Ergodic properties of quantized toral automorphisms

DOI10.1063/1.531835zbMath0890.47006arXivchao-dyn/9512003OpenAlexW1967207666MaRDI QIDQ2785735

Andrzej Lesniewski, Ron Rubin, Neepa Maitra, Sławomir Klimek-Chudy

Publication date: 28 June 1998

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

Full work available at URL: https://arxiv.org/abs/chao-dyn/9512003

zbMATH Keywords

ergodicityquantizationmixingergodic propertiesquantum mapsquantized toral automorphismscat mapsalgebraic Toeplitz quantization schemequantized Kronecker dynamicsunitary endomorphismsvector bundle over a torus

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Applications of operator theory in the physical sciences (47N50) Geometry and quantization, symplectic methods (81S10)

Related Items (7)

Large supremum norms and small Shannon entropy for Hecke eigenfunctions of quantized cat maps ⋮ Beyond irreducibility and back ⋮ Large newforms of the quantized cat map revisited ⋮ Disheveled Arnold's cat and the problem of quantum-classic correspondence ⋮ A canonical quantization of the baker's map ⋮ Hecke theory and equidistribution for the quantization of linear maps of the torus ⋮ Ergodic properties of the quantum geodesic flow on tori

Cites Work

• A non-commutative version of the Arnold cat map
• Quantization of linear maps on a torus-Fresnel diffraction by a periodic grating
• Ergodicity and eigenfunctions of the Laplacian
• Quantized chaotic dynamics and non-commutative \(KS\) entropy
• Classical limit of the quantized hyperbolic toral automorphisms
• Quantum ergodicity of \(C^*\) dynamical systems

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