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Mathematical Aspects of Quantum Maps

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The Mathematical Aspects of Quantum Maps

Part of the book series: Lecture Notes in Physics ((LNP,volume 618))

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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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, 40127, Bologna, Italy

    Sandro Graffi

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  1. Mirko Degli Esposti
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  2. Sandro Graffi
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Editors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127, Bologna, Italy

    Mirko Degli Esposti  & Sandro Graffi  & 

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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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  • DOI: https://doi.org/10.1007/3-540-37045-5_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-02623-5

  • Online ISBN: 978-3-540-37045-1

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