Výsledky vyhledávání - "Stéphane Nonnenmacher"

LOCAL EIGENVALUE STATISTICS OF ONE DIMENSIONAL RANDOM NONSELFADJOINT PSEUDODIFFERENTIAL OPERATORS

Autor: Martin Vogel, Stéphane Nonnenmacher

Publikováno v: Journal of the European Mathematical Society
Journal of the European Mathematical Society, European Mathematical Society, 2021, 23 (5), ⟨10.4171/JEMS/1039⟩

International audience; We consider a class of one-dimensional nonselfadjoint semiclassical pseudo-differential operators, subject to small random perturbations, and study the statistical properties of their (discrete) spectra, in the semiclassical l

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::53fff15c09558453ab1191d5924d8273
https://hal.archives-ouvertes.fr/hal-01781397

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Control of eigenfunctions on surfaces of variable curvature

Autor: Semyon Dyatlov, Long Jin, Stéphane Nonnenmacher

We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows. This implies controllability for the Schr\"odinger equa

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Strong scarring of logarithmic quasimodes

Autor: Stéphane Nonnenmacher, Suresh Eswarathasan

Publikováno v: Annales de l'Institut Fourier
Annales de l'Institut Fourier, 2017, Annales de l'Institut Fourier, 67 (6), pp.2307-2347
Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2017, Annales de l'Institut Fourier, 67 (6), pp.2307-2347

We consider a semiclassical (pseudo)differential operator on a compact surface $(M,g)$, such that the Hamiltonian flow generated by its principal symbol admits a hyperbolic periodic orbit $\gamma$ at some energy $E_0$. For any $\epsilon>0$, we then e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a01df9c6a5c0ba9fa0beff7d64c648b
https://orca.cardiff.ac.uk/id/eprint/86438/1/AIF_2017__67_6_2307_0.pdf

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Fractal Weyl law for open quantum chaotic maps

Autor: Johannes Sjöstrand, Stéphane Nonnenmacher, Maciej Zworski

Publikováno v: Annals of Mathematics
Annals of Mathematics, Princeton University, Department of Mathematics, 2014, 179 (1), pp.179-251. ⟨10.4007/annals.2014.179.1.3⟩
Annals of Mathematics, 2014, 179 (1), pp.179-251. ⟨10.4007/annals.2014.179.1.3⟩
Annals of Mathematics, Princeton University, Department of Mathematics, 2014, 179 (1), pp.179-251. 〈10.4007/annals.2014.179.1.3〉

We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small dom

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a92a02371e67007523db12465cc70bd2
https://doi.org/10.4007/annals.2014.179.1.3

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Anatomy of quantum chaotic eigenstates

Autor: Stéphane Nonnenmacher

Publikováno v: Chaos. Poincaré Seminar 2010
Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau. Chaos. Poincaré Seminar 2010, Spinger, pp.194-238, 2013, Progress in Mathematical Physics 66, 978-3-0348-0696-1. ⟨10.1007/978-3-0348-0697-8_6⟩
Chaos ISBN: 9783034806961

International audience; The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c745ec42ee4818150ec7bf28a1e280cd
https://hal.archives-ouvertes.fr/hal-00486062

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On the resonance eigenstates of an open quantum baker map

Autor: Martin Sieber, Stéphane Nonnenmacher, Jon P Keating, Marcel Novaes

Publikováno v: Nonlinearity
Nonlinearity, IOP Publishing, 2008, 21 (11), pp.2591. ⟨10.1088/0951-7715/21/11/007⟩
Nonlinearity, 2008, 21 (11), pp.2591. ⟨10.1088/0951-7715/21/11/007⟩

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2066cb9d654f096b28724ed8b7585d33
https://doi.org/10.1088/0951-7715/21/11/007

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Resonant eigenstates for a quantized chaotic system

Autor: Mathieu Rubin, Stéphane Nonnenmacher

Publikováno v: Nonlinearity. 20:1387-1420

We study the spectrum of quantized open maps as a model for the resonance spectrum of quantum scattering systems. We are particularly interested in open maps admitting a fractal repeller. Using the 'open baker's map' as an example, we numerically inv

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7b883c33a871fafa1e27d603d96c2bfc
https://doi.org/10.1088/0951-7715/20/6/004

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Décroissance des corrélations pour un ensemble capté normalement hyperbolique

Autor: Maciej Zworski, Stéphane Nonnenmacher

Publikováno v: Inventiones Mathematicae
Inventiones Mathematicae, 2015, Inventiones Mathematicae, 200, pp.345-438. ⟨10.1007/s00222-014-0527-y⟩
Inventiones Mathematicae, Springer Verlag, 2015, Inventiones Mathematicae, 200, pp.345-438. ⟨10.1007/s00222-014-0527-y⟩

International audience; We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normal hyperbolic trapping means that the trapped set is smooth and symplectic and that the flow

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b65cd6b8796435fd9501067b62789930
https://hal.science/hal-00951495

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