Quantum ergodicity of \(C^*\) dynamical systems

DOI10.1007/BF02101904zbMath0856.58019arXivmath-ph/0002008MaRDI QIDQ1918108

Steven Zelditch

Publication date: 3 March 1997

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

Full work available at URL: https://arxiv.org/abs/math-ph/0002008

zbMATH Keywords

quantum ergodicity\(C^*\)-dynamical systems

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Geometric quantization (53D50)

Related Items (21)

Quantum ergodicity of boundary values of eigenfunctions ⋮ Complex zeros of real ergodic eigenfunctions ⋮ High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows ⋮ Classical and quantum ergodicity on orbifolds ⋮ Almost all eigenfunctions of a rational polygon are uniformly distributed ⋮ \(L^{p}\) norms, nodal sets, and quantum ergodicity ⋮ Unnamed Item ⋮ On the rate of quantum ergodicity on hyperbolic surfaces and for billiards ⋮ Variations on quantum ergodic theorems, II ⋮ Random matrix spectral form factor of dual-unitary quantum circuits ⋮ Index and dynamics of quantized contact transformations ⋮ Quantized Kronecker flows and almost periodic quantum field theory ⋮ Quantum and classical ergodicity of spinning particles ⋮ Ergodic properties of quantized toral automorphisms ⋮ Appendix to Kaplan-Heller ⋮ Quantum ergodicity on graphs: from spectral to spatial delocalization ⋮ Ergodic properties of the quantum geodesic flow on tori ⋮ High-energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows ⋮ Quantum ergodicity on large regular graphs ⋮ Scaling asymptotics for Szegő kernels on Grauert tubes ⋮ Around quantum ergodicity

Cites Work

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• Residue traces for certain algebras of Fourier integral operators
• The behaviour of eigenstates of arithmetic hyperbolic manifolds
• Semiclassical asymptotics, gauge fields, and quantum chaos
• Ergodicity of eigenfunctions for ergodic billiards
• Quantum transition amplitudes for ergodic and for completely integrable systems
• Some Problems in Integral Geometry and Some Related Problems in Micro-Local Analysis
• The Spectral Theory of Toeplitz Operators. (AM-99)

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