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  • 11
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    Gluing Construction of Initial Data with Kerr–de Sitter Ends (2012)
    Springer
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    Publication Date: 2012-11-10
    Description:    We construct initial data sets which satisfy the vacuum constraint equations of General Relativity with positive cosmological constant. More precisely, we deform initial data with ends asymptotic to Schwarzschild–de Sitter to obtain non-trivial initial data with exactly Kerr–de Sitter ends. The method is inspired from Corvino’s gluing method. We obtain here a extension of a previous result for the time-symmetric case by Chruściel and Pollack (Ann H Poincaré 9(4):639–654, 2008 ). We also deal with the case of asymptotically Kerr–de Sitter initial data. Content Type Journal Article Pages 1-26 DOI 10.1007/s00023-012-0210-z Authors Julien Cortier, Max-Planck-Institut für Gravitationsphysik, (Albert-Einstein-Institut), Am Mühlenberg 1, 14476 Golm, Germany Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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    Topics: Mathematics , Physics
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  • 12
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    On the Optimality of the Assumptions Used to Prove the Existence and Symmetry of Minimizers of Some Fractional Constrained Variational Problems (2012)
    Springer
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    Publication Date: 2012-11-10
    Description:    In this paper, we discuss the optimality of the assumptions used, in a previous paper, to prove existence and symmetry of minimizers of the fractional constrained variational problem: inf    ì í î \frac12 ó õ | Ñ s u | 2 - ó õ F ( | x | , u ):   u Î H s (\mathbb R N ) and ó õ u 2 = c 2 ü ý þ , where c is a prescribed number. More precisely, we will show that if one of the conditions, used to prove that all minimizers of the above constrained variational problem, are radial and radially decreasing for all c , do not hold true, then there are several interesting situations: –  There is no minimizer at all. –  The infimum is achieved but no minimizer is radial. –  For some values of c there is no minimizer. For large values, the minimizer is radial and radially decreasing. In the fractional setting, such a study is more subtle than in the classical one. We take advantage of some brilliant results obtained recently in Cabre and Sire (Anal. PDEs, 2012 ), Dyda (Fractional calculus for power functions, 2012 ) and Hajaiej et al. (Necessary and sufficient conditions for the fractional Gagliardo–Nirenberg inequalities and applications to Navier–Stokes and generalized Boson equations, 2012 ). Content Type Journal Article Pages 1-9 DOI 10.1007/s00023-012-0212-x Authors Hichem Hajaiej, Department of Mathematics, King Saud University, 11451 Riyadh, Kingdom of Saudi Arabia Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 13
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    Ground States for a Stationary Mean-Field Model for a Nucleon (2012)
    Springer
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    Publication Date: 2012-11-12
    Description:    In this paper we consider a variational problem related to a model for a nucleon interacting with the ω and σ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit, which is of a very different nature than the nonrelativistic limit in the atomic physics. Ground states are shown to exist for a large class of values for the parameters of the problem, which are determined by the values of some physical constants. Content Type Journal Article Pages 1-17 DOI 10.1007/s00023-012-0211-y Authors Maria J. Esteban, Ceremade, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775 Paris Cédex 16, France Simona Rota Nodari, Laboratoire Jacques-Louis Lions, UMR 7598, CNRS, 75005 Paris, France Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 14
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    Future Non-Linear Stability for Reflection Symmetric Solutions of the Einstein–Vlasov System of Bianchi Types II and VI0 (2012)
    Springer
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    Publication Date: 2012-09-24
    Description:    Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein–Vlasov system of Bianchi types II and VI 0 . These solutions are asymptotic to the Collins–Stewart solution with dust and the Ellis–MacCallum solution, respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However, we needed to assume small data. For Bianchi VI 0 there is no analogous previous result. Content Type Journal Article Pages 1-33 DOI 10.1007/s00023-012-0201-0 Authors Ernesto Nungesser, Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Am Mühlenberg 1, 14476 Golm, Germany Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 15
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    On a General Class of Nonlocal Equations (2012)
    Springer
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    Publication Date: 2012-09-25
    Description:    Motivated by recent developments in cosmology and string theory, we introduce a functional calculus appropriate for the study of non-linear nonlocal equations of the form f (Δ) u = U ( x ,  u ( x )) on Euclidean space. We prove that under some technical assumptions, these equations admit smooth solutions. We also consider nonlocal equations on compact Riemannian manifolds, and we prove the existence of smooth solutions. Moreover, in the Euclidean case we present conditions on f which guarantee that the solutions we find are, in fact, real-analytic. Content Type Journal Article Pages 1-20 DOI 10.1007/s00023-012-0202-z Authors Przemysław Górka, Department of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland Humberto Prado, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile Enrique G. Reyes, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 16
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    Repeated Quantum Non-Demolition Measurements: Convergence and Continuous Time Limit (2012)
    Springer
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    Publication Date: 2012-09-27
    Description:    We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which von Neumann direct measurements are performed. We prove, under suitable hypotheses, that the system state probability distribution converges after a large number of repeated indirect measurements, in a way compatible with quantum wave function collapse. We extend this result to mixed states and we prove similar results for the system density matrix. We show that the convergence is exponential with a rate given by some relevant mean relative entropies. We also prove that, under appropriate rescaling of the system and probe interactions, the state probability distribution and the system density matrix are solutions of stochastic differential equations modeling continuous-time quantum measurements. We analyze the large time behavior of these continuous time processes and prove convergence. Content Type Journal Article Pages 1-41 DOI 10.1007/s00023-012-0204-x Authors Michel Bauer, Institut de Physique Théorique, CEA/DSM/IPhT, Unité de recherche associée au CNRS, Point Courrier 136, CEA-Saclay, 91191 Gif sur Yvette Cedex, France Tristan Benoist, Laboratoire de Physique Théorique de l’ENS, CNRS & École Normale Supérieure de Paris, 24, rue Lhomond, 75005 Paris, France Denis Bernard, Laboratoire de Physique Théorique de l’ENS, CNRS & École Normale Supérieure de Paris, 24, rue Lhomond, 75005 Paris, France Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 17
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    Analyticity of the Planar Limit of a Matrix Model (2012)
    Springer
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    Publication Date: 2012-08-02
    Description:    Using Chebyshev polynomials combined with some mild combinatorics, we provide an alternative approach to the analytical and formal planar limits of a random matrix model with a 1-cut potential V . For potentials V ( x )= x 2 /2 - å n ³ 1   a n x n / n , as a power series in all a n , the formal Taylor expansion of the analytic planar limit is exactly the formal planar limit. In the case V is analytic in infinitely many variables { a n } n  ≥ 1 (on the appropriate spaces), the planar limit is also an analytic function in infinitely many variables and we give quantitative versions of where this is defined. Particularly useful in enumerative combinatorics are the gradings of V , V t ( x )= x 2 /2 - å n ³ 1   a n t n /2 x n / n and V t ( x )= x 2 /2 - å n ³ 3   a n t n /2 - 1 x n / n . The associated planar limits F ( t ) as functions of t count planar diagram sorted by the number of edges respectively faces. We point out a method of computing the asymptotic of the coefficients of F ( t ) using the combination of the wzb method and the resolution of singularities. This is illustrated in several computations revolving around the important extreme potential V t ( x )= x 2 /2+log(1 - Ö t x ) and its variants. This particular example gives a quantitative and sharp answer to a conjecture of ’t Hooft’s, which states that if the potential is analytic, the planar limit is also analytic. Content Type Journal Article Pages 1-67 DOI 10.1007/s00023-012-0191-y Authors Stavros Garoufalidis, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA Ionel Popescu, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 18
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    Existence of Wave Operators with Time-Dependent Modifiers for the Schrödinger Equations with Long-Range Potentials on Scattering Manifolds (2012)
    Springer
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    Publication Date: 2012-08-21
    Description:    We construct time-dependent wave operators for Schrödinger equations with long-range potentials on a manifold M with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space of the form \mathbb R × ¶ M , where ¶ M is the boundary of M at infinity. We construct exact solutions to the Hamilton–Jacobi equation on the reference system \mathbb R × ¶ M and prove the existence of the modified wave operators. Content Type Journal Article Pages 1-28 DOI 10.1007/s00023-012-0200-1 Authors Shinichiro Itozaki, Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 19
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    Precise Arrhenius Law for p-forms: The Witten Laplacian and Morse–Barannikov Complex (2012)
    Springer
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    Publication Date: 2012-08-21
    Description:    Accurate asymptotic expressions are given for the exponentially small eigenvalues of Witten Laplacians acting on p -forms. The key ingredient, which replaces explicit formulas for global quasimodes in the case p  = 0, is Barannikov’s presentation of Morse theory in Barannikov (Adv Soviet Math 21:93–115, 1994 ). Content Type Journal Article Pages 1-44 DOI 10.1007/s00023-012-0193-9 Authors Dorian Le Peutrec, Département de Mathématiques, UMR-CNRS 8628, Bât. 425, Université Paris 11, 91405 Orsay Cedex, France Francis Nier, IRMAR, UMR-CNRS 6625, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France Claude Viterbo, CMLS, UMR-CNRS 7640, Ecole Polytechnique, 91128 Palaiseau Cedex, France Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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  • 20
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    The Translation Invariant Massive Nelson Model: II. The Continuous Spectrum below the Two-Boson Threshold (2012)
    Springer
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    Publication Date: 2012-10-23
    Description:    In this paper we continue the study of the energy-momentum spectrum of a class of translation invariant, linearly coupled, and massive Hamiltonians from non-relativistic quantum field theory. The class contains the Hamiltonians of E. Nelson (J Math Phys 5:1190–1197, 1964 ) and H. Fröhlich (Adv Phys 3:325–362, 1954 ). In Møller (Ann Henri Poincaré 6:1091–1135, 2005 ; Rev Math Phys 18:485–517, 2006 ) one of us previously investigated the structure of the ground state mass shell and the bottom of the continuous energy-momentum spectrum. Here we study the continuous energy-momentum spectrum itself up to the two-boson threshold, the threshold for energetic support of two-boson scattering states. We prove that non-threshold embedded mass shells have finite multiplicity and can accumulate only at thresholds. We furthermore establish the non-existence of singular continuous energy-momentum spectrum. Our results hold true for all values of the particle-field coupling strength but only below the two-boson threshold. The proof revolves around the construction of a certain relative velocity vector field used to construct a conjugate operator in the sense of Mourre. Content Type Journal Article Pages 1-60 DOI 10.1007/s00023-012-0208-6 Authors Jacob Schach Møller, Department of Mathematics, Aarhus University, Aarhus, Denmark Morten Grud Rasmussen, Department of Engineering, Aarhus University, Aarhus, Denmark Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
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