Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Stéphane Nonnenmacher"'
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⟩
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
https://hal.archives-ouvertes.fr/hal-01781397
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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d65a587a8f70a32206beda2db009db3
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
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
https://orca.cardiff.ac.uk/id/eprint/86438/1/AIF_2017__67_6_2307_0.pdf
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〉
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
https://doi.org/10.4007/annals.2014.179.1.3
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⟩
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
https://doi.org/10.1088/0951-7715/21/11/007
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
https://doi.org/10.1088/0951-7715/20/6/004
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
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
https://hal.archives-ouvertes.fr/hal-00486062
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⟩
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
https://hal.science/hal-00951495
Publikováno v:
Annales Henri Poincaré. 7:161-198
We introduce the notion of relaxation time for noisy quantum maps on the 2d-dimensional torus – generalization of previously studied dissipation time. We show that the relaxation time is sensitive to the chaotic behavior of the corresponding classi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1e54b4b020d589daec200123662f87e9
https://doi.org/10.1007/s00023-005-0246-4
https://doi.org/10.1007/s00023-005-0246-4
This twelfth volume in the Poincaré Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This book expounds some of the most