Download PDF by Vincent Rivasseau (Chief Editor): Annales Henri Poincaré - Volume 8

By Vincent Rivasseau (Chief Editor)

Articles during this volume:

Smoothness of Correlations within the Anderson version at robust Disorder
Jean V. Bellissard and Peter D. Hislop

Eigenfunction facts within the Localized Anderson Model
Rowan Killip and Fumihiko Nakano

Entropy of Semiclassical Measures of the Walsh-Quantized Baker’s Map
Nalini Anantharaman and Stéphane Nonnenmacher

Bounds on Supremum Norms for Hecke Eigenfunctions of Quantized Cat Maps
Pär Kurlberg

A Phase-Space learn of the Quantum Loschmidt Echo within the Semiclassical Limit
Monique Combescure and Didier Robert

Lower Bounds at the Lowest Spectral hole of Singular strength Hamiltonians
Sylwia Kondej and Ivan Veselić

Effective versions for Excitons in Carbon Nanotubes
Horia D. Cornean, Pierre Duclos and Benjamin Ricaud

Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions
Bruno Nachtergaele, Wolfgang Spitzer and Shannon Starr

Gauge-Invariant Characterization of Yang–Mills–Higgs Equations
Marco Castrillón López and Jaime Muñoz Masqué

Non-Singular, Vacuum, desk bound Space-Times with a detrimental Cosmological Constant
Piotr T. Chruściel and Erwann Delay

Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R3
Pavel Exner and Rupert L. Frank

The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials I: Mellin rework Techniques
Giorgio Mantica and Sandro Vaienti

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

The HVZ Theorem for a Pseudo-Relativistic Operator
Doris H. Jakubaβa-Amundsen

Patterson–Sullivan Distributions and Quantum Ergodicity
Nalini Anantharaman and Steve Zelditch

Renormalization of the Orientable Non-commutative Gross–Neveu Model
Fabien Vignes-Tourneret

Flow-Invariant Hypersurfaces in Semi-Dispersing Billiards
Nikolai Chernov and Nandor Simányi

Large Time Asymptotics for the BBM–Burgers Equation
Nakao Hayashi, Elena I. Kaikina and Pavel I. Naumkin

Scattering Poles close to the genuine Axis for 2 Strictly Convex Obstacles
Alexei Iantchenko

On the Quasi-Static Evolution of Nonequilibrium regular States
Walid ok. Abou Salem

On the life and balance of the Penrose Compactification
Justin Corvino

Quantum Diffusion for the Anderson version within the Scaling Limit
László Erdős, Manfred Salmhofer and Horng-Tzer Yau

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

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

Relativistic Hydrogenic Atoms in powerful Magnetic Fields
Jean Dolbeault, Maria J. Esteban and Michael Loss

Continuity houses of crucial Kernels linked to Schrödinger Operators on Manifolds
Jochen Brüning, Vladimir Geyler and Konstantin Pankrashkin

Static Vacuum ideas from Convergent Null info Expansions at Space-Like Infinity
Helmut Friedrich

Semiclassical L p Estimates
Herbert Koch, Daniel Tataru and Maciej Zworski

Long diversity Scattering and converted Wave Operators for the Maxwell–Schrödinger process II. the final Case
Jean Ginibre and Giorgio Velo

Triviality of Bloch and Bloch–Dirac Bundles
Gianluca Panati

The Green–Kubo formulation for in the neighborhood Interacting Fermionic Open Systems
Vojkan Jakšić, Yoshiko Ogata and Claude-Alain Pillet

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

Semiclassical research for Magnetic Scattering by means of Solenoidal Fields: overall go Sections
Hideo Tamura

The Inverse challenge for Perturbed Harmonic Oscillator at the Half-Line with a Dirichlet Boundary Condition
Dmitry Chelkak and Evgeny Korotyaev

Schrödinger Operators on Zigzag Nanotubes
Evgeny Korotyaev and Igor Lobanov

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

On Surface-Symmetric Spacetimes with Collisionless and Charged Matter
Sophonie Blaise Tchapnda

A Floquet Operator with basically aspect Spectrum and effort Instability
César R. de Oliveira and Mariza S. Simsen

The Rotation quantity for the Generalized Kronig–Penney Hamiltonians
Hiroaki Niikuni

Global Dispersive strategies for the Gross–Pitaevskii Equation in and 3 Dimensions
Stephen Gustafson, Kenji Nakanishi and Tai-Peng Tsai

The Bipolaron within the robust Coupling Limit
Tadahiro Miyao and Herbert Spohn

Distant Perturbations of the Laplacian in a Multi-Dimensional Space
Denis I. Borisov

Spectral research for Adjacency Operators on Graphs
Marius Măntoiu, Serge Richard and Rafael Tiedra de Aldecoa

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

Relative Haag Duality for the unfastened box in Fock Representation
Paolo Camassa

Correlation Inequalities for Spin Glasses
Pierluigi Contucci and Joel Lebowitz

Decay of Quantum Correlations on a Lattice by means of warmth Kernel Methods
Laurent Amour, Claudy Cancelier, Pierre Lévy-Bruhl and Jean Nourrigat

Localization for the Anderson version on bushes with Finite Dimensions
Jonathan Breuer

Asymptotics of Random Density Matrices
Ion Nechita

Theory of Non-Equilibrium desk bound States as a concept of Resonances
Marco Merkli, Matthias Mück and Israel Michael Sigal

Scaling Diagram for the Localization size at a Band Edge
Christian Sadel and Hermann Schulz-Baldes

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Additional resources for Annales Henri Poincaré - Volume 8

Example text

Some explicit eigenstates of Bk The interest of the quantization Bk lies in the fact that its spectrum and eigenstates can be analytically computed. Vol. 1. 15) and the periodicity of the Fourier transform) is that this operator is periodic, with period 2k (when D = 2) or 4k (when D ≥ 3): D = 2 =⇒ ∀k ≥ 1, (Bk )2k = I2k D ≥ 2 =⇒ ∀k ≥ 1, (Bk )4k = IDk . 1) where Π is the “parity operator” on C , which sends e to e¯, with +¯ ≡ 0 mod D. log h| As we noticed above, k = |log D is the Ehrenfest time of the system, so the above periodicity can be compared with the “short quantum periods” of the quantum cat map [5, 12], which allowed one to construct eigenstates with a partial localization on some periodic orbits.

Indeed, the following “Entropic Uncertainty Principle”, first conjectured 56 N. Anantharaman and S. Nonnenmacher Ann. Henri Poincar´e by Kraus [19] and proven in [26], directly provides the desired lower bound for h(w). 1 (Entropic uncertainty principle [26]). For any M ∈ N∗ , let U be a def unitary M × M matrix and c(U ) = supi,j |Uij |. Then, for any normalized state ψ ∈ CM , one has h(ψ) + h(U ψ) ≥ −2 log c(U ) , where the entropy is defined as h(ψ) = − i |ψi |2 log |ψi |2 . 2, see Section 5) is outlined in the Appendix.

We will use here a different quantization, based on the Walsh–Fourier transform [31]: this choice makes the quantum model amenable to an analytic treatment. The map and its quantization will be described in more detail in Sections 2–3. The localization in phase space of an eigenfunction ψ will be analyzed using its Walsh–Husimi measure W Hψ , which is a probability measure on the torus, associated with the state ψ . For any sequence of eigenfunctions (ψ ) →0 of the quantized map, one can extract a subsequence of W Hψ j j →0 which weakly converges towards a probability measure µ.

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