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MATHEMATICS (711 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: 4)
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: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
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: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
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: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 5)
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 Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
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: 5)
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: 4)
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   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
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)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
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: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
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: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
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 Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
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: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
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: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
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: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
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: 5)
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: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
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: 29)
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)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     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 Combinatorics     Open Access  
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: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)

        1 2 3 4 | Last

Journal Cover
Communications in Mathematical Physics
Journal Prestige (SJR): 1.682
Citation Impact (citeScore): 2
Number of Followers: 2  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0916 - ISSN (Online) 0010-3616
Published by Springer-Verlag Homepage  [2350 journals]
  • A Geometric Perspective on the Method of Descent
    • Authors: Qian Wang
      Pages: 827 - 850
      Abstract: We derive a first order representation formula for the tensorial wave equation \({\Box_\mathbf{g} \phi^I=F^I}\) in globally hyperbolic Lorentzian spacetimes \({(\mathcal{M}^{2+1}, \mathbf{g})}\) by giving a geometric formulation of the method of descent which is applicable for any dimension.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3151-7
      Issue No: Vol. 360, No. 3 (2018)
  • Classical Affine $${\mathcal W}$$ W -Algebras and the Associated
           Integrable Hamiltonian Hierarchies for Classical Lie Algebras
    • Authors: Alberto De Sole; Victor G. Kac; Daniele Valeri
      Pages: 851 - 918
      Abstract: We prove that any classical affine W-algebra \({\mathcal{W}}\) ( \({\mathfrak{g}, f)}\) , where \({\mathfrak{g}}\) is a classical Lie algebra and f is an arbitrary nilpotent element of \({\mathfrak{g}}\) , carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of generalized Adler type operators and of generalized quasideterminants, which we develop in the paper. Moreover, we show that under certain conditions, the product of two generalized Adler type operators is a Lax type operator. We use this fact to construct a large number of integrable Hamiltonian systems, recovering, as a special case, all KdV type hierarchies constructed by Drinfeld and Sokolov.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3142-8
      Issue No: Vol. 360, No. 3 (2018)
  • BPS Jumping Loci are Automorphic
    • Authors: Shamit Kachru; Arnav Tripathy
      Pages: 919 - 933
      Abstract: We show that BPS jumping loci–loci in the moduli space of string compactifications where the number of BPS states jumps in an upper semi-continuous manner—naturally appear as Fourier coefficients of (vector space-valued) automorphic forms. For the case of T2 compactification, the jumping loci are governed by a modular form studied by Hirzebruch and Zagier, while the jumping loci in K3 compactification appear in a story developed by Oda and Kudla–Millson in arithmetic geometry. We also comment on some curious related automorphy in the physics of black hole attractors and flux vacua.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3090-3
      Issue No: Vol. 360, No. 3 (2018)
  • The 1/ N Expansion of Tensor Models with Two Symmetric Tensors
    • Authors: Razvan Gurau
      Pages: 985 - 1007
      Abstract: It is well known that tensor models for a tensor with no symmetry admit a 1/N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/N expansion dominated by melonic graphs.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3055-y
      Issue No: Vol. 360, No. 3 (2018)
  • Quantum Groups, Property (T), and Weak Mixing
    • Authors: Michael Brannan; David Kerr
      Pages: 1043 - 1059
      Abstract: For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant vectors. This is a generalization of a theorem of Bekka and Valette from the group setting and was previously established in the case of low dual by Daws, Skalski, and Viselter. Our approach uses spectral techniques and is completely different from those of Bekka–Valette and Daws–Skalski–Viselter. By a separate argument we furthermore extend the result to second countable nonunimodular locally compact quantum groups, which are shown in particular not to have property (T), generalizing a theorem of Fima from the discrete setting. We also obtain quantum group versions of characterizations of property (T) of Kerr and Pichot in terms of the Baire category theory of weak mixing representations and of Connes and Weiss in terms of the prevalence of strongly ergodic actions.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3037-0
      Issue No: Vol. 360, No. 3 (2018)
  • Profinite Completions of Burnside-Type Quotients of Surface Groups
    • Authors: Louis Funar; Pierre Lochak
      Pages: 1061 - 1082
      Abstract: Using quantum representations of mapping class groups, we prove that profinite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic quotients of surface groups.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3126-8
      Issue No: Vol. 360, No. 3 (2018)
  • Dimension of the SLE Light Cone, the SLE Fan, and $${{\rm
           SLE}_\kappa(\rho)}$$ SLE κ ( ρ ) for $${\kappa \in (0,4)}$$ κ ∈ ( 0 ,
           4 ) and $${\rho \in}$$ ρ ∈ $${\big[{\tfrac{\kappa}{2}}-4,-2\big)}$$ [
           κ 2 - 4 , - 2 )
    • Authors: Jason Miller
      Pages: 1083 - 1119
      Abstract: Suppose that h is a Gaussian free field (GFF) on a planar domain. Fix \({\kappa \in (0,4)}\) . The \({{\rm SLE}_\kappa}\) light cone L \({(\theta)}\) of h with opening angle \({\theta \in [0,\pi]}\) is the set of points reachable from a given boundary point by angle-varying flow lines of the (formal) vector field \({e^{ih/\chi}}\) , \({\chi = \tfrac{2}{\sqrt{\kappa}} - \tfrac{\sqrt{\kappa}}{2}}\) , with angles in \({[-\tfrac{\theta}{2},\tfrac{\theta}{2}]}\) . We derive the Hausdorff dimension of L \({(\theta)}\) . If \({\theta =0}\) then L \({(\theta)}\) is an ordinary \({{\rm SLE}_{\kappa}}\) curve (with \({\kappa < 4}\) ); if \({\theta = \pi}\) then L \({(\theta)}\) is the range of an \({{\rm SLE}_{\kappa'}}\) curve ( \({\kappa' = 16/\kappa > 4}\) ). In these extremes, this leads to a new proof of the Hausdorff dimension formula for \({{\rm SLE}}\) . We also consider \({{\rm SLE}_\kappa(\rho)}\) processes, which were originally only defined for \({\rho > -\,2}\) , but which can also be defined for \({\rho \leq -2}\) using Lévy compensation. The range of an \({{\rm SLE}_\kappa(\rho)}\) is qualitatively different when \({\rho \leq -2}\) . In particular, these curves are self-intersecting for \({\kappa < 4}\) and double points are dense, while ordinary \({{\rm SLE}_\kappa}\) is simple. It was previously shown (Miller and Sheffield in Gaussian free field light cones and \({{\rm SLE}_\kappa(\rho)}\) , 2016) that certain \({{\rm SLE}_\kappa(\rho)}\) curves agree in law with certain light cones. Combining this with other known results, we obtain a general formula for the Hausdorff dimension of \({{\rm SLE}_\kappa(\rho)}\) ...
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3109-9
      Issue No: Vol. 360, No. 3 (2018)
  • A Spectral Approach for Quenched Limit Theorems for Random Expanding
           Dynamical Systems
    • Authors: D. Dragičević; G. Froyland; C. González-Tokman; S. Vaienti
      Pages: 1121 - 1187
      Abstract: We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form \({T_{\sigma^{n-1} \omega} \circ\cdots\circ T_{\sigma\omega}\circ T_\omega}\) . An important aspect of our results is that we only assume ergodicity and invertibility of the random driving \({\sigma:\Omega\to\Omega}\) ; in particular no expansivity or mixing properties are required.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3083-7
      Issue No: Vol. 360, No. 3 (2018)
  • Correction to: Hamiltonian and Algebraic Theories of Gapped Boundaries in
           Topological Phases of Matter
    • Authors: Iris Cong; Meng Cheng; Zhenghan Wang
      Pages: 1189 - 1190
      Abstract: There were two errors in the original publication. First, the term B K in Eq. (2.20) was not well-defined in the case of non-normal subgroups K.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3134-8
      Issue No: Vol. 360, No. 3 (2018)
  • Chemical Distances for Percolation of Planar Gaussian Free Fields and
           Critical Random Walk Loop Soups
    • Authors: Jian Ding; Li Li
      Pages: 523 - 553
      Abstract: We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3140-x
      Issue No: Vol. 360, No. 2 (2018)
  • Inverse Problems for Semilinear Wave Equations on Lorentzian Manifolds
    • Authors: Matti Lassas; Gunther Uhlmann; Yiran Wang
      Pages: 555 - 609
      Abstract: We consider inverse problems in space–time (M, g), a 4-dimensional Lorentzian manifold. For semilinear wave equations \({\square_g u + H(x, u) = f}\) , where \({\square_g}\) denotes the usual Laplace–Beltrami operator, we prove that the source-to-solution map \({L: f \rightarrow u _V}\) , where V is a neighborhood of a time-like geodesic \({\mu}\) , determines the topological, differentiable structure and the conformal class of the metric of the space–time in the maximal set, where waves can propagate from \({\mu}\) and return back. Moreover, on a given space–time (M, g), the source-to-solution map determines some coefficients of the Taylor expansion of H in u.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3135-7
      Issue No: Vol. 360, No. 2 (2018)
  • Topology and Singularities in Cosmological Spacetimes Obeying the Null
           Energy Condition
    • Authors: Gregory J. Galloway; Eric Ling
      Pages: 611 - 617
      Abstract: We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3  +  1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3020-9
      Issue No: Vol. 360, No. 2 (2018)
  • Averages of Eigenfunctions Over Hypersurfaces
    • Authors: Yaiza Canzani; Jeffrey Galkowski; John A. Toth
      Pages: 619 - 637
      Abstract: Let (M, g) be a compact, smooth, Riemannian manifold and \({\{ \phi_h \}}\) an L2-normalized sequence of Laplace eigenfunctions with defect measure \({\mu}\) . Let H be a smooth hypersurface with unit exterior normal \(\nu\) . Our main result says that when \(\mu\) is not concentrated conormally to H, the eigenfunction restrictions to H satisfy $$\int_H \phi_h d\sigma_H = o(1) \quad {\rm and} \quad \int_H h D_{\nu} \phi_h d\sigma_H = o(1),$$ \({h \to 0^+}\) .
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3081-9
      Issue No: Vol. 360, No. 2 (2018)
  • The Conditional Entropy Power Inequality for Bosonic Quantum Systems
    • Authors: Giacomo De Palma; Dario Trevisan
      Pages: 639 - 662
      Abstract: We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under the heat semigroup evolution. The beam-splitter and the squeezing are the central elements of quantum optics, and can model the attenuation, the amplification and the noise of electromagnetic signals. This conditional Entropy Power Inequality will have a strong impact in quantum information and quantum cryptography. Among its many possible applications there is the proof of a new uncertainty relation for the conditional Wehrl entropy.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3082-8
      Issue No: Vol. 360, No. 2 (2018)
  • Dichromatic State Sum Models for Four-Manifolds from Pivotal Functors
    • Authors: Manuel Bärenz; John Barrett
      Pages: 663 - 714
      Abstract: A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf–Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3012-9
      Issue No: Vol. 360, No. 2 (2018)
  • Decay of Complex-Time Determinantal and Pfaffian Correlation Functionals
           in Lattices
    • Authors: N. J. B. Aza; J.-B. Bru; W. de Siqueira Pedra
      Pages: 715 - 726
      Abstract: We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903–931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time correlations. Our proof uses the analyticity of correlation functions via the Hadamard three-line theorem. We show that the dynamical localization for the one-particle system yields the dynamical localization for the many-point fermionic correlation functions, with respect to the Hausdorff distance in the determinantal case. In Sims and Warzel (2016), a stronger notion of decay for many-particle configurations was used but only at dimension one and for real times. Considering determinantal and Pfaffian correlation functionals for complex times is important in the study of weakly interacting fermions.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3121-0
      Issue No: Vol. 360, No. 2 (2018)
  • The Infinitesimal Moduli Space of Heterotic G 2 Systems
    • Authors: Xenia de la Ossa; Magdalena Larfors; Eirik E. Svanes
      Pages: 727 - 775
      Abstract: Heterotic string compactifications on integrable G 2 structure manifolds Y with instanton bundles \({(V,A), (TY,\tilde{\theta})}\) yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant exterior derivative \({\mathcal{D}}\) and show that it is equivalent to a heterotic G 2 system encoding the geometry of the heterotic string compactifications. This operator \({\mathcal{D}}\) acts on a bundle \({\mathcal{Q}=T^*Y \oplus {\rm End}(V) \oplus {\rm End}(TY)}\) and satisfies a nilpotency condition \({\check{{\mathcal{D}}}^2=0}\) , for an appropriate projection of \({\mathcal D}\) . Furthermore, we determine the infinitesimal moduli space of these systems and show that it corresponds to the finite-dimensional cohomology group \({\check H^1_{\check{{\mathcal{D}}}}(\mathcal{Q})}\) . We comment on the similarities and differences of our result with Atiyah’s well-known analysis of deformations of holomorphic vector bundles over complex manifolds. Our analysis leads to results that are of relevance to all orders in the \({\alpha'}\) expansion.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3013-8
      Issue No: Vol. 360, No. 2 (2018)
  • Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion
    • Authors: A. Alexandrov; G. Chapuy; B. Eynard; J. Harnad
      Pages: 777 - 826
      Abstract: A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda \({\tau}\) -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel–Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-017-3065-9
      Issue No: Vol. 360, No. 2 (2018)
  • A Robust Proof of the Instability of Naked Singularities of a Scalar Field
           in Spherical Symmetry
    • Authors: Jue Liu; Junbin Li
      Abstract: Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical symmetry. In this paper, appropriate a priori estimates for the solution are obtained. These estimates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In a companion paper, we are able to prove certain instability theorems of the spherically symmetric naked singularities of a scalar field under gravitational perturbations without symmetries. The argument given in this paper plays a central role.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3157-1
  • Coupling the Gaussian Free Fields with Free and with Zero Boundary
           Conditions via Common Level Lines
    • Authors: Wei Qian; Wendelin Werner
      Abstract: We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary-touching zero-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free boundary GFF. Constructions and couplings of the free boundary GFF and its level lines via soups of reflected Brownian loops and their clusters are also discussed. Such considerations show for instance that in a domain with an axis of symmetry, if one looks at the overlay of a single usual Conformal Loop Ensemble CLE3 with its own symmetric image, one obtains the CLE4-type collection of level lines of a GFF with mixed zero/free boundary conditions in the half-domain.
      PubDate: 2018-06-01
      DOI: 10.1007/s00220-018-3159-z
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