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Mathematical Aspects of Quantum Maps

  • Mirko Degli Esposti
  • Sandro Graffi
Conference paper
Part of the Lecture Notes in Physics book series (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

Keywords

Periodic Orbit Heisenberg Group Mathematical Aspect Generalize Riemann Hypothesis Toral Automorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mirko Degli Esposti
  • Sandro Graffi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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