Distribution of resonances for open quantum maps

DOI10.1007/s00220-006-0131-0zbMath1114.81043arXivmath-ph/0505034OpenAlexW3103535709MaRDI QIDQ883008

Maciej Zworski, Stéphane Nonnenmacher

Publication date: 31 May 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0505034

Mathematics Subject Classification ID

Quantum chaos (81Q50) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Fractals (28A80) Quantum scattering theory (81U99)

Related Items (19)

The Failure of the Fractal Uncertainty Principle for the Walsh–Fourier Transform ⋮ Resonances for open quantum maps and a fractal uncertainty principle ⋮ Fractal Weyl laws for asymptotically hyperbolic manifolds ⋮ Fractal upper bounds on the density of semiclassical resonances ⋮ Ulam method and fractal Weyl law for Perron-Frobenius operators ⋮ Quantum decay rates in chaotic scattering ⋮ Uniform hyperbolicity of a class of scattering maps ⋮ Almost sure Weyl law for quantized tori ⋮ Weyl laws for open quantum maps ⋮ Resonances in a single-lead reflection from a disordered medium: \(\sigma\)-model approach ⋮ Fractal Weyl law for open quantum chaotic maps ⋮ Upper bound on the density of Ruelle resonances for Anosov flows ⋮ Mathematical study of scattering resonances ⋮ Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold ⋮ Distribution of Resonances for Hyperbolic Surfaces ⋮ From open quantum systems to open quantum maps ⋮ Probabilistic Weyl laws for quantized tori ⋮ Lieb–Thirring estimates for non-self-adjoint Schrödinger operators ⋮ Circular law and arc law for truncation of random unitary matrix

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical study of quantum resonances in chaotic scattering
• Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems
• Fractal upper bounds on the density of semiclassical resonances
• Geometric bounds on the density of resonances for semiclassical problems
• Quantization of linear maps on a torus-Fresnel diffraction by a periodic grating
• Autour de l'approximation semi-classique. (Around semiclassical approximation)
• The quantized Baker's transformation
• Oscillatory integrals with singular symbols
• Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces
• Towards a semiclassical theory of the quantum Baker's map
• Quantum monodromy and semi-classical trace formulæ.
• The Selberg zeta function for convex co-compact Schottky groups
• Shifts on a finite qubit string: A class of quantum baker's maps
• Poincaré's recurrence theorem and the unitarity of the \(S\)-matrix
• Discrete Wigner functions and the phase space representation of quantum computers
• The divisor of Selberg's zeta function for Kleinian groups. Appendix A by Charles Epstein
• Equipartition of the eigenfunctions of quantized ergodic maps on the torus
• Elementary linear algebra for advanced spectral problems
• Mathematical physics of quantum mechanics. Selected and refereed lectures from the QMath9 conference, Giens, France, September 12--16, 2004.
• Identification of Berezin-Toeplitz deformation quantization
• Résonances en limite semi-classique
• Semiclassical quantization of multidimensional systems
• Semiclassical quantization of chaotic billiards: a scattering theory approach
• Ergodic properties of Anosov maps with rectangular holes
• The classical limit for a class of quantum baker s maps
• Truncations of random unitary matrices
• Spectral statistics for unitary transfer matrices of binary graphs
• The quantized D-transformation
• Growth of the zeta function for a quadratic map and the dimension of the Julia set
• General quantum surface-of-section method
• A Carleson type theorem for a Cantor group model of the scattering transform
• Fractal Weyl laws in discrete models of chaotic scattering
• Classical and quantum lifetimes on some non-compact Riemann surfaces

This page was built for publication: Distribution of resonances for open quantum maps