Quantization of a class of piecewise affine transformations on the torus

DOI10.1007/BF02099363zbMath0840.58019arXivhep-th/9502035OpenAlexW3101907878MaRDI QIDQ1907627

Yanyan Li

Publication date: 13 February 1996

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

Full work available at URL: https://arxiv.org/abs/hep-th/9502035

zbMATH Keywords

quantizationphase spacediscrete dynamical systemspiecewise affine mapstwo-torus

Mathematics Subject Classification ID

Geometric quantization (53D50)

Related Items (8)

Pair correlation for quadratic polynomials mod 1 ⋮ Crossover from diffusive to ballistic transport in periodic quantum maps ⋮ Equipartition of the eigenfunctions of quantized ergodic maps on the torus ⋮ Two body relativistic wave equations ⋮ Unnamed Item ⋮ On the notion of ergodicity for finite quantum systems ⋮ A canonical quantization of the baker's map ⋮ QUANTUM MAPS WITH SPACE EXTENT: A PARADIGM FOR LATTICE QUANTUM WALKS

Cites Work

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• General concept of quantization
• Classical structures in the quantized Baker transformation
• Quantization of linear maps on a torus-Fresnel diffraction by a periodic grating
• The quantized Baker's transformation
• Ergodic properties of the discontinuous sawtooth map
• Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2-torus
• Classical limit of the quantized hyperbolic toral automorphisms
• Asymptotic properties of the periodic orbits of the cat maps
• The cat maps: quantum mechanics and classical motion
• Exact eigenfunctions for a quantised map
• Quantization and unitary representations

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