Chaos pp 97-124 | Cite as

Discrete Graphs – A Paradigm Model for Quantum Chaos

Chapter
First Online:
Part of the Progress in Mathematical Physics book series (PMP, volume 66)

Abstract

The research in Quantum Chaos attempts to uncover the fingerprints of classical chaotic dynamics in the corresponding quantum description. To get to the roots of this problem, various simplified models were proposed and used. Here a very simple model of a random walker on large d-regular graphs, and its quantum analogue are proposed as a paradigm which shares many salient features with realistic models – namely the affinity of the spectral statistics with random matrix theory, the role of cycles and their statistics, and percolation of level sets of the eigenvectors. These concepts will be explained and reviewed with reference to the original publications for further details.

Keywords

Periodic Orbit Regular Graph Trace Formula Random Matrix Theory Random Wave 
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 Basel 2013

Authors and Affiliations

  1. 1.Department of Physics of Complex SystemsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.School of MathematicsCardiff UniversityCardiffWales, UK

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