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Communications in Mathematical Physics

, Volume 161, Issue 1, pp 195–213 | Cite as

The behaviour of eigenstates of arithmetic hyperbolic manifolds

  • Zeév Rudnick
  • Peter Sarnak
Article

Abstract

In this paper we study some problems arising from the theory of Quantum Chaos, in the context of arithmetic hyperbolic manifolds. We show that there is no strong localization (“scarring”) onto totally geodesic submanifolds. Arithmetic examples are given, which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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 1994

Authors and Affiliations

  • Zeév Rudnick
    • 1
  • Peter Sarnak
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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