Fractal upper bounds on the density of semiclassical resonances
By J. Sjoestrand, Maciej Zworski. 2005
115 citations recorded by the source corpus.
For semiclassical problems we establish upper bounds on the number of resonances in boxes of size $h$ along the real axis, in terms of the dimension of the set of trapped trajectories. The proof uses second microlocalization.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/49b974c8689e71213d153bac37023a20ba64b723
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Resonance projectors and asymptotics for r -normally hyperbolic trapped sets (2013, background): “s in strips near the real axis have been proved in dierent situations, both for normally hyperbolic and for hyperbolic trapping, by Sjostrand [Sj90], Guillope{Lin{Zworski [GLZ], Sjostrand{Zworski [SjZw07], Nonnenmacher{Sjostrand{Zworski [NSZ11,NSZ14], Faure{Sjostrand [FaSj], Datchev{ Dyatlov [DaDy],”
- Semiclassical non-concentration near hyperbolic orbits (2006, methodology): “,...lN, adOpw h (l1) ◦adOpw h (l2) ◦···◦adOpw h (lN)A= O(h N) L2→L2. The following lemma (given more generally in [BoCh]) will be used in the proof of Theorem 1. We include a sketch of the proof from [SjZw2] here for completeness. It is easiest to phrase in terms of orderfunctions. A smooth function”