Abstract
In this contribution we will review the basic mathematical aspects of quantum maps. Here is a brief outline of the topics covered in this contribution. Most of the material comes from [13], [12], [9] and also [24], [23]. 1. The space of the states and quantization of observables 2. Quantum dynamics over the torus 3. Quantized cat maps 4. The quantum baker’s map and the sawtooth maps 5. Equidistribution of eigenfunctions 6. The period of Amod N and an introduction to the Hecke operators 7. Value distribution of eigenfunctions 8. Equidistribution of Eigenfunctions for discontinuous maps
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Esposti, M.D., Graffi, S. (2003). Mathematical Aspects of Quantum Maps. In: Esposti, M.D., Graffi, S. (eds) The Mathematical Aspects of Quantum Maps. Lecture Notes in Physics, vol 618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37045-5_3
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