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  • Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-16
    Masayuki Fukuda, Yusuke Ohkubo, Jun’ichi Shiraishi

    An explicit formula is obtained for the generalized Macdonald functions on the N-fold Fock tensor spaces, calculating a certain matrix element of a composition of several screened vertex operators. As an application, we prove the factorization property of the arbitrary matrix elements of the multi-valent intertwining operator (or refined topological vertex operator) associated with the Ding–Iohara–Miki

    更新日期:2020-10-17
  • Maximal Fluctuations Around the Wulff Shape for Edge-Isoperimetric Sets in $$\varvec{{\mathbb {Z}}^d}$$ Z d : A Sharp Scaling Law
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-15
    Edoardo Mainini, Bernd Schmidt

    We derive a sharp scaling law for deviations of edge-isoperimetric sets in the lattice \({\mathbb {Z}}^d\) from the limiting Wulff shape in arbitrary dimensions. As the number n of elements diverges, we prove that the symmetric difference to the corresponding Wulff set consists of at most \(O(n^{(d-1+2^{1-d})/d})\) lattice points and that the exponent \((d-1+2^{1-d})/d\) is optimal. This extends the

    更新日期:2020-10-16
  • Exact WKB and Abelianization for the $$T_3$$ T 3 Equation
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-13
    Lotte Hollands, Andrew Neitzke

    We describe the exact WKB method from the point of view of abelianization, both for Schrödinger operators and for their higher-order analogues (opers). The main new example which we consider is the “\(T_3\) equation,” an order 3 equation on the thrice-punctured sphere, with regular singularities at the punctures. In this case the exact WKB analysis leads to consideration of a new sort of Darboux coordinate

    更新日期:2020-10-13
  • Super Quantum Airy Structures
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-13
    Vincent Bouchard, Paweł Ciosmak, Leszek Hadasz, Kento Osuga, Błażej Ruba, Piotr Sułkowski

    We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations

    更新日期:2020-10-13
  • Correction to: Equidistribution of Eisenstein Series in the Level Aspect
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-10
    Ikuya Kaneko, Shin-ya Koyama

    The second author formulated quantum unique ergodicity for Eisenstein series in the prime level aspect in “Equidistribution of Eisenstein series in the level aspect”, Commun. Math. Phys. 289(3) 1150 (2009). We point out errors and correct the proofs with partially weakened claims.

    更新日期:2020-10-11
  • Extending Landau-Ginzburg Models to the Point
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-07
    Nils Carqueville, Flavio Montiel Montoya

    We classify framed and oriented 2-1-0-extended TQFTs with values in the bicategories of Landau-Ginzburg models, whose objects and 1-morphisms are isolated singularities and (either \(\mathbb {Z}_2\)- or \((\mathbb {Z}_2 \times \mathbb {Q})\)-graded) matrix factorisations, respectively. For this we present the relevant symmetric monoidal structures and find that every object \(W\in \mathbb {k}[x_1,\dots

    更新日期:2020-10-07
  • Ripples in Graphene: A Variational Approach
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-06
    Manuel Friedrich, Ulisse Stefanelli

    Suspended graphene samples are observed to be gently rippled rather than being flat. In Friedrich et al. (Z Angew Math Phys 69:70, 2018), we have checked that this nonplanarity can be rigorously described within the classical molecular-mechanical frame of configurational-energy minimization. There, we have identified all ground-state configurations with graphene topology with respect to classes of

    更新日期:2020-10-07
  • Twisted Modules and G -equivariantization in Logarithmic Conformal Field Theory
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-06
    Robert McRae

    A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic conformal field theory (in which correlation functions have logarithmic singularities arising from non-semisimple modules for the chiral algebra) because of the logarithmic

    更新日期:2020-10-07
  • Vertex Algebras for S-duality
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-06
    Thomas Creutzig, Davide Gaiotto

    We define new deformable families of vertex operator algebras \(\mathfrak {A}[\mathfrak {g}, \Psi , \sigma ]\) associated to a large set of S-duality operations in four-dimensional supersymmetric gauge theory. They are defined as algebras of protected operators for two-dimensional supersymmetric junctions which interpolate between a Dirichlet boundary condition and its S-duality image. The \(\mathfrak

    更新日期:2020-10-07
  • Spectral Decimation of the Magnetic Laplacian on the Sierpinski Gasket: Solving the Hofstadter–Sierpinski Butterfly
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-06
    Joe P. Chen, Ruoyu Guo

    The magnetic Laplacian (also called the line bundle Laplacian) on a connected weighted graph is a self-adjoint operator wherein the real-valued adjacency weights are replaced by unit complex-valued weights \(\{\omega _{xy}\}_{xy\in E}\), satisfying the condition that \(\omega _{xy}=\overline{\omega _{yx}}\) for every directed edge xy. When properly interpreted, these complex weights give rise to magnetic

    更新日期:2020-10-06
  • Deformations and Homotopy Theory of Relative Rota–Baxter Lie Algebras
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-04
    Andrey Lazarev, Yunhe Sheng, Rong Tang

    We determine the \(L_\infty \)-algebra that controls deformations of a relative Rota–Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying \(\mathsf {Lie}\mathsf {Rep}\) pair by the dg Lie algebra controlling deformations of the relative Rota–Baxter operator. Consequently, we define the cohomology of relative Rota–Baxter Lie algebras and

    更新日期:2020-10-04
  • Decay of Hamiltonian Breathers Under Dissipation
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-03
    Jean-Pierre Eckmann, C. Eugene Wayne

    We study metastable behavior in a discrete nonlinear Schrödinger equation from the viewpoint of Hamiltonian systems theory. When there are \(n<\infty \) sites in this equation, we consider initial conditions in which almost all the energy is concentrated in one end of the system. We are interested in understanding how energy flows through the system, so we add a dissipation of size \(\gamma \) at the

    更新日期:2020-10-04
  • On Ergodic Embeddings of Factors
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-01
    Sorin Popa

    An inclusion of von Neumann factors \(M \subset \mathcal {M}\) is ergodic if it satisfies the irreducibility condition \(M'\cap \mathcal {M}=\mathbb {C}\). We investigate the relation between this and several stronger ergodicity properties, such as R-ergodicity, which requires M to admit an embedding of the hyperfinite II\(_1\) factor \(R\hookrightarrow M\) that’s ergodic in \(\mathcal {M}\). We prove

    更新日期:2020-10-02
  • Representations of Cohomological Hall Algebras and Donaldson–Thomas Theory with Classical Structure Groups
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-10-01
    Matthew B. Young

    We introduce a new class of representations of the cohomological Hall algebras of Kontsevich and Soibelman, which we call cohomological Hall modules, or CoHM for short. These representations are constructed from self-dual representations of a quiver with contravariant involution \(\sigma \) and provide a mathematical model for the space of BPS states in orientifold string theory. We use the CoHM to

    更新日期:2020-10-02
  • Refined Topological Branes
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-30
    Can Kozçaz, Shamil Shakirov, Cumrun Vafa, Wenbin Yan

    We study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary conditions of open amplitudes (which in particular satisfy the required integrality properties). We also derive the refined holonomies using the refined Chern–Simons theory.

    更新日期:2020-09-30
  • S-Duality and Refined BPS Indices
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-30
    Sergei Alexandrov, Jan Manschot, Boris Pioline

    Whenever available, refined BPS indices provide considerably more information on the spectrum of BPS states than their unrefined version. Extending earlier work on the modularity of generalized Donaldson–Thomas invariants counting D4-D2-D0 brane bound states in type IIA strings on a Calabi–Yau threefold \(\mathfrak {Y}\), we construct the modular completion of generating functions of refined BPS indices

    更新日期:2020-09-30
  • Coexistency on Hilbert Space Effect Algebras and a Characterisation of Its Symmetry Transformations
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-30
    György Pál Gehér, Peter Šemrl

    The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig’s formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper’s

    更新日期:2020-09-30
  • Couplings via Comparison Principle and Exponential Ergodicity of SPDEs in the Hypoelliptic Setting
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-29
    Oleg Butkovsky, Michael Scheutzow

    We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence of transition probabilities of an order-preserving Markov process. As an application, we show exponential ergodicity and exponentially fast synchronization-by-noise

    更新日期:2020-09-30
  • Adiabatic Invariants for the FPUT and Toda Chain in the Thermodynamic Limit
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-29
    T. Grava, A. Maspero, G. Mazzuca, A. Ponno

    We consider the Fermi–Pasta–Ulam–Tsingou (FPUT) chain composed by \(N \gg 1\) particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature \(\beta ^{-1}\). Given a fixed \({1\le m \ll N}\), we prove that the first m integrals of motion of the periodic Toda chain are adiabatic invariants of FPUT (namely they are approximately constant along the Hamiltonian

    更新日期:2020-09-29
  • Quantization of Dynamical Symplectic Reduction
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-26
    Martin Bojowald, Artur Tsobanjan

    A long-standing problem in quantum gravity and cosmology is the quantization of systems in which time evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented, together with new structures and results, which show that specific conditions need to be satisfied in order for well-defined evolution to be possible.

    更新日期:2020-09-26
  • Propagation of Massive Scalar Fields in Pre-Big Bang Cosmologies
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-24
    Alain Bachelot

    We investigate the linear and semilinear massive Klein–Gordon equations in geometrical frameworks of type “Conformal Cyclic Cosmology” of R. Penrose, or “Singular Bouncing Scenario” as well. We give sufficient conditions on the decay of the mass to the fields be able to propagate across the Big-Bang.

    更新日期:2020-09-25
  • Discrete Symmetries of Complete Intersection Calabi–Yau Manifolds
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-24
    Andre Lukas, Challenger Mishra

    In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi–Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi–Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for

    更新日期:2020-09-24
  • Entropy Accumulation
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-23
    Frédéric Dupuis, Omar Fawzi, Renato Renner

    We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an n-partite system \(A = (A_1, \ldots A_n)\) corresponds to the sum of the entropies of its parts \(A_i\). The Asymptotic Equipartition Property implies that this is indeed the case to first order in n—under the assumption that the parts \(A_i\) are identical and independent of each

    更新日期:2020-09-23
  • A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-23
    Yannis Angelopoulos, Stefanos Aretakis, Dejan Gajic

    It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence yields a much milder blueshift effect when viewed in the

    更新日期:2020-09-23
  • Conformal 3-Point Functions and the Lorentzian OPE in Momentum Space
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-20
    Marc Gillioz

    In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that the Wightman function of three scalar operators is a double hypergeometric series of the Appell \(F_4\) type. We extend this simple closed-form expression

    更新日期:2020-09-22
  • Positive Lyapunov Exponent for Some Schrödinger Cocycles Over Strongly Expanding Circle Endomorphisms
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-16
    Kristian Bjerklöv

    We show that for a large class of potential functions and big coupling constant \(\lambda \) the Schrödinger cocycle over the expanding map \(x\mapsto bx ~( \text{ mod } 1)\) on \(\mathbb {T}\) has a Lyapunov exponent \(>(\log \lambda )/4\) for all energies, provided that the integer \(b\ge \lambda ^3\).

    更新日期:2020-09-22
  • Integral Formulas of ASEP and q -TAZRP on a Ring
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-16
    Zhipeng Liu, Axel Saenz, Dong Wang

    In this paper, we obtain the transition probability formulas for the asymmetric simple exclusion process and the q-deformed totally asymmetric zero range process on the ring by applying the coordinate Bethe ansatz. We also compute the distribution function for a tagged particle with general initial condition.

    更新日期:2020-09-22
  • Asymmetric Unimodal Maps with Non-universal Period-Doubling Scaling Laws
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-18
    Oleg Kozlovski, Sebastian van Strien

    We consider a family of strongly-asymmetric unimodal maps \(\{f_t\}_{t\in [0,1]}\) of the form \(f_t=t\cdot f\) where \(f:[0,1]\rightarrow [0,1]\) is unimodal, \(f(0)=f(1)=0\), \(f(c)=1\) is of the form and $$\begin{aligned} f(x)=\left\{ \begin{array}{ll} 1-K_-|x-c|+o(|x-c|)&{} \text{ for } xc, \end{array}\right. \end{aligned}$$ where we assume that \(\beta >1\). We show that such a family contains

    更新日期:2020-09-22
  • Limiting Absorption Principle and Well-Posedness for the Time-Harmonic Maxwell Equations with Anisotropic Sign-Changing Coefficients
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-16
    Hoai-Minh Nguyen, Swarnendu Sil

    We study the limiting absorption principle and the well-posedness of Maxwell equations with anisotropic sign-changing coefficients in the time-harmonic domain. The starting point of the analysis is to obtain Cauchy problems associated with two Maxwell systems using a change of variables. We then derive a priori estimates for these Cauchy problems using two different approaches. The Fourier approach

    更新日期:2020-09-22
  • Random Walk on the Simple Symmetric Exclusion Process
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-26
    Marcelo R. Hilário, Daniel Kious, Augusto Teixeira

    We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole, so that its asymptotic behavior is expected to depend on the density \(\rho \in [0, 1]\) of the underlying SSEP. Our first

    更新日期:2020-09-22
  • Set-Theoretic Solutions of the Pentagon Equation
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-19
    Ilaria Colazzo, Eric Jespers, Łukasz Kubat

    A set-theoretic solution of the Pentagon Equation on a non-empty set S is a map \(s:S^2\rightarrow S^2\) such that \(s_{23}s_{13}s_{12}=s_{12}s_{23}\), where \(s_{12}=s\times {{{\,\mathrm{id}\,}}}\), \(s_{23}={{{\,\mathrm{id}\,}}}\times s\) and \(s_{13}=(\tau \times {{{\,\mathrm{id}\,}}})({{{\,\mathrm{id}\,}}}\times s)(\tau \times {{{\,\mathrm{id}\,}}})\) are mappings from \(S^3\) to itself and \(\tau

    更新日期:2020-09-20
  • Partition Functions as C*-Dynamical Invariants and Actions of Congruence Monoids
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-19
    Chris Bruce, Marcelo Laca, Takuya Takeishi

    We study KMS states for the C*-algebras of \(ax+b\)-semigroups of algebraic integers in which the multiplicative part is restricted to a congruence monoid, as in recent work of Bruce. We realize the extremal low-temperature KMS states as generalized Gibbs states in concrete representations induced from extremal traces of certain group C*-algebras. We use these representations to compute the type of

    更新日期:2020-09-20
  • Positive Energy Representations of Affine Vertex Algebras
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-19
    Vyacheslav Futorny, Libor Křižka

    We construct new families of positive energy representations of affine vertex algebras together with their free field realizations by using localization technique. We introduce the twisting functor \(T_\alpha \) on the category of modules over the universal affine vertex algebra \(\mathcal {V}_\kappa (\mathfrak {g})\) of level \(\kappa \) for any positive root \(\alpha \) of \(\mathfrak {g}\), and

    更新日期:2020-09-20
  • Absence of Eigenvalues of Dirac and Pauli Hamiltonians via the Method of Multipliers
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-18
    Lucrezia Cossetti, Luca Fanelli, David Krejčiřík

    By developing the method of multipliers, we establish sufficient conditions on the magnetic field and the complex, matrix-valued electric potential, which guarantee that the corresponding system of Schrödinger operators has no point spectrum. In particular, this allows us to prove analogous results for Pauli operators under the same electromagnetic conditions and, in turn, as a consequence of the supersymmetric

    更新日期:2020-09-20
  • Physics and Geometry of Knots-Quivers Correspondence
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-18
    Tobias Ekholm, Piotr Kucharski, Pietro Longhi

    The recently conjectured knots-quivers correspondence (Kucharski et al. in Phys Rev D 96(12):121902, 2017. arXiv:1707.02991, Adv Theor Math Phys 23(7):1849–1902, 2019. arXiv:1707.04017) relates gauge theoretic invariants of a knot K in the 3-sphere to the representation theory of a quiver \(Q_{K}\) associated to the knot. In this paper we provide geometric and physical contexts for this conjecture

    更新日期:2020-09-20
  • Hodge–GUE Correspondence and the Discrete KdV Equation
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-17
    Boris Dubrovin, Si-Qi Liu, Di Yang, Youjin Zhang

    We prove the conjectural relationship recently proposed in Dubrovin and Yang (Commun Number Theory Phys 11:311–336, 2017) between certain special cubic Hodge integrals of the Gopakumar–Mariño–Vafa type (Gopakumar and Vafa in Adv Theor Math Phys 5:1415–1443, 1999, Mariño and Vafa in Contemp Math 310:185–204, 2002) and GUE correlators, and the conjecture proposed in Dubrovin et al. (Adv Math 293:382–435

    更新日期:2020-09-18
  • Invariance Principle for the Random Lorentz Gas—Beyond the Boltzmann-Grad Limit
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-16
    Christopher Lutsko, Bálint Tóth

    We prove the invariance principle for a random Lorentz-gas particle in 3 dimensions under the Boltzmann-Grad limit and simultaneous diffusive scaling. That is, for the trajectory of a point-like particle moving among infinite-mass, hard-core, spherical scatterers of radius r, placed according to a Poisson point process of density \(\varrho \), in the limit \(\varrho \rightarrow \infty \), \(r\rightarrow

    更新日期:2020-09-16
  • Asymptotic Expansions for the Lagrangian Trajectories from Solutions of the Navier–Stokes Equations
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-16
    Luan Hoang

    Consider any Leray–Hopf weak solution of the three-dimensional Navier–Stokes equations for incompressible, viscous fluid flows. We prove that any Lagrangian trajectory associated with such a velocity field has an asymptotic expansion, as time tends to infinity, which describes its long-time behavior very precisely.

    更新日期:2020-09-16
  • Burkholder–Davis–Gundy Inequalities in UMD Banach Spaces
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-16
    Ivan Yaroslavtsev
    更新日期:2020-09-16
  • Self-similar Asymptotics for a Modified Maxwell–Boltzmann Equation in Systems Subject to Deformations
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-15
    Alexander Bobylev, Alessia Nota, Juan J. L. Velázquez

    In this paper we study a generalized class of Maxwell–Boltzmann equations which in addition to the usual collision term contains a linear deformation term described by a matrix A. This class of equations arises, for instance, from the analysis of homoenergetic solutions for the Boltzmann equation considered by many authors since 1950s. Our main goal is to study a large time asymptotics of solutions

    更新日期:2020-09-16
  • Existence and Rigidity of Quantum Isometry Groups for Compact Metric Spaces
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-15
    Alexandru Chirvasitu, Debashish Goswami

    We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed probability measure. In the former case it also follows from recent results of the second author that the quantum isometry group is classical, i.e. the commutative \(C^*\)-algebra

    更新日期:2020-09-16
  • Scattering with Critically-Singular and $$\delta $$ δ -Shell Potentials
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-15
    Pedro Caro, Andoni Garcia

    We consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz hypersurface. We study direct and inverse point-source scattering under the assumptions that the potentials are real-valued and compactly supported. To solve the direct scattering problem, we

    更新日期:2020-09-16
  • Microlocal Analysis of the Bulk-Edge Correspondence
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-15
    Alexis Drouot

    The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods. It suggests novel perspectives for the analysis of topologically protected transport.

    更新日期:2020-09-16
  • Low-Energy Spectrum of Toeplitz Operators with a Miniwell
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-28
    Alix Deleporte

    We study the concentration properties of low-energy states for quantum systems in the semiclassical limit, in the setting of Toeplitz operators, which include quantum spin systems as a large class of examples. We establish tools proper to Toeplitz quantization to give a general subprincipal criterion for localisation. In addition, we build up symplectic normal forms in two particular settings, including

    更新日期:2020-09-16
  • Sign Choices for Orientifolds
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-18
    Pedram Hekmati, Michael K. Murray, Richard J. Szabo, Raymond F. Vozzo

    We analyse the problem of assigning sign choices to O-planes in orientifolds of type II string theory. We show that there exists a sequence of invariant p-gerbes with \(p\ge -1\), which give rise to sign choices and are related by coboundary maps. We prove that the sign choice homomorphisms stabilise with the dimension of the orientifold and we derive topological constraints on the possible sign configurations

    更新日期:2020-09-16
  • FC Sets and Twisters: The Basics of Orbifold Deconstruction
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-15
    Peter Bantay

    We present a detailed account of the properties of \(\text {twister}\)s and their generalizations, \(\text {FC set}\)s, which are essential ingredients of the orbifold deconstruction procedure aimed at recognizing whether a given conformal model may be obtained as an orbifold of another one, and if so, to identify the twist group and the original model. The close analogy with the character theory of

    更新日期:2020-09-15
  • Non-tracial Free Graph von Neumann Algebras
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-14
    Michael Hartglass, Brent Nelson

    Given a finite, directed, connected graph \(\Gamma \) equipped with a weighting \(\mu \) on its edges, we provide a construction of a von Neumann algebra equipped with a faithful, normal, positive linear functional \((\mathcal {M}(\Gamma ,\mu ),\varphi )\). When the weighting \(\mu \) is instead on the vertices of \(\Gamma \), the first author showed the isomorphism class of \((\mathcal {M}(\Gamma

    更新日期:2020-09-14
  • Inviscid Damping and Enhanced Dissipation of the Boundary Layer for 2D Navier–Stokes Linearized Around Couette Flow in a Channel
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-11
    Jacob Bedrossian, Siming He

    We study the 2D Navier–Stokes equations linearized around the Couette flow \((y,0)^t\) in the periodic channel \({\mathbb {T}} \times [-1,1]\) with no-slip boundary conditions in the vanishing viscosity \(\nu \rightarrow 0\) limit. We split the vorticity evolution into the free evolution (without a boundary) and a boundary corrector that is exponentially localized to at most an \(O(\nu ^{1/3})\) boundary

    更新日期:2020-09-11
  • Analytic Torsion for Surfaces with Cusps I: Compact Perturbation Theorem and Anomaly Formula
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-09-01
    Siarhei Finski

    We define the analytic torsion associated with a Riemann surface endowed with a metric having Poincaré-type singularities in the neighborhood of a finite number of points and a Hermitian vector bundle with at most logarithmic singularities at those points, coming from the metric on the negative power of the canonical line bundle twisted by the divisor of the points. Then we provide a relation between

    更新日期:2020-09-01
  • $$\underline{p}$$ p ̲ -reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$ W -algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ W ( gl N , p ̲ )
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-04
    Sylvain Carpentier, Alberto De Sole, Victor G. Kac, Daniele Valeri, Johan van de Leur

    For each partition \(\underline{p}\) of an integer \(N\ge 2\), consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the \(\underline{p}\)-reduced r-component KP hierarchy produces a solution of this integrable hierarchy. Along the way we provide an algorithm for the explicit construction

    更新日期:2020-08-05
  • Dispersionless Integrable Hierarchy via Kodaira–Spencer Gravity
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-08-03
    Weiqiang He, Si Li, Xinxing Tang, Philsang Yoo

    We explain how dispersionless integrable hierarchy in 2d topological field theory arises from the Kodaira–Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians are given by the current observables associated to the infinite abelian symmetries of the Kodaira–Spencer gravity. We describe a BV framework of effective field theories that leads to the B-model interpretation of dispersionless

    更新日期:2020-08-04
  • Quantum Fields and Local Measurements
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-27
    Christopher J. Fewster; Rainer Verch

    The process of quantum measurement is considered in the algebraic framework of quantum field theory on curved spacetimes. Measurements are carried out on one quantum field theory, the “system”, using another, the “probe”. The measurement process involves a dynamical coupling of “system” and “probe” within a bounded spacetime region. The resulting “coupled theory” determines a scattering map on the

    更新日期:2020-07-27
  • Almost Sure Weyl Law for Quantized Tori
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-25
    Martin Vogel

    We study the eigenvalues of the Toeplitz quantization of complex-valued functions on the torus subject to small random perturbations given by a complex-valued random matrix whose entries are independent copies of a random variable with mean 0, variance 1 and bounded fourth moment. We prove that the eigenvalues of the perturbed operator satisfy a Weyl law with probability close to one, which proves

    更新日期:2020-07-25
  • Pollicott-Ruelle Resonant States and Betti Numbers.
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-22
    Benjamin Küster,Tobias Weich

    Given a closed orientable hyperbolic manifold of dimension \(\ne 3\) we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector

    更新日期:2020-07-22
  • The Geometry of the Space of BPS Vortex–Antivortex Pairs
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-21
    N. M. Romão, J. M. Speight

    The gauged sigma model with target \({\mathbb {P}}^1\), defined on a Riemann surface \(\Sigma \), supports static solutions in which \(k_{+}\) vortices coexist in stable equilibrium with \(k_{-}\) antivortices. Their moduli space is a noncompact complex manifold \({\textsf {M}}_{(k_{+},k_{-})}(\Sigma )\) of dimension \(k_{+}+k_{-}\) which inherits a natural Kähler metric \(g_{L^2}\) governing the model’s

    更新日期:2020-07-21
  • Equivariant K -Theory and Refined Vafa–Witten Invariants
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-20
    Richard P. Thomas

    In Maulik and Thomas (in preparation) the Vafa–Witten theory of complex projective surfaces is lifted to oriented \({\mathbb {C}}^*\)-equivariant cohomology theories. Here we study the K-theoretic refinement. It gives rational functions in \(t^{1/2}\) invariant under \(t^{1/2}\leftrightarrow t^{-1/2}\) which specialise to numerical Vafa–Witten invariants at \(t=1\). On the “instanton branch” the invariants

    更新日期:2020-07-20
  • Hodge and Prym Tau Functions, Strebel Differentials and Combinatorial Model of $${\mathcal {M}}_{g,n}$$ M g , n
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-20
    M. Bertola; D. Korotkin

    The goal of the paper is to apply the theory of integrable systems to construct explicit sections of line bundles over the combinatorial model of the moduli space of pointed Riemann surfaces based on Strebel differentials. These line bundles are tensor products of the determinants of the Hodge or Prym vector bundles with the standard tautological line bundles \(\mathcal {L}_j\), and the sections are

    更新日期:2020-07-20
  • Critical Behavior of Non-intersecting Brownian Motions
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-18
    Tom Claeys; Thorsten Neuschel; Martin Venker

    We study n non-intersecting Brownian motions corresponding to initial configurations which have a vanishing density in the large n limit at an interior point of the support. It is understood that the point of vanishing can propagate up to a critical time, and we investigate the nature of the microscopic space-time correlations near the critical point and critical time. We show that they are described

    更新日期:2020-07-18
  • Measuring Mass via Coordinate Cubes
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-16
    Pengzi Miao

    Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat 3-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral angle, the resulting mass formula relates to Gromov’s scalar curvature comparison theory for cubic Riemannian polyhedra. In terms of the geodesic curvature and turning

    更新日期:2020-07-16
  • State Convertibility in the von Neumann Algebra Framework
    Commun. Math. Phys. (IF 2.102) Pub Date : 2020-07-16
    Jason Crann; David W. Kribs; Rupert H. Levene; Ivan G. Todorov

    We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation to this setting of Nielsen’s theorem on the convertibility of quantum states under local operations and classical communication (LOCC) schemes. Along the way, we

    更新日期:2020-07-16
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