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

By Vincent Rivasseau (Chief Editor)

Articles during this volume:

1-26
Smoothness of Correlations within the Anderson version at robust 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 learn 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 detrimental 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 rework 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 genuine Axis for 2 Strictly Convex Obstacles
Alexei Iantchenko

569-596
On the Quasi-Static Evolution of Nonequilibrium regular States
Walid ok. 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 crucial Kernels linked to Schrödinger Operators on Manifolds
Jochen Brüning, Vladimir Geyler and Konstantin Pankrashkin

817-884
Static Vacuum ideas from Convergent Null info 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 converted Wave Operators for the Maxwell–Schrödinger process 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 by means of Solenoidal Fields: overall go 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 basically 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 strategies for the Gross–Pitaevskii Equation in and 3 Dimensions
Stephen Gustafson, Kenji Nakanishi and Tai-Peng Tsai

1333-1370
The Bipolaron within the robust 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 unfastened 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 means 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 concept 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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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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