Fractal upper bounds on the density of semiclassical resonances

Abstract

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.

References in corpus (5)

• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical estimates in asymptotically Euclidean scattering
• Numerical Study of Quantum Resonances in Chaotic Scattering
• Approximating resonances with the Complex Absorbing Potential Method

Cited by in corpus (2)

• Quantum Monodromy and Non-concentration near a Closed Semi-Hyperbolic Orbit
• Semiclassical second microlocalization at linear coisotropic submanifolds in the torus