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  • Matroid connectivity and singularities of configuration hypersurfaces
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-25
    Graham Denham, Mathias Schulze, Uli Walther

    Consider a linear realization of a matroid over a field. One associates with it a configuration polynomial and a symmetric bilinear form with linear homogeneous coefficients. The corresponding configuration hypersurface and its non-smooth locus support the respective first and second degeneracy scheme of the bilinear form. We show that these schemes are reduced and describe the effect of matroid connectivity:

    更新日期:2021-01-25
  • Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-25
    Fredy Díaz García, Andrey Krutov, Réamonn Ó Buachalla, Petr Somberg, Karen R. Strung

    We construct covariant q-deformed holomorphic structures for all finitely generated relative Hopf modules over the irreducible quantum flag manifolds endowed with their Heckenberger–Kolb calculi. In the classical limit, these reduce to modules of sections of holomorphic homogeneous vector bundles over irreducible flag manifolds. For the case of simple relative Hopf modules, we show that this covariant

    更新日期:2021-01-25
  • Spectral curves are transcendental
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-22
    H. W. Braden

    Some arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge \(n\ge 2\) Euclidean BPS monopole is not defined over \(\overline{\mathbb {Q}}\) if smooth.

    更新日期:2021-01-24
  • On Segal–Sugawara vectors and Casimir elements for classical Lie algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-19
    A. I. Molev

    We consider the centers of the affine vertex algebras at the critical level associated with simple Lie algebras. We derive new formulas for generators of the centers in the classical types. We also give a new formula for the Capelli-type determinant for the symplectic Lie algebras and calculate the Harish-Chandra images of the Casimir elements arising from the characteristic polynomial of the matrix

    更新日期:2021-01-19
  • The Virasoro fusion kernel and Ruijsenaars’ hypergeometric function
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-09
    Julien Roussillon

    We show that the Virasoro fusion kernel is equal to Ruijsenaars’ hypergeometric function up to normalization. More precisely, we prove that the Virasoro fusion kernel is a joint eigenfunction of four difference operators. We find a renormalized version of this kernel for which the four difference operators are mapped to four versions of the quantum relativistic hyperbolic Calogero–Moser Hamiltonian

    更新日期:2021-01-10
  • Supersymmetric W -algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-08
    Alexander Molev, Eric Ragoucy, Uhi Rinn Suh

    We explain a general theory of W-algebras in the context of supersymmetric vertex algebras. We describe the structure of W-algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As an application, we produce explicit free generators of the W-algebra associated with the odd principal nilpotent element of the Lie superalgebra \(\mathfrak {gl}(n+1|n)\)

    更新日期:2021-01-08
  • $${\varvec{\pi }}$$ π -systems of symmetrizable Kac–Moody algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-07
    Lisa Carbone, K. N. Raghavan, Biswajit Ransingh, Krishanu Roy, Sankaran Viswanath

    As part of his classification of regular semisimple subalgebras of semisimple Lie algebras, Dynkin introduced the notion of a \(\pi \)-system. This is a subset of the set of roots such that pairwise differences of its elements are not roots. Such systems arise as simple systems of regular semisimple subalgebras. Morita and Naito generalized this notion to all symmetrizable Kac–Moody algebras. In this

    更新日期:2021-01-08
  • Cluster realization of Weyl groups and q -characters of quantum affine algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-05
    Rei Inoue

    We consider an infinite quiver \(Q({\mathfrak {g}})\) and a family of periodic quivers \(Q_m({\mathfrak {g}})\) for a finite-dimensional simple Lie algebra \({\mathfrak {g}}\) and \(m \in {\mathbb Z}_{>1}\). The quiver \(Q({\mathfrak {g}})\) is essentially same as what introduced in Hernandez and Leclerc (J Eur Math Soc 18:1113–1159, 2016) for the quantum affine algebra \({\hat{{\mathfrak {g}}}}\)

    更新日期:2021-01-05
  • Improved resolvent bounds for radial potentials
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-04
    Georgi Vodev

    We prove semiclassical resolvent estimates for the Schrödinger operator in \({\mathbb {R}}^d\), \(d\ge 3\), with real-valued radial potentials \(V\in L^\infty ({\mathbb {R}}^d)\). In particular, we show that if \(V(x)={{\mathcal {O}}}\left( \langle x\rangle ^{-\delta }\right) \) with \(\delta >2\), then the resolvent bound is of the form \(\exp \left( Ch^{-4/3}\right) \) with some constant \(C>0\)

    更新日期:2021-01-05
  • An explicit formula of the normalized Mumford form
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-04
    Takashi Ichikawa

    We give an explicit formula of the normalized Mumford form which expresses the second tautological line bundle by the Hodge line bundle defined on the moduli space of algebraic curves of any genus. This formula is represented as an infinite product which is a higher genus version of the Ramanujan delta function under the trivialization by normalized abelian differentials and Eichler integrals of their

    更新日期:2021-01-05
  • Nonconstant hexagon relations and their cohomology
    Lett. Math. Phys. (IF 1.371) Pub Date : 2021-01-02
    Igor G. Korepanov

    A construction of hexagon relations—algebraic realizations of four-dimensional Pachner moves—is proposed. It goes in terms of “permitted colorings” of 3-faces of pentachora (4-simplices), and its main feature is that the set of permitted colorings is nonconstant—varies from pentachoron to pentachoron. Further, a cohomology theory is formulated for these hexagon relations, and its nontriviality is demonstrated

    更新日期:2021-01-05
  • Modulated crystals and almost periodic measures
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-11-17
    Jeong-Yup Lee, Daniel Lenz, Christoph Richard, Bernd Sing, Nicolae Strungaru

    Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyze these structures using methods from modern mathematical diffraction theory, thereby

    更新日期:2020-11-17
  • A note on the dimensional crossover critical exponent
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-11-04
    Pablo A. Gomes, Rémy Sanchis, Roger W. C. Silva

    We consider independent anisotropic bond percolation on \({\mathbb {Z}}^d\times {\mathbb {Z}}^s\) where edges parallel to \({\mathbb {Z}}^d\) are open with probability \(p

    更新日期:2020-11-04
  • The trigonometric $$E_8$$ E 8 R -matrix
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-23
    Paul Zinn-Justin

    An expression for the R-matrix associated with \({\mathcal {U}}_q({\widehat{\mathfrak e_8}})\) in its 249-dimensional representation is given using the diagrammatic calculus of \({\mathcal {U}}_q({\mathfrak {e}_8})\) invariants.

    更新日期:2020-10-27
  • Aharonov–Bohm superselection sectors
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-17
    Claudio Dappiaggi, Giuseppe Ruzzi, Ezio Vasselli

    We show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper

    更新日期:2020-10-17
  • Formal power series for asymptotically hyperbolic Bach-flat metrics
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-13
    Aghil Alaee, Eric Woolgar

    It has been observed by Maldacena that one can extract asymptotically anti-de Sitter Einstein 4-metrics from Bach-flat spacetimes by imposing simple principles and data choices. We cast this problem in a conformally compact Riemannian setting. Following an approach pioneered by Fefferman and Graham for the Einstein equation, we find formal power series for conformally compactifiable, asymptotically

    更新日期:2020-10-13
  • A Lorentz-covariant interacting electron–photon system in one space dimension
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-08
    Michael K.-H. Kiessling, Matthias Lienert, A. Shadi Tahvildar-Zadeh

    A Lorentz-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, i.e., wave functions \(\Psi ^{{(2)}}(\mathbf {x}_{\text{ ph }},\mathbf {x}_{\text{ el }})\) where \(\mathbf {x}_{\text{ el }},\mathbf {x}_{\text{

    更新日期:2020-10-08
  • An operational construction of the sum of two non-commuting observables in quantum theory and related constructions
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-04
    Nicolò Drago, Sonia Mazzucchi, Valter Moretti

    The existence of a real linear space structure on the set of observables of a quantum system—i.e., the requirement that the linear combination of two generally non-commuting observables A, B is an observable as well—is a fundamental postulate of the quantum theory yet before introducing any structure of algebra. However, it is by no means clear how to choose the measuring instrument of a general observable

    更新日期:2020-10-04
  • Bulk-boundary asymptotic equivalence of two strict deformation quantizations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-01
    Valter Moretti, Christiaan J. F. van de Ven

    The existence of a strict deformation quantization of \(X_k=S(M_k({\mathbb {C}}))\), the state space of the \(k\times k\) matrices \(M_k({\mathbb {C}})\) which is canonically a compact Poisson manifold (with stratified boundary), has recently been proved by both authors and Landsman (Rev Math Phys 32:2050031, 2020. https://doi.org/10.1142/S0129055X20500312). In fact, since increasing tensor powers

    更新日期:2020-10-02
  • Duality for Bethe algebras acting on polynomials in anticommuting variables
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-09-13
    V. Tarasov, F. Uvarov

    We consider actions of the current Lie algebras \(\mathfrak {gl}_{n}[t]\) and \(\mathfrak {gl}_{k}[t]\) on the space of polynomials in kn anticommuting variables. The actions depend on parameters \(\bar{z}=(z_{1},\dots ,z_{k})\) and \({\bar{\alpha }}=(\alpha _{1},\dots ,\alpha _{n})\), respectively. We show that the images of the Bethe algebras \(\mathcal {B}_{{\bar{\alpha }}}^{\langle n \rangle }\subset

    更新日期:2020-09-13
  • An optimal semiclassical bound on commutators of spectral projections with position and momentum operators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-09-08
    Søren Fournais, Søren Mikkelsen

    We prove an optimal semiclassical bound on the trace norm of the following commutators \([{\varvec{1}}_{(-\infty ,0]}(H_\hbar ),x]\), \([{\varvec{1}}_{(-\infty ,0]}(H_\hbar ),-i\hbar \nabla ]\) and \([{\varvec{1}}_{(-\infty ,0]}(H_\hbar ),e^{i\langle t, x\rangle }]\), where \(H_\hbar \) is a Schrödinger operator with a semiclassical parameter \(\hbar \), x is the position operator, \(-\,i\hbar \nabla

    更新日期:2020-09-08
  • Full colored HOMFLYPT invariants, composite invariants and congruence skein relations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-09-07
    Qingtao Chen, Shengmao Zhu

    In this paper, we investigate the properties of certain quantum invariants of links by using the HOMFLY skein theory. First, we obtain the limit behavior for the full colored HOMFLYPT invariant which is the natural generalization of the colored HOMFLYPT invariant. Then we focus on the composite invariant which is a certain combination of the full colored HOMFLYPT invariants. Motivated by the study

    更新日期:2020-09-08
  • Correction to: Solving q -Virasoro constraints
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-31
    Rebecca Lodin, Aleksandr Popolitov, Shamil Shakirov, Maxim Zabzine

    The publication of this article unfortunately contained a mistake. One affiliation of the author Shamil Shakirow was missing; you can find the corrected affiliations above.

    更新日期:2020-09-01
  • Tropical limit of matrix solitons and entwining Yang–Baxter maps
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-11
    Aristophanes Dimakis, Folkert Müller-Hoissen

    We consider a matrix refactorization problem, i.e., a “Lax representation,” for the Yang–Baxter map that originated as the map of polarizations from the “pure” 2-soliton solution of a matrix KP equation. Using the Lax matrix and its inverse, a related refactorization problem determines another map, which is not a solution of the Yang–Baxter equation, but satisfies a mixed version of the Yang–Baxter

    更新日期:2020-08-12
  • Approximation of one-dimensional relativistic point interactions by regular potentials revised
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-12
    Matěj Tušek

    We show that the one-dimensional Dirac operator with quite general point interaction may be approximated in the norm resolvent sense by the Dirac operator with a scaled regular potential of the form \(1/\varepsilon ~h(x/\varepsilon )\otimes B\), where B is a suitable \(2\times 2\) matrix. Moreover, we prove that the limit does not depend on the particular choice of h as long as it integrates to a constant

    更新日期:2020-08-12
  • Infinity-enhancing of Leibniz algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-11
    Sylvain Lavau, Jakob Palmkvist

    We establish a correspondence between infinity-enhanced Leibniz algebras, recently introduced in order to encode tensor hierarchies (Bonezzi and Hohm in Commun Math Phys 377:2027–2077, 2020), and differential graded Lie algebras, which have been already used in this context. We explain how any Leibniz algebra gives rise to a differential graded Lie algebra with a corresponding infinity-enhanced Leibniz

    更新日期:2020-08-11
  • On the Hamiltonian formulation of the trigonometric spin Ruijsenaars–Schneider system
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-10
    Oleg Chalykh, Maxime Fairon

    We suggest a Hamiltonian formulation for the spin Ruijsenaars–Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian

    更新日期:2020-08-11
  • Level one Weyl modules for toroidal Lie algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-10
    Ryosuke Kodera

    We identify level one global Weyl modules for toroidal Lie algebras with certain twists of modules constructed by Moody–Eswara Rao–Yokonuma via vertex operators for type ADE and by Iohara–Saito–Wakimoto and Eswara Rao for general type. The twist is given by an action of \(\mathrm {SL}_{2}(\mathbb {Z})\) on the toroidal Lie algebra. As a by-product, we obtain a formula for the character of the level

    更新日期:2020-08-10
  • A classification of SNC log symplectic structures on blow-up of projective spaces
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-10
    Katsuhiko Okumura

    It is commonly recognized that the classfication of Poisson manifold is a major problem. From the viewpoint of algebraic geometry, holomorphic projective Poisson manifold is the most important target. Poisson structures on the higher dimensional projective varieties was first studied by Lima and Pereira (Lond Math Soc 46(6):1203–1217, 2014). They proved that any Poisson structures with the reduced

    更新日期:2020-08-10
  • The duality between F-theory and the heterotic string in $$D=8$$ D = 8 with two Wilson lines
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-07
    Adrian Clingher, Thomas Hill, Andreas Malmendier

    We construct non-geometric string compactifications by using the F-theory dual of the heterotic string compactified on a two-torus with two Wilson line parameters, together with a close connection between modular forms and the equations for certain K3 surfaces of Picard rank 16. We construct explicit Weierstrass models for all inequivalent Jacobian elliptic fibrations supported on this family of K3

    更新日期:2020-08-08
  • Twisted characters and holomorphic symmetries
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-03
    Ingmar Saberi; Brian R. Williams

    We 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 as a family over the space of nilpotent supercharges in minimal supersymmetry. The BV formalism allows one to work with or without auxiliary fields

    更新日期:2020-08-03
  • Cyclotomic expansions of HOMFLY-PT colored by rectangular Young diagrams
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-31
    Masaya Kameyama; Satoshi Nawata; Runkai Tao; Hao Derrick Zhang

    We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots colored by rectangular Young diagrams where the twist is encoded in interpolation Macdonald polynomials. We also put forth a conjecture of cyclotomic expansions of HOMFLY-PT polynomials colored by rectangular Young diagrams for any knot.

    更新日期:2020-07-31
  • The Coxeter relations and KP map for non-commuting symbols
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-27
    Adam Doliwa; Masatoshi Noumi

    We give an action of the symmetric group on non-commuting indeterminates in terms of series in the corresponding Mal’cev–Newmann division ring. The action is constructed from the non-Abelian Hirota–Miwa (discrete KP) system. The corresponding companion map, which gives generators of the action, is discussed in the generic case, and the corresponding explicit formulas have been found in the periodic

    更新日期:2020-07-27
  • p -adic boundary laws and Markov chains on trees
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-26
    A. Le Ny; L. Liao; U. A. Rozikov

    In this paper, we consider a potential on general infinite trees with q spin values and nearest-neighbor p-adic interactions given by a stochastic matrix. We show the uniqueness of the associated Markov chain (splitting Gibbs measures) under some sufficient conditions on the stochastic matrix. Moreover, we find a family of stochastic matrices for which there are at least two p-adic Markov chains on

    更新日期:2020-07-26
  • The topology of mobility-gapped insulators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-18
    Jacob Shapiro

    Studying deterministic operators, we define a topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our “insulator” condition makes sense from the point of view of the localization theory using the fractional moments method.

    更新日期:2020-07-18
  • General derivative Thomae formula for singular half-periods
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-16
    J. Bernatska

    The paper develops second Thomae theorem in hyperelliptic case. The main formula, called general Thomae formula, provides expressions for values at zero of the lowest non-vanishing derivatives of theta functions with singular characteristics of arbitrary multiplicity in terms of branch points and period matrix. We call these values derivative theta constants. First and second Thomae formulas follow

    更新日期:2020-07-16
  • Degenerate band edges in periodic quantum graphs
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-13
    Gregory Berkolaiko, Minh Kha

    Edges of bands of continuous spectrum of periodic structures arise as maxima and minima of the dispersion relation of their Floquet–Bloch transform. It is often assumed that the extrema generating the band edges are non-degenerate. This paper constructs a family of examples of \({\mathbb {Z}}^3\)-periodic quantum graphs where the non-degeneracy assumption fails: the maximum of the first band is achieved

    更新日期:2020-07-14
  • Irreducibility of the Fermi surface for planar periodic graph operators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-13
    Wei Li; Stephen P. Shipman

    We prove that the Fermi surface of a connected doubly periodic self-adjoint discrete graph operator is irreducible at all but finitely many energies provided that the graph (1) can be drawn in the plane without crossing edges, (2) has positive coupling coefficients, (3) has two vertices per period. If “positive” is relaxed to “complex,” the only cases of reducible Fermi surface occur for the graph

    更新日期:2020-07-13
  • Semiclassical asymptotic behavior of orthogonal polynomials
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-09
    D. R. Yafaev

    Our goal is to find asymptotic formulas for orthonormal polynomials \(P_{n}(z)\) with the recurrence coefficients slowly stabilizing as \(n\rightarrow \infty \). To that end, we develop scattering theory of Jacobi operators with long-range coefficients and study the corresponding second-order difference equation. We introduce the Jost solutions \(f_{n}(z)\) of this equation by a condition for \(n\rightarrow

    更新日期:2020-07-09
  • Finite-dimensional irreducible modules of the Bannai–Ito algebra at characteristic zero
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-02
    Hau-Wen Huang

    Assume that \({\mathbb {F}}\) is algebraically closed with characteristic 0. A central extension \({\mathfrak {BI}}\) of the Bannai–Ito algebras is a unital associative \({\mathbb {F}}\)-algebra generated by X, Y, Z, and the relations assert that each of$$\begin{aligned} \{X,Y\}-Z, \quad \{Y,Z\}-X, \quad \{Z,X\}-Y \end{aligned}$$is central in \({\mathfrak {BI}}\). In this paper, we classify the finite-dimensional

    更新日期:2020-07-02
  • Higher depth quantum modular forms and plumbed 3-manifolds
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-02
    Kathrin Bringmann; Karl Mahlburg; Antun Milas

    In this paper, we study new invariants \(\widehat{Z}_{{{\varvec{a}}}}(q)\) attached to plumbed 3-manifolds that were introduced by Gukov, Pei, Putrov, and Vafa. These remarkable q-series at radial limits conjecturally compute WRT invariants of the corresponding plumbed 3-manifold. Here, we investigate the series \(\widehat{Z}_{0}(q)\) for unimodular plumbing H-graphs with six vertices. We prove that

    更新日期:2020-07-02
  • New integrable two-centre problem on sphere in Dirac magnetic field
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-30
    A. P. Veselov, Y. Ye

    We present a new family of integrable versions of the Euler two-centre problem on two-dimensional sphere in the presence of the Dirac magnetic monopole of arbitrary charge. The new systems have very special algebraic potential and additional integral quadratic in momenta, both in classical and quantum versions.

    更新日期:2020-06-30
  • Two-dimensional twistor manifolds and Teukolsky operators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-30
    Bernardo Araneda

    The Teukolsky equations are currently the leading approach for analysing stability of linear massless fields propagating in rotating black holes. It has recently been shown that the geometry of these equations can be understood in terms of a connection constructed from the conformal and complex structure of Petrov type D spaces. Since the study of linear massless fields by a combination of conformal

    更新日期:2020-06-30
  • Higher spin $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ s l 2 R -matrix from equivariant (co)homology
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-29
    Dmitri Bykov; Paul Zinn-Justin

    We compute the rational \({{\mathfrak {s}}}{{\mathfrak {l}}}_2\)R-matrix acting in the product of two spin-\(\ell \over 2\) (\({\ell \in {\mathbb {N}}}\)) representations, using a method analogous to the one of Maulik and Okounkov, i.e., by studying the equivariant (co)homology of certain algebraic varieties. These varieties, first considered by Nekrasov and Shatashvili, are typically singular. They

    更新日期:2020-06-29
  • Uniqueness of Gibbs fields with unbounded random interactions on unbounded degree graphs
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-29
    Dorota Kȩpa-Maksymowicz; Yuri Kozitsky

    Gibbs fields with continuous spins are studied, the underlying graphs of which can be of unbounded vertex degree and the spin–spin pair interaction potentials are random and unbounded. A high-temperature uniqueness of such fields is proved to hold under the following conditions: (a) the vertex degree is of tempered growth, i.e., controlled in a certain way; (b) the interaction potentials \(W_{xy}\)

    更新日期:2020-06-29
  • Compactness property of Lie polynomials in the creation and annihilation operators of the q -oscillator
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-28
    Rafael Reno S. Cantuba

    Given a real number q such that \(0

    更新日期:2020-06-28
  • Discriminant and Hodge classes on the space of Hitchin covers
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-27
    Mikhail Basok

    We continue the study of the rational Picard group of the moduli space of Hitchin spectral covers started in Korotkin and Zograf (J Math Phys 59(9):091412, 2018). In the first part of the paper we expand the “boundary”, “Maxwell stratum” and “caustic” divisors introduced in Korotkin and Zograf (2018) via the set of standard generators of the rational Picard group. This generalizes the result of Korotkin

    更新日期:2020-06-27
  • Complexes of marked graphs in gauge theory
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-24
    Marko Berghoff; Andre Knispel

    We review the gauge and ghost cyle graph complexes as defined by Kreimer, Sars and van Suijlekom in “Quantization of gauge fields, graph polynomials and graph homology” and compute their cohomology. These complexes are generated by labelings on the edges or cycles of graphs and the differentials act by exchanging these labels. We show that both cases are instances of a more general construction of

    更新日期:2020-06-24
  • Time operators for quantum walks
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-20
    Daiju Funakawa; Yasumichi Matsuzawa; Itaru Sasaki; Akito Suzuki; Noriaki Teranishi

    We study time operators for discrete-time quantum systems. Quantum walks are typical examples. We construct time operators for one-dimensional homogeneous quantum walks and determine their deficiency indices and spectra. Our time operators always have self-adjoint extensions. This is in contrast to the fact that time operators for continuous-time quantum systems generally have no self-adjoint extensions

    更新日期:2020-06-20
  • Amortized channel divergence for asymptotic quantum channel discrimination
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-18
    Mark M. Wilde; Mario Berta; Christoph Hirche; Eneet Kaur

    It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi (IEEE Trans Inf Theory 55(8):3807–3820, 2009. arXiv:0804.0686) showed that in the asymptotic regime, the exponential error rate for the discrimination of classical channels is not improved in the

    更新日期:2020-06-18
  • Perfect state transfer on weighted graphs of the Johnson scheme
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-17
    Luc Vinet; Hanmeng Zhan

    We characterize quantum perfect state transfer on real-weighted graphs of the Johnson scheme \({\mathcal {J}}(n,k)\), which represent spin networks with non-nearest neighbor couplings. Given \({\mathcal {J}}(n,k)=\{A_{1},A_{2},\ldots ,A_{k}\}\) and \(A(X) = w_0A_0 + \cdots + w_m A_m\), we show that X has perfect state transfer at time \(\tau \) if and only if \(n=2k\), \(m\ge 2^{\lfloor {\log _2(k)}

    更新日期:2020-06-17
  • Strong integrability of the bi-YB–WZ model
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-15
    Ctirad Klimčík

    We identify the r-matrix governing the Poisson brackets of the matrix elements of the Lax operator of the bi-YB–WZ model.

    更新日期:2020-06-15
  • A gravitational collapse singularity theorem consistent with black hole evaporation
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-11
    E. Minguzzi

    The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work, I show that the causality conditions in Penrose’s theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in the absence of predictability and hence

    更新日期:2020-06-11
  • Spacelike deformations: higher-helicity fields from scalar fields
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-11
    Vincenzo Morinelli; Karl-Henning Rehren

    In contrast to Hamiltonian perturbation theory which changes the time evolution, “spacelike deformations” proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of spacelike deformations of the complex massless Klein–Gordon quantum field into fields of higher helicity. A similar but simpler instance of spacelike deformation

    更新日期:2020-06-11
  • A formula for the relative entropy in chiral CFT
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-09
    Lorenzo Panebianco

    We prove the QNEC on the Virasoro nets for a class of unitary states extending the coherent states, that is states obtained by applying an exponentiated stress energy tensor to the vacuum. We also verify the Bekenstein Bound by computing the relative entropy on a bounded interval.

    更新日期:2020-06-09
  • Characteristic (Fedosov-)class of a twist constructed by Drinfel’d
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-31
    Jonas Schnitzer

    In a seminal paper, Drinfel’d explained how to associate with every classical r-matrix, which are called triangular r-matrices by some authors, for a Lie algebra \( \mathfrak {g}\) a twisting element based on \({\mathcal {U}}(\mathfrak {g})[[\hbar ]]\), or equivalently a left invariant star product quantizing the left-invariant Poisson structure corresponding to r on the 1-connected Lie group G of

    更新日期:2020-05-31
  • Characters of tangent spaces at torus fixed points and 3 d -mirror symmetry
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-29
    Andrey Smirnov; Hunter Dinkins

    Let X be a Nakajima quiver variety and \(X'\) its 3d-mirror. We consider the action of the Picard torus \({\mathsf {K}}=\mathrm {Pic}(X)\otimes {\mathbb {C}}^{\times }\) on \(X'\). Assuming that \((X')^{{\mathsf {K}}}\) is finite, we propose a procedure for obtaining the \({\mathsf {K}}\)-character of the tangent spaces at the fixed points in terms of certain enumerative invariants of X known as vertex

    更新日期:2020-05-29
  • Poisson vertex algebras in supersymmetric field theories
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-25
    Jihwan Oh; Junya Yagi

    A large class of supersymmetric quantum field theories, including all theories with \({\mathcal {N}}= 2\) supersymmetry in three dimensions and theories with \({\mathcal {N}}= 2\) supersymmetry in four dimensions, possess topological–holomorphic sectors. We formulate Poisson vertex algebras in such topological–holomorphic sectors and discuss some examples. For a four-dimensional \({\mathcal {N}}= 2\)

    更新日期:2020-05-25
  • Chern–Simons–Schrödinger theory on a one-dimensional lattice
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-23
    Hyungjin Huh; Swaleh Hussain; Dmitry E. Pelinovsky

    We propose a gauge-invariant system of the Chern–Simons–Schrödinger type on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global well-posedness of the initial-value problem in the space of square summable sequences for the scalar field. We also study the existence region of the stationary bound states, which depends on the lattice spacing and the nonlinearity power

    更新日期:2020-05-23
  • Variational representations related to Tsallis relative entropy
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-07
    Guanghua Shi; Frank Hansen

    We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden–Thompson’s trace inequality to deformed exponentials with deformation parameter \( q\in [0,1], \) thus complementing the second author’s previous study of the cases with deformation parameter

    更新日期:2020-05-07
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