6533b7d6fe1ef96bd1265d3e

RESEARCH PRODUCT

Fractal Weyl law for open quantum chaotic maps

Johannes SjöstrandStéphane NonnenmacherMaciej Zworski

subject

[ NLIN.NLIN-CD ] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD][PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciencesSemiclassical physicsDynamical Systems (math.DS)35B34 37D20 81Q50 81U05Upper and lower boundsMSC: 35B34 37D20 81Q50 81U05Fractal Weyl lawQuantization (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 SystemsQuantumMathematical physicsMathematicsScattering[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Nonlinear Sciences - Chaotic DynamicsWeyl lawResonancesQuantum 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 UncertaintyOpen quantum mapComplex planeAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2014-01-01Annals of Mathematics
https://doi.org/10.4007/annals.2014.179.1.3