from Poisson reductionJun 06 2019We rederive the Hamiltonian structure of the $N$-particle hyperbolic spin Ruijsenaars-Schneider model by means of Poisson reduction of a suitable initial phase space. This phase space is realised as the direct product of the Heisenberg double of a factorisable ... More
Global stability for nonlinear wave equations with multi-localized initial dataJun 06 2019In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite collection ... More
BRST-BFV and BRST-BV Lagrangians for Bosonic Fields with Continuous Spin on $R^{1,d-1}$Jun 06 2019Gauge-invariant Lagrangian descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST--BFV approach we propose. The resulting ... More
BRST-BFV and BRST-BV Lagrangians for Bosonic Fields with Continuous Spin on $R^{1,d-1}$Jun 06 2019Jun 10 2019Gauge-invariant Lagrangian descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST--BFV approach we propose. The resulting ... More
How the High-energy Part of the Spectrum Affects the Adiabatic Computation GapJun 06 2019Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps counter-intuitively, ... More
On four-point connectivities in the critical 2d Potts modelJun 06 2019We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates ... More
Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex modelJun 06 2019Jun 12 2019We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as structure constants ... More
Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex modelJun 06 2019We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as structure constants ... More
Criticality of measures on 2-d Ising configurations: from square to hexagonal graphsJun 06 2019On the space of Ising configurations on the 2-d square lattice, we consider a family of non Gibbsian measures introduced by using a pair Hamiltonian, depending on an additional inertial parameter $q$. These measures are related to the usual Gibbs measure ... More
Ihara Zeta EntropyJun 06 2019In this article, we introduce an entropy based on the formal power series expansion of the Ihara Zeta function. We find a number of inequalities based on the values of the Ihara zeta function. These new entropies are applicable in symbolic dynamics and ... More
Quantum strips in higher dimensionsJun 06 2019We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero, we establish ... More
Families of Supermanifolds: Splitting Types and Obstruction MapsJun 06 2019In this article we study the notion of supermanifolds families, starting from Green's general classification of supermanifolds. The topics studied divide this article into two distinct parts, labelled I and II respectively. Part I concerns the splitting ... More
Sobolev spaces for multi-black hole initial dataJun 05 2019In this article we introduce weighted Sobolev spaces that are well suited to treat initial data for multiple black hole systems. We prove general results for elliptic operators on these spaces and give a simple proof of existence of a class of initial ... More
Locality and causality in perturbative AQFTJun 05 2019In this paper we introduce a notion of \textit{a group with causality}, which is a natural generalization of \textit{a locality group}, introduced by P.~Clavier, L.~Guo, S.~Paycha, and B.~Zhang. We also propose a generalization of the \textit{Hammerstein ... More
Virial inversion and density functionalsJun 05 2019We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces and apply it to the inversion of the density-activity relation for inhomogeneous systems. This provides a rigorous framework to prove convergence for ... More
The Standard Model $β$-function and a matrix model renormalization of Yukawa interactionsJun 05 2019We show that gauge-independent terms in the one-loop and multi-loops $\beta$-functions of the Standard Model can be equivalently computed from the Wetterich functional renormalization of a matrix model. Our framework is associated to the finite spectral ... More
The entanglement and relative entropy of a chiral fermion on the torusJun 05 2019We derive the entanglement entropy of chiral fermions on the circle at arbitrary temperature. The spin-sector contribution depends only on the total length of the entangling region, regardless of the configuration of the intervals. Thus mutual information ... More
Aspects of Scattering Amplitudes and Moduli Space LocalizationJun 05 2019We elaborate on the recent proposal that intersection numbers of certain cohomology classes on the moduli space of genus-zero Riemann surfaces with punctures compute tree-level scattering amplitudes in quantum field theories. The relevant cohomology classes ... More
Zero Measure and Singular Continuous Spectra for Quantum GraphsJun 05 2019We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial singular continuous part. A new local Borg--Marchenko uniqueness result is ... More
Symmetries of shamrocks IV: The self-complementary caseJun 05 2019In this paper we enumerate the centrally symmetric lozenge tilings of a hexagon with a shamrock removed from its center. Our proof is based on a variant of Kuo's graphical condensation method in which only three of the four involved vertices are on the ... More
Correlation of a macroscopic dent in a wedge with mixed boundary conditionsJun 05 2019As part of our ongoing work on the enumeration of symmetry classes of lozenge tilings of hexagons with certain four-lobed structures removed from their center, we consider the case of the tilings which are both vertically and horizontally symmetric. In ... More
On localized and coherent states on some new fuzzy spheresJun 05 2019We construct various systems of coherent states (SCS) on the $O(D)$-covariant fuzzy spheres $S^d_\Lambda$ ($d=1,2$, $D=d\!+\!1$) constructed in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451] and study their localizations in configuration ... More
Probabilistic Explanations and the Derivation of Macroscopic LawsJun 05 2019We will discuss the link between scientific explanations and probabilities, specially in relationship with statistical mechanics and the derivation of macroscopic laws from microscopic ones.
Maxwell's equations are universal for locally conserved quantitiesJun 04 2019A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's equations. ... More
The ambiguity function and the displacement operator basis in quantum mechanicsJun 04 2019We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner--Weyl position-momentum phase-space, but another space. Here, the quantity representing the quantum system is ... More
The information in a waveJun 04 2019We provide the notion of entropy for a classical Klein-Gordon real wave, that we derive as particular case of a notion entropy for a vector in a Hilbert space with respect to a real linear subspace. We then consider a localised automorphism on the Rindler ... More
Solution of the Kolmogorov equation for TASEPJun 04 2019We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP ... More
Global existence for systems of nonlinear wave equations with bounded, stable asymptotic systemsJun 04 2019Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain systems -- most famously ... More
One-shot entanglement distillation beyond LOCCJun 04 2019We study the task of entanglement distillation in the one-shot setting under different classes of quantum operations which extend the set of local operations and classical communication (LOCC). Establishing a general formalism which allows for a straightforward ... More