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MATHEMATICS (656 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
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: 8)
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: 22)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 8)
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: 1)
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: 8)
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: 9)
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: 6)
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: 19)
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: 2)
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: 1)
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: 8)
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  
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: 5)
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: 2)
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)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
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  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)

        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  [2352 journals]
  • Stochastic Stability of Pollicott–Ruelle Resonances
    • Authors: Alexis Drouot
      Pages: 357 - 396
      Abstract: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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)
  • Inverse Scattering for the Magnetic Schrödinger Operator on Surfaces
           with Euclidean Ends
    • Authors: Valter Pohjola; Leo Tzou
      Pages: 107 - 142
      Abstract: Abstract We prove a fixed frequency inverse scattering result for the magnetic Schrödinger operator (or connection Laplacian) on surfaces with Euclidean ends. We show that, under suitable decaying conditions, the scattering matrix for the operator determines both the gauge class of the connection and the zeroth order potential.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2982-y
      Issue No: Vol. 356, No. 1 (2017)
  • Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the
           High-Density Limit
    • Authors: Maximilian Jeblick; David Mitrouskas; Sören Petrat; Peter Pickl
      Pages: 143 - 187
      Abstract: Abstract The dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the model for coupling parameter g = 1 (i.e., not in the weak coupling regime), and prove closeness of the time evolution to an effective dynamics for large densities of the gas and for long time scales of the order of some power of the density. The effective dynamics is generated by the free Hamiltonian with a large but constant energy shift which is given at leading order by the spatially homogeneous mean field potential of the gas particles. Here, the mean field approximation turns out to be accurate although the fluctuations of the potential around its mean value can be arbitrarily large. Our result is in contrast to a dense bosonic gas in which the free motion of a tracer particle would be disturbed already on a very short time scale. The proof is based on the use of strong phase cancellations in the deviations of the microscopic dynamics from the mean field time evolution.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2970-2
      Issue No: Vol. 356, No. 1 (2017)
  • Local Density for Two-Dimensional One-Component Plasma
    • Authors: Roland Bauerschmidt; Paul Bourgade; Miika Nikula; Horng-Tzer Yau
      Pages: 189 - 230
      Abstract: Abstract We study the classical two-dimensional one-component plasma of N positively charged point particles, interacting via the Coulomb potential and confined by an external potential. For the specific inverse temperature \({\beta=1}\) (in our normalization), the charges are the eigenvalues of random normal matrices, and the model is exactly solvable as a determinantal point process. For any positive temperature, using a multiscale scheme of iterated mean-field bounds, we prove that the equilibrium measure provides the local particle density down to the optimal scale of \({N^{o(1)}}\) particles. Using this result and the loop equation, we further prove that the particle configurations are rigid, in the sense that the fluctuations of smooth linear statistics on any scale are \({N^{o(1)}}\) .
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2932-8
      Issue No: Vol. 356, No. 1 (2017)
  • Structure Function and Fractal Dissipation for an Intermittent Inviscid
           Dyadic Model
    • Authors: Luigi Amedeo Bianchi; Francesco Morandin
      Pages: 231 - 260
      Abstract: Abstract We study a generalization of the original tree-indexed dyadic model by Katz and Pavlović for the turbulent energy cascade of the three-dimensional Euler equation. We allow the coefficients to vary with some restrictions, thus giving the model a realistic spatial intermittency. By introducing a forcing term on the first component, the fixed point of the dynamics is well defined and some explicit computations allow us to prove the rich multifractal structure of the solution. In particular the exponent of the structure function is concave in accordance with other theoretical and experimental models. Moreover, anomalous energy dissipation happens in a fractal set of dimension strictly less than 3.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2974-y
      Issue No: Vol. 356, No. 1 (2017)
  • Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence
    • Authors: Juhan Aru; Yichao Huang; Xin Sun
      Pages: 261 - 283
      Abstract: Abstract 2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David et al. (Liouville quantum gravity on the Riemann sphere. Commun Math Phys 342(3):869–907, 2016) and Duplantier et al. (Liouville quantum gravity as a mating of trees. ArXiv e-prints: arXiv:1409.7055, 2014) both provide a probabilistic perspective of the LQG on the 2D sphere. In particular, in each of them one may find a definition of the so-called unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2979-6
      Issue No: Vol. 356, No. 1 (2017)
  • Stability of a Fermionic N  + 1 Particle System with Point
    • Authors: Thomas Moser; Robert Seiringer
      Pages: 329 - 355
      Abstract: Abstract We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2980-0
      Issue No: Vol. 356, No. 1 (2017)
  • Convergence of Local Statistics of Dyson Brownian Motion
    • Authors: Benjamin Landon; Horng-Tzer Yau
      Pages: 949 - 1000
      Abstract: Abstract We analyze the rate of convergence of the local statistics of Dyson Brownian motion to the GOE/GUE for short times t = o(1) with deterministic initial data V. Our main result states that if the density of states of V is bounded both above and away from 0 down to scales \({\ell \ll t}\) in a small interval of size \({G \gg t}\) around an energy \({E_0}\) , then the local statistics coincide with the GOE/GUE near the energy \({E_0}\) after time t. Our methods are partly based on the idea of coupling two Dyson Brownian motions from Bourgade et al. (Commun Pure Appl Math, 2016), the parabolic regularity result of Erdős and Yau (J Eur Math Soc 17(8):1927–2036, 2015), and the eigenvalue rigidity results of Lee and Schnelli (J Math Phys 54(10):103504, 2013).
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2955-1
      Issue No: Vol. 355, No. 3 (2017)
  • Complex Bounds for Real Maps
    • Authors: Trevor Clark; Sebastian van Strien; Sofia Trejo
      Pages: 1001 - 1119
      Abstract: Abstract In this paper we prove complex bounds, also referred to as a priori bounds for C 3, and, in particular, for analytic maps of the interval. Any C 3 mapping of the interval has an asymptotically holomorphic extension to a neighbourhood of the interval. We associate to such a map, a complex box mapping, which provides a kind of Markov structure for the dynamics. Moreover, we prove universal geometric bounds on the shape of the domains and on the moduli between components of the range and domain. Such bounds show that the first return maps to these domains are well controlled, and consequently such bounds form one of the corner stones in many recent results in one-dimensional dynamics, for example: renormalization theory, rigidity, density of hyperbolicity, and local connectivity of Julia sets.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2958-y
      Issue No: Vol. 355, No. 3 (2017)
  • Justification of the Nonlinear Schrödinger Approximation for a
           Quasilinear Klein–Gordon Equation
    • Authors: Wolf-Patrick Düll
      Pages: 1189 - 1207
      Abstract: Abstract We consider a nonlinear Klein–Gordon equation with a quasilinear quadratic term. The Nonlinear Schrödinger (NLS) equation can be derived as a formal approximation equation describing the evolution of the envelopes of slowly modulated spatially and temporarily oscillating wave packet-like solutions to the quasilinear Klein–Gordon equation. It is the purpose of this paper to present a method that allows one to prove error estimates in Sobolev norms between exact solutions of the quasilinear Klein–Gordon equation and the formal approximation obtained via the NLS equation. The paper contains the first validity proof of the NLS approximation of a nonlinear hyperbolic equation with a quasilinear quadratic term by error estimates in Sobolev spaces. We expect that the method developed in the present paper will allow an answer to the relevant question of the validity of the NLS approximation for other quasilinear hyperbolic systems.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2966-y
      Issue No: Vol. 355, No. 3 (2017)
  • String-Localized Free Vector and Tensor Potentials for Massive Particles
           with Any Spin: I. Bosons
    • Authors: Jens Mund; Erichardson T. de Oliveira
      Pages: 1243 - 1282
      Abstract: Abstract It is well-known that a (point-localized) free quantum field for massive particles with spin s acting in a Hilbert space has at best scaling dimension s + 1, which excludes its use in the perturbative construction of renormalizable interacting models for higher spin ( \({s\geq 1}\) ). Up to date, such models have been constructed only in the context of gauge theory, at the cost of introducing additional unphysical (ghost) fields and an unphysical (indefinite metric) state space. The unphysical degrees of freedom are divided out by requiring gauge (or BRST) invariance. We construct free quantum fields for higher spin particles that have the same good UV behaviour as the scalar field (scaling dimension one), and at the same time act on a Hilbert space without ghosts. They are localized on semi-infinite strings extending to space-like infinity, but are linearly related to their point-local counterparts. We argue that this is sufficient locality for a perturbative construction of interacting models of the gauge theory type, with a string-independent S-matrix and point-localized interacting observable fields. The usual principle of gauge-invariance is here replaced by the (deeper) principle of locality.
      PubDate: 2017-11-01
      DOI: 10.1007/s00220-017-2968-9
      Issue No: Vol. 355, No. 3 (2017)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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