Fractal Weyl law for open quantum chaotic maps

Autor: Johannes Sjöstrand, Stéphane Nonnenmacher, Maciej Zworski
Přispěvatelé: Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Department of Mathematics [Berkeley], University of California [Berkeley], University of California-University of California, National Science Fundation - DMS-0635607, ANR-09-JCJC-0099,METHCHAOS,Méthodes spectrales en chaos classique et quantique(2009), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), University of California [Berkeley] (UC Berkeley), University of California (UC)-University of California (UC), Institut de Physique Théorique - UMR CNRS 3681 ( IPHT ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Mathematics Department, UC Berkeley ( UC BERKELEY MATHS ), ANR-09-JCJC-0099-01,ANR-09-JCJC-0099-01
Rok vydání: 2014
Předmět:
[ NLIN.NLIN-CD ] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
FOS: Physical sciences
Semiclassical physics
Dynamical Systems (math.DS)
35B34
37D20
81Q50
81U05
Upper and lower bounds
MSC: 35B34
37D20
81Q50
81U05
Fractal Weyl law
Quantization (physics)
Mathematics - Analysis of PDEs
[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]
Mathematics (miscellaneous)
Fractal
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Mathematics - Dynamical Systems
Quantum
Mathematical physics
Mathematics
Scattering
[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]
Nonlinear Sciences - Chaotic Dynamics
Weyl law
Resonances
Quantum chaotic scattering
[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]
[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]
Chaotic Dynamics (nlin.CD)
Statistics
Probability and Uncertainty
Open quantum map
Complex plane
Analysis of PDEs (math.AP)
Zdroj: 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〉
ISSN: 0003-486X
DOI: 10.4007/annals.2014.179.1.3
Popis: 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 domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
Comment: 69 pages, 7 figures
Databáze: OpenAIRE
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