Spectral problems in open quantum chaos
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Publication:3107991
DOI10.1088/0951-7715/24/12/R02zbMath1229.35223arXiv1105.2457MaRDI QIDQ3107991
Publication date: 28 December 2011
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1105.2457
Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Quantum chaos (81Q50) PDEs in connection with quantum mechanics (35Q40) Spectral theory; eigenvalue problems on manifolds (58C40) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)
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Resonances for open quantum maps and a fractal uncertainty principle ⋮ Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions ⋮ Scattering resonances of large weakly open quantum graphs ⋮ Dolgopyat's method and the fractal uncertainty principle ⋮ Fractal Weyl laws for asymptotically hyperbolic manifolds ⋮ Fourier dimension and spectral gaps for hyperbolic surfaces ⋮ Uniform hyperbolicity of a class of scattering maps ⋮ Average localization of resonances on the quantum repeller ⋮ Fractal Weyl laws and wave decay for general trapping ⋮ Microlocal limits of Eisenstein functions away from the unitarity axis ⋮ Resolvent estimates in strips for obstacle scattering in 2D and local energy decay for the wave equation ⋮ Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps ⋮ Spectral gaps without the pressure condition ⋮ Mathematical study of scattering resonances ⋮ An introduction to fractal uncertainty principle ⋮ Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets ⋮ Resonance chains and geometric limits on Schottky surfaces ⋮ Random Lindblad dynamics
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