By Vincent Rivasseau (Chief Editor)

Articles during this volume:

1-26

Smoothness of Correlations within the Anderson version at powerful Disorder

Jean V. Bellissard and Peter D. Hislop

27-36

Eigenfunction facts within the Localized Anderson Model

Rowan Killip and Fumihiko Nakano

37-74

Entropy of Semiclassical Measures of the Walsh-Quantized Baker’s Map

Nalini Anantharaman and Stéphane Nonnenmacher

75-89

Bounds on Supremum Norms for Hecke Eigenfunctions of Quantized Cat Maps

Pär Kurlberg

91-108

A Phase-Space examine of the Quantum Loschmidt Echo within the Semiclassical Limit

Monique Combescure and Didier Robert

109-134

Lower Bounds at the Lowest Spectral hole of Singular strength Hamiltonians

Sylwia Kondej and Ivan Veselić

135-163

Effective versions for Excitons in Carbon Nanotubes

Horia D. Cornean, Pierre Duclos and Benjamin Ricaud

165-201

Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions

Bruno Nachtergaele, Wolfgang Spitzer and Shannon Starr

203-217

Gauge-Invariant Characterization of Yang–Mills–Higgs Equations

Marco Castrillón López and Jaime Muñoz Masqué

219-239

Non-Singular, Vacuum, desk bound Space-Times with a damaging Cosmological Constant

Piotr T. Chruściel and Erwann Delay

241-263

Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R3

Pavel Exner and Rupert L. Frank

265-300

The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials I: Mellin remodel Techniques

Giorgio Mantica and Sandro Vaienti

301-336

The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics

Giorgio Mantica and Davide Guzzetti

337-360

The HVZ Theorem for a Pseudo-Relativistic Operator

Doris H. Jakubaβa-Amundsen

361-426

Patterson–Sullivan Distributions and Quantum Ergodicity

Nalini Anantharaman and Steve Zelditch

427-474

Renormalization of the Orientable Non-commutative Gross–Neveu Model

Fabien Vignes-Tourneret

475-483

Flow-Invariant Hypersurfaces in Semi-Dispersing Billiards

Nikolai Chernov and Nandor Simányi

485-511

Large Time Asymptotics for the BBM–Burgers Equation

Nakao Hayashi, Elena I. Kaikina and Pavel I. Naumkin

513-568

Scattering Poles close to the true Axis for 2 Strictly Convex Obstacles

Alexei Iantchenko

569-596

On the Quasi-Static Evolution of Nonequilibrium regular States

Walid okay. Abou Salem

597-620

On the life and balance of the Penrose Compactification

Justin Corvino

621-685

Quantum Diffusion for the Anderson version within the Scaling Limit

László Erdős, Manfred Salmhofer and Horng-Tzer Yau

687-730

Positive Lyapunov Exponent and Minimality for the continual 1-d Quasi-Periodic Schrödinger Equation with easy Frequencies

Kristian Bjerklöv

731-748

Non-Isotropic Cusp stipulations and Regularity of the Electron Density of Molecules on the Nuclei

Søren Fournais, Thomas Østergaard Sørensen, Maria Hoffmann-Ostenhof and Thomas Hoffmann-Ostenhof

749-779

Relativistic Hydrogenic Atoms in powerful Magnetic Fields

Jean Dolbeault, Maria J. Esteban and Michael Loss

781-816

Continuity houses of critical Kernels linked to Schrödinger Operators on Manifolds

Jochen Brüning, Vladimir Geyler and Konstantin Pankrashkin

817-884

Static Vacuum ideas from Convergent Null information Expansions at Space-Like Infinity

Helmut Friedrich

885-916

Semiclassical L p Estimates

Herbert Koch, Daniel Tataru and Maciej Zworski

917-994

Long diversity Scattering and transformed Wave Operators for the Maxwell–Schrödinger approach II. the final Case

Jean Ginibre and Giorgio Velo

995-1011

Triviality of Bloch and Bloch–Dirac Bundles

Gianluca Panati

1013-1036

The Green–Kubo formulation for in the neighborhood Interacting Fermionic Open Systems

Vojkan Jakšić, Yoshiko Ogata and Claude-Alain Pillet

1037-1069

Semi-Classical research for Hartree Equations in a few Supercritical Cases

Satoshi Masaki

1071-1114

Semiclassical research for Magnetic Scattering through Solenoidal Fields: overall move Sections

Hideo Tamura

1115-1150

The Inverse challenge for Perturbed Harmonic Oscillator at the Half-Line with a Dirichlet Boundary Condition

Dmitry Chelkak and Evgeny Korotyaev

1151-1176

Schrödinger Operators on Zigzag Nanotubes

Evgeny Korotyaev and Igor Lobanov

1177-1219

Existence and balance of the log–log Blow-up Dynamics for the L 2-Critical Nonlinear Schrödinger Equation in a Domain

Fabrice Planchon and Pierre Raphaël

1221-1253

On Surface-Symmetric Spacetimes with Collisionless and Charged Matter

Sophonie Blaise Tchapnda

1255-1277

A Floquet Operator with in simple terms aspect Spectrum and effort Instability

César R. de Oliveira and Mariza S. Simsen

1279-1301

The Rotation quantity for the Generalized Kronig–Penney Hamiltonians

Hiroaki Niikuni

1303-1331

Global Dispersive ideas for the Gross–Pitaevskii Equation in and 3 Dimensions

Stephen Gustafson, Kenji Nakanishi and Tai-Peng Tsai

1333-1370

The Bipolaron within the powerful Coupling Limit

Tadahiro Miyao and Herbert Spohn

1371-1399

Distant Perturbations of the Laplacian in a Multi-Dimensional Space

Denis I. Borisov

1401-1423

Spectral research for Adjacency Operators on Graphs

Marius Măntoiu, Serge Richard and Rafael Tiedra de Aldecoa

1425-1431

Erratum to “Resonance loose domain names for Non Globally Analytic Potentials” Ann. Henri Poincaré 3(4) (2002), 739–756

André Martinez

1433-1459

Relative Haag Duality for the loose box in Fock Representation

Paolo Camassa

1461-1467

Correlation Inequalities for Spin Glasses

Pierluigi Contucci and Joel Lebowitz

1469-1506

Decay of Quantum Correlations on a Lattice by way of warmth Kernel Methods

Laurent Amour, Claudy Cancelier, Pierre Lévy-Bruhl and Jean Nourrigat

1507-1520

Localization for the Anderson version on bushes with Finite Dimensions

Jonathan Breuer

1521-1538

Asymptotics of Random Density Matrices

Ion Nechita

1539-1593

Theory of Non-Equilibrium desk bound States as a idea of Resonances

Marco Merkli, Matthias Mück and Israel Michael Sigal

1595-1621

Scaling Diagram for the Localization size at a Band Edge

Christian Sadel and Hermann Schulz-Baldes

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**Extra resources for Annales Henri Poincaré - Volume 8**

**Example text**

3. A slightly more complicated example In the case of D = 2, although none of the eigenvectors of F2 has any vanishing component, one can still construct eigenstates converging to a fractal measure def 1 supported on a proper subset of T2 . Indeed, we notice that F2 e0 = e0√+e = e+ , 2 2 and F2 = I2 . 6) is an eigenstate of Bk . It becomes normalized in the limit k → ∞, and one can check that the associated semiclassical measure is µ = 1/2 (ν1 (dq) × ν2 (dp) + ν2 (dq)× ν1 (dp)), where ν1 (resp.

2)), the topological entropy can be expressed using cylinder sets. Given two sequences , of ﬁnite lengths | | = n, | | = n , we deﬁne the cylinder set [ · ] ⊂ Σ as the set of sequences starting with on the right side and with on the left side. If n = n , 44 N. Anantharaman and S. Nonnenmacher Ann. Henri Poincar´e it is a ball of radius D−n for the distance dΣ . The image of [ · ] on the torus is the rectangle j j+1 j j +1 , , × , Dn Dn Dn Dn j j where n = 0. 1 · · · n , n = 0. 1 · · · n . D D In the following we will often identify cylinders and rectangles.

8) and j(k) ∈ Jk for all k ≥ 1, then the sequence of Husimi k, (k) measures (W Hψk,j(k) ) weakly converges to the Lebesgue measure on T2 . Remark 3. 3). For any state ψ ∈ HDk , the measure W Hψk,k assigns the weight | q j |ψ |2 to each vertical quantum rectangle [· ], | | = k. With respect to the partition P (n) , all Husimi measures W Hψk, , n ≤ ≤ k are equivalent: for any cylinder [·α] ∈ P (n) , we indeed have ∀ , n ≤ ≤ k, W Hψk, ([·α]) = W Hψk,k ([·α]) . 19) 4. Some explicit eigenstates of Bk The interest of the quantization Bk lies in the fact that its spectrum and eigenstates can be analytically computed.