18 results match your criteria Annales Henri Poincare[Journal]

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On Multimatrix Models Motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model.

Ann Henri Poincare 2022 23;23(6):1979-2023. Epub 2022 Apr 23.

Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland.

We continue the study of fuzzy geometries inside Connes' spectral formalism and their relation to multimatrix models. In this companion paper to Pérez-Sánchez (Ann Henri Poincaré 22:3095-3148, 2021, arXiv:2007.10914), we propose a gauge theory setting based on noncommutative geometry, which-just as the traditional formulation in terms of almost-commutative manifolds-has the ability to also accommodate a Higgs field. Read More

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Black Hole Quasinormal Modes and Seiberg-Witten Theory.

Ann Henri Poincare 2022 18;23(6):1951-1977. Epub 2021 Dec 18.

Department of Physics, Rikkyo University, Toshima, Tokyo  171-8501 Japan.

We present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the -background. Read More

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December 2021

A Large Deviation Principle in Many-Body Quantum Dynamics.

Ann Henri Poincare 2021 8;22(8):2595-2618. Epub 2021 Apr 8.

Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.

We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates that are consistent with central limit theorems that have been established in the last years. Read More

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Gravitational Constraints on a Lightlike Boundary.

Ann Henri Poincare 2021 17;22(9):3149-3198. Epub 2021 Mar 17.

Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.

We analyse the boundary structure of general relativity in the coframe formalism in the case of a lightlike boundary, i.e. when the restriction of the induced Lorentzian metric to the boundary is degenerate. Read More

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Effect of Periodic Arrays of Defects on Lattice Energy Minimizers.

Ann Henri Poincare 2021 27;22(9):2995-3023. Epub 2021 Mar 27.

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

We consider interaction energies between a point , , and a lattice containing , where the interaction potential is assumed to be radially symmetric and decaying sufficiently fast at infinity. We investigate the conservation of optimality results for when integer sublattices are removed (periodic arrays of vacancies) or substituted (periodic arrays of substitutional defects). We consider separately the non-shifted ( ) and shifted ( ) cases and we derive several general conditions ensuring the (non-)optimality of a universal optimizer among lattices for the new energy including defects. Read More

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2-Group Symmetries of 6D Little String Theories and T-Duality.

Ann Henri Poincare 2021 16;22(7):2451-2474. Epub 2021 Feb 16.

School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 USA.

We determine the 2-group structure constants for all the six-dimensional little string theories (LSTs) geometrically engineered in F-theory without frozen singularities. We use this result as a consistency check for T-duality: the 2-groups of a pair of T-dual LSTs have to match. When the T-duality involves a discrete symmetry twist, the 2-group used in the matching is modified. Read More

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February 2021

The Dilute Fermi Gas via Bogoliubov Theory.

Ann Henri Poincare 2021 16;22(7):2283-2353. Epub 2021 Apr 16.

Mathematics Area, SISSA, Via Bonomea 265, 34136 Trieste, Italy.

We study the ground state properties of interacting Fermi gases in the dilute regime, in three dimensions. We compute the ground state energy of the system, for positive interaction potentials. We recover a well-known expression for the ground state energy at second order in the particle density, which depends on the interaction potential only via its scattering length. Read More

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Spectral Properties of Schrödinger Operators Associated with Almost Minimal Substitution Systems.

Ann Henri Poincare 2021 3;22(5):1377-1427. Epub 2020 Nov 3.

Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany.

We study the spectral properties of ergodic Schrödinger operators that are associated with a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go beyond minimality, unique ergodicity and linear complexity. In some parameter region, we are naturally in the setting of an infinite ergodic measure. Read More

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November 2020

On the Absolutely Continuous Spectrum of Generalized Indefinite Strings.

Ann Henri Poincare 2021 11;22(11):3529-3564. Epub 2021 Jun 11.

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria.

We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite strings under rather wide perturbations. In particular, one of these results allows us to prove that the absolutely continuous spectrum of the isospectral problem associated with the conservative Camassa-Holm flow in the dispersive regime is essentially supported on the interval . Read More

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Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime.

Ann Henri Poincare 2021 26;22(4):1163-1233. Epub 2020 Dec 26.

Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.

We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order , for . Assuming that , we show that low-energy states exhibit Bose-Einstein condensation and we provide bounds on the expectation and on higher moments of the number of excitations. Read More

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December 2020

Ruelle Zeta Function from Field Theory.

Ann Henri Poincare 2020 6;21(12):3835-3867. Epub 2020 Oct 6.

Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland.

We propose a field-theoretic interpretation of Ruelle zeta function and show how it can be seen as the partition function for theory when an unusual gauge-fixing condition on contact manifolds is imposed. This suggests an alternative rephrasing of a conjecture due to Fried on the equivalence between Ruelle zeta function and analytic torsion, in terms of homotopies of Lagrangian submanifolds. Read More

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October 2020

On the Spectrum of the Local Mirror Curve.

Ann Henri Poincare 2020 29;21(11):3479-3497. Epub 2020 Sep 29.

Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 Australia.

We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi-Yau threefold called local in the case of complex values of Planck's constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations. Read More

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September 2020

A Supersymmetric Hierarchical Model for Weakly Disordered 3 Semimetals.

Ann Henri Poincare 2020 6;21(11):3499-3574. Epub 2020 Oct 6.

Mathematics Area, SISSA, Via Bonomea 265, 34136 Trieste, Italy.

In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. Read More

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October 2020

Dimerization and Néel Order in Different Quantum Spin Chains Through a Shared Loop Representation.

Ann Henri Poincare 2020 16;21(8):2737-2774. Epub 2020 Jun 16.

Munich Center for Quantum Science and Technology, 80799 Munich, Germany.

The ground-states of the spin- antiferromagnetic chain with a projection-based interaction and the spin-1/2 XXZ-chain  at anisotropy parameter share a common loop representation in terms of a two-dimensional functional integral which is similar to the classical planar -state Potts model at . The multifaceted relation is used here to directly relate the distinct forms of translation symmetry breaking which are manifested in the ground-states of these two models: dimerization for at all , and Néel order for at . The results presented include: (i) a translation to the above quantum spin systems of the results which were recently proven by Duminil-Copin-Li-Manolescu for a broad class of two-dimensional random-cluster models, and (ii) a short proof of the symmetry breaking in a manner similar to the recent structural proof by Ray-Spinka of the discontinuity of the phase transition for . Read More

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Self-Adjoint Dirac Operators on Domains in .

Ann Henri Poincare 2020 20;21(8):2681-2735. Epub 2020 Jun 20.

Departament de Matemàtiques, Universitat Politècnica de Catalunya, Campus Diagonal Besòs, Edifici A (EEBE), Av. Eduard Maristany 16, 08019 Barcelona, Spain.

In this paper, the spectral and scattering properties of a family of self-adjoint Dirac operators in , where is either a bounded or an unbounded domain with a compact -smooth boundary, are studied in a systematic way. These operators can be viewed as the natural relativistic counterpart of Laplacians with boundary conditions as of Robin type. Our approach is based on abstract boundary triple techniques from extension theory of symmetric operators and a thorough study of certain classes of (boundary) integral operators, that appear in a Krein-type resolvent formula. Read More

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Variance Continuity for Lorenz Flows.

Ann Henri Poincare 2020 2;21(6):1873-1892. Epub 2020 May 2.

Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands.

The classical Lorenz flow, and any flow which is close to it in the -topology, satisfies a Central Limit Theorem (CLT). We prove that the variance in the CLT varies continuously. Read More

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Wave Propagation on Microstate Geometries.

Joe Keir

Ann Henri Poincare 2020 14;21(3):705-760. Epub 2019 Dec 14.

Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter (550) Woodstock Road, Oxford, OX2 6GG UK.

Supersymmetric microstate geometries were recently conjectured (Eperon et al. in JHEP 10:031, 2016. 10. Read More

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December 2019

Determinantal Structures in Space-Inhomogeneous Dynamics on Interlacing Arrays.

Ann Henri Poincare 2020 6;21(3):909-940. Epub 2020 Jan 6.

Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK.

We introduce a space-inhomogeneous generalization of the dynamics on interlacing arrays considered by Borodin and Ferrari (Commun Math Phys 325:603-684, 2014). We show that for a certain class of initial conditions the point process associated with the dynamics has determinantal correlation functions, and we calculate explicitly, in the form of a double contour integral, the correlation kernel for one of the most classical initial conditions, the densely packed. En route to proving this, we obtain some results of independent interest on non-intersecting general pure-birth chains, that generalize the Charlier process, the discrete analogue of Dyson's Brownian motion. Read More

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January 2020
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