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MATHEMATICS (658 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 25)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 9)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 7)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 3)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 9)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 1)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 6)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  

        1 2 3 4 | Last

Journal Cover Communications in Mathematical Physics
  [SJR: 1.76]   [H-I: 101]   [1 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0916 - ISSN (Online) 0010-3616
   Published by Springer-Verlag Homepage  [2354 journals]
  • The Dynamic $${\Phi^4_3}$$ Φ 3 4 Model Comes Down from Infinity
    • Authors: Jean-Christophe Mourrat; Hendrik Weber
      Pages: 673 - 753
      Abstract: We prove an a priori bound for the dynamic \({\Phi^4_3}\) model on the torus which is independent of the initial condition. In particular, this bound rules out the possibility of finite time blow-up of the solution. It also gives a uniform control over solutions at large times, and thus allows one to construct invariant measures via the Krylov–Bogoliubov method. It thereby provides a new dynamic construction of the Euclidean \({\Phi^4_3}\) field theory on finite volume. Our method is based on the local-in-time solution theory developed recently by Gubinelli, Imkeller, Perkowski and Catellier, Chouk. The argument relies entirely on deterministic PDE arguments (such as embeddings of Besov spaces and interpolation), which are combined to derive energy inequalities.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2997-4
      Issue No: Vol. 356, No. 3 (2017)
  • Global Normal Form and Asymptotic Spectral Gap for Open Partially
           Expanding Maps
    • Authors: Frédéric Faure; Tobias Weich
      Pages: 755 - 822
      Abstract: We consider a \({\mathbb{R}}\) -extension of one dimensional uniformly expanding open dynamical systems and prove a new explicit estimate for the asymptotic spectral gap. To get these results, we use a new application of a “global normal form” for the dynamical system, a “semiclassical expression beyond the Ehrenfest time” that expresses the transfer operator at large time as a sum over rank one operators (each is associated to one orbit). In this paper we establish the validity of the so-called “diagonal approximation” up to twice the local Ehrenfest time.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-3000-0
      Issue No: Vol. 356, No. 3 (2017)
  • Beyond Aztec Castles: Toric Cascades in the dP 3 Quiver
    • Authors: Tri Lai; Gregg Musiker
      Pages: 823 - 881
      Abstract: Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi–Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In combinatorial language, a brane tiling is a bipartite graph on a torus and its perfect matchings are of interest to both combinatorialists and physicists alike. A cluster algebra may also be associated to such quivers and in this paper we study the generators of this algebra, known as cluster variables, for the quiver associated to the cone over the del Pezzo surface d P 3. In particular, mutation sequences involving mutations exclusively at vertices with two in-coming arrows and two out-going arrows are referred to as toric cascades in the string theory literature. Such toric cascades give rise to interesting discrete integrable systems on the level of cluster variable dynamics. We provide an explicit algebraic formula for all cluster variables that are reachable by toric cascades as well as a combinatorial interpretation involving perfect matchings of subgraphs of the d P 3 brane tiling for these formulas in most cases.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2993-8
      Issue No: Vol. 356, No. 3 (2017)
  • Gibbs Measures of Nonlinear Schrödinger Equations as Limits of Many-Body
           Quantum States in Dimensions $${d \leqslant 3}$$ d ⩽ 3
    • Authors: Jürg Fröhlich; Antti Knowles; Benjamin Schlein; Vedran Sohinger
      Pages: 883 - 980
      Abstract: We prove that Gibbs measures of nonlinear Schrödinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing interactions in dimensions \({d =1,2,3}\) . The many-body quantum thermal states that we consider are the grand canonical ensemble for d = 1 and an appropriate modification of the grand canonical ensemble for \({d =2,3}\) . In dimensions d = 2, 3, the Gibbs measures are supported on singular distributions, and a renormalization of the chemical potential is necessary. On the many-body quantum side, the need for renormalization is manifested by a rapid growth of the number of particles. We relate the original many-body quantum problem to a renormalized version obtained by solving a counterterm problem. Our proof is based on ideas from field theory, using a perturbative expansion in the interaction, organized by using a diagrammatic representation, and on Borel resummation of the resulting series.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2994-7
      Issue No: Vol. 356, No. 3 (2017)
  • Modular Data for the Extended Haagerup Subfactor
    • Authors: Terry Gannon; Scott Morrison
      Pages: 981 - 1015
      Abstract: We compute the modular data (that is, the S and T matrices) for the centre of the extended Haagerup subfactor [BMPS12]. The full structure (i.e., the associativity data, also known as 6-j symbols or F matrices) still appears to be inaccessible. Nevertheless, starting with just the number of simple objects and their dimensions (obtained by a combinatorial argument in [MW14]) we find that it is surprisingly easy to leverage knowledge of the representation theory of \({SL (2, \mathbb{Z})}\) into a complete description of the modular data. We also investigate the possible character vectors associated with this modular data. This is the published version of arXiv:1606.07165.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-3003-x
      Issue No: Vol. 356, No. 3 (2017)
  • Anyonic Chains, Topological Defects, and Conformal Field Theory
    • Authors: Matthew Buican; Andrey Gromov
      Pages: 1017 - 1056
      Abstract: Motivated by the three-dimensional topological field theory/two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, which can give rise to an enormously rich (and largely unexplored) space of two-dimensional critical theories in the thermodynamic limit. One remarkable feature of these systems is the appearance of non-local microscopic “topological symmetries” that descend to topological defects of the resulting CFTs. We derive various model-independent properties of these theories and of this topological symmetry/topological defect correspondence. For example, by studying precursors of certain twist and defect fields directly in the anyonic chains, we argue that (under mild assumptions) the two-dimensional CFTs correspond to particular modular invariants with respect to their maximal chiral algebras and that the topological defects descending from topological symmetries commute with these maximal chiral algebras. Using this map, we apply properties of defect Hilbert spaces to show how topological symmetries give a handle on the set of allowed relevant deformations of these theories. Throughout, we give a unified perspective that treats the constraints from discrete symmetries on the same footing as the constraints from topological ones.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2995-6
      Issue No: Vol. 356, No. 3 (2017)
  • Quantum Algorithm for Linear Differential Equations with Exponentially
           Improved Dependence on Precision
    • Authors: Dominic W. Berry; Andrew M. Childs; Aaron Ostrander; Guoming Wang
      Pages: 1057 - 1081
      Abstract: We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-3002-y
      Issue No: Vol. 356, No. 3 (2017)
  • Random Walks on Homeo( S 1 )
    • Authors: Dominique Malicet
      Pages: 1083 - 1116
      Abstract: In this paper, we study random walks \({g_n=f_{n-1}\ldots f_0}\) on the group Homeo (S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure \({\nu}\) . We prove that under the only condition that there is no probability measure invariant by \({\nu}\) -almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on \({\nu}\) were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k ’s. We deduce various dynamical consequences on the random walk (g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana’s invariance principle, working for continuous cocycles on a space fibred in circles.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2996-5
      Issue No: Vol. 356, No. 3 (2017)
  • Trace of the Twisted Heisenberg Category
    • Authors: Can Ozan Oğuz; Michael Reeks
      Pages: 1117 - 1154
      Abstract: We show that the trace decategorification, or zeroth Hochschild homology, of the twisted Heisenberg category defined by Cautis and Sussan is isomorphic to a quotient of \({W^-}\) , a subalgebra of \({W_{1+\infty}}\) defined by Kac, Wang, and Yan. Our result is a twisted analogue of that by Cautis, Lauda, Licata, and Sussan relating \({W_{1+\infty}}\) and the trace decategorification of the Heisenberg category.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2992-9
      Issue No: Vol. 356, No. 3 (2017)
  • Time-Periodic Einstein–Klein–Gordon Bifurcations of Kerr
    • Authors: Otis Chodosh; Yakov Shlapentokh-Rothman
      Pages: 1155 - 1250
      Abstract: We construct one-parameter families of solutions to the Einstein–Klein–Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-periodic. An immediate corollary is that for these Klein–Gordon masses, the Kerr family is not asymptotically stable as a solution to the Einstein–Klein–Gordon equations.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2998-3
      Issue No: Vol. 356, No. 3 (2017)
  • Stochastic Stability of Pollicott–Ruelle Resonances
    • Authors: Alexis Drouot
      Pages: 357 - 396
      Abstract: Kinetic Brownian motion on the cosphere bundle of a Riemannian manifold \({\mathbb{M}}\) is a stochastic process that models the geodesic equation perturbed by a random white force of size \({\varepsilon}\) . When \({\mathbb{M}}\) is compact and negatively curved, we show that the L 2-spectrum of the infinitesimal generator of this process converges to the Pollicott–Ruelle resonances of \({\mathbb{M}}\) as \({\varepsilon}\) goes to 0.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2956-0
      Issue No: Vol. 356, No. 2 (2017)
  • Exact Solution of the Classical Dimer Model on a Triangular Lattice:
           Monomer–Monomer Correlations
    • Authors: Estelle Basor; Pavel Bleher
      Pages: 397 - 425
      Abstract: We obtain an asymptotic formula, as \({n\to\infty}\) , for the monomer–monomer correlation function \({K_2(n)}\) in the classical dimer model on a triangular lattice, with the horizontal and vertical weights \({w_h=w_v=1}\) and the diagonal weight \({w_d=t > 0}\) , between two monomers at vertices q and r that are n spaces apart in adjacent rows. We find that \({t_c=\frac{1}{2}}\) is a critical value of t. We prove that in the subcritical case, \({0 < t < \frac{1}{2}}\) , as \({n\to\infty, K_2(n)=K_2(\infty)\left[1-\frac{e^{-n/\xi}}{n}\,\Big(C_1+C_2(-1)^n+ \mathcal{O}(n^{-1})\Big) \right]}\) , with explicit formulae for \({K_2(\infty), \xi, C_1}\) , and \({C_2}\) . In the supercritical case, \({\frac{1}{2} < t < 1}\) , we prove that as \({n\to\infty, K_2(n)=K_2(\infty)\Bigg[1-\frac{e^{-n/\xi}}{n}\, \Big(C_1\cos(\omega n+\varphi_1)+C_2(-1)^n\cos(\omega n+\varphi_2)+ C_3+C_4(-1)^n + \mathcal{O}(n^{-1})\Big)\Bigg]}\) , with explicit formulae for \({K_2(\infty), \xi,\omega}\) , and \({C_1, C_2, C_3, C_4, \varphi_1, \varphi_2}\) . The proof is based on an extension of the Borodin–Okounkov–Case–Geronimo formula to block Toeplitz determinants and on an asymptotic analysis of the Fredholm determinants in hand.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2985-8
      Issue No: Vol. 356, No. 2 (2017)
  • Parallel Transport Along Seifert Manifolds and Fractional Monodromy
    • Authors: N. Martynchuk; K. Efstathiou
      Pages: 427 - 449
      Abstract: The notion of fractional monodromy was introduced by Nekhoroshev, Sadovskií and Zhilinskií as a generalization of standard (‘integer’) monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a general result that allows one to compute fractional monodromy in various integrable Hamiltonian systems. In particular, we show that the non-triviality of fractional monodromy in 2 degrees of freedom systems with a Hamiltonian circle action is related only to the fixed points of the circle action. Our approach is based on the study of a specific notion of parallel transport along Seifert manifolds.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2988-5
      Issue No: Vol. 356, No. 2 (2017)
  • Complexity of Quantum Impurity Problems
    • Authors: Sergey Bravyi; David Gosset
      Pages: 451 - 500
      Abstract: We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem called an impurity. The full system consists of n fermionic modes and has a Hamiltonian \({H=H_0+H_{imp}}\) , where H 0 is quadratic in creation–annihilation operators and H imp is an arbitrary Hamiltonian acting on a subset of O(1) modes. We show that the ground energy of H can be approximated with an additive error \({2^{-b}}\) in time \({n^3 \exp{[O(b^3)]}}\) . Our algorithm also finds a low energy state that achieves this approximation. The low energy state is represented as a superposition of \({\exp{[O(b^3)]}}\) fermionic Gaussian states. To arrive at this result we prove several theorems concerning exact ground states of impurity models. In particular, we show that eigenvalues of the ground state covariance matrix decay exponentially with the exponent depending very mildly on the spectral gap of H 0. A key ingredient of our proof is Zolotarev’s rational approximation to the \({\sqrt{x}}\) function. We anticipate that our algorithms may be used in hybrid quantum-classical simulations of strongly correlated materials based on dynamical mean field theory. We implemented a simplified practical version of our algorithm and benchmarked it using the single impurity Anderson model.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2976-9
      Issue No: Vol. 356, No. 2 (2017)
  • Refined and Microlocal Kakeya–Nikodym Bounds of Eigenfunctions in
           Higher Dimensions
    • Authors: Matthew D. Blair; Christopher D. Sogge
      Pages: 501 - 533
      Abstract: We prove a Kakeya–Nikodym bound on eigenfunctions and quasimodes, which sharpens a result of the authors (Blair and Sogge in Anal PDE 8:747–764, 2015) and extends it to higher dimensions. As in the prior work, the key intermediate step is to prove a microlocal version of these estimates, which involves a phase space decomposition of these modes that is essentially invariant under the bicharacteristic/geodesic flow. In a companion paper (Blair and Sogge in J Differ Geom, 2015), it will be seen that these sharpened estimates yield improved L q (M) bounds on eigenfunctions in the presence of nonpositive curvature when \({2 < q < \frac{2(d+1)}{d-1}}\) .
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2977-8
      Issue No: Vol. 356, No. 2 (2017)
  • Integrability of Limit Shapes of the Six Vertex Model
    • Authors: Nicolai Reshetikhin; Ananth Sridhar
      Pages: 535 - 565
      Abstract: The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the six vertex model on a cylinder. This suggests that the limit shape equation is an integrable PDE with gradient constraints. At the free fermionic point this equation becomes the complex Burgers equation.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2983-x
      Issue No: Vol. 356, No. 2 (2017)
  • A Metric for Heterotic Moduli
    • Authors: Philip Candelas; Xenia de la Ossa; Jock McOrist
      Pages: 567 - 612
      Abstract: Heterotic vacua of string theory are realised, at large radius, by a compact threefold with vanishing first Chern class together with a choice of stable holomorphic vector bundle. These form a wide class of potentially realistic four-dimensional vacua of string theory. Despite all their phenomenological promise, there is little understanding of the metric on the moduli space of these. What is sought is the analogue of special geometry for these vacua. The metric on the moduli space is important in phenomenology as it normalises D-terms and Yukawa couplings. It is also of interest in mathematics, since it generalises the metric, first found by Kobayashi, on the space of gauge field connections, to a more general context. Here we construct this metric, correct to first order in \({\alpha^{\backprime}}\) , in two ways: first by postulating a metric that is invariant under background gauge transformations of the gauge field, and also by dimensionally reducing heterotic supergravity. These methods agree and the resulting metric is Kähler, as is required by supersymmetry. Checking the metric is Kähler is intricate and the anomaly cancellation equation for the H field plays an essential role. The Kähler potential nevertheless takes a remarkably simple form: it is the Kähler potential of special geometry with the Kähler form replaced by the \({\alpha^{\backprime}}\) -corrected hermitian form.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2978-7
      Issue No: Vol. 356, No. 2 (2017)
  • Some Characterizations of Dirac Type Singularity of Monopoles
    • Authors: Takuro Mochizuki; Masaki Yoshino
      Pages: 613 - 625
      Abstract: We study singular monopoles on open subsets in the 3-dimensional Euclidean space. We give two characterizations of Dirac type singularities. One is given in terms of the growth order of the norms of sections which are invariant by the scattering map. The other is given in terms of the growth order of the norms of the Higgs fields.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2981-z
      Issue No: Vol. 356, No. 2 (2017)
  • Isomonodromic Deformations and Very Stable Vector Bundles of Rank Two
    • Authors: Indranil Biswas; Viktoria Heu; Jacques Hurtubise
      Pages: 627 - 640
      Abstract: For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this universal deformation. In a previous work we proved that the vector bundle corresponding to a general parameter of this family is stable. Here we prove that the vector bundle corresponding to a general parameter is in fact very stable, meaning it does not admit any nonzero nilpotent Higgs field.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2987-6
      Issue No: Vol. 356, No. 2 (2017)
  • Periods and Motives in the Spectral Action of Robertson–Walker
    • Authors: Farzad Fathizadeh; Matilde Marcolli
      Pages: 641 - 671
      Abstract: We show that, when considering the scaling factor as an affine variable, the coefficients of the asymptotic expansion of the spectral action on a (Euclidean) Robertson–Walker spacetime are periods of mixed Tate motives, involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces and divisors given by unions of coordinate hyperplanes.
      PubDate: 2017-12-01
      DOI: 10.1007/s00220-017-2991-x
      Issue No: Vol. 356, No. 2 (2017)
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