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.
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Communicated by Ya. G. Sinai
Supported by NSF grant DMS-9102082
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Rudnick, Z., Sarnak, P. The behaviour of eigenstates of arithmetic hyperbolic manifolds. Commun.Math. Phys. 161, 195–213 (1994). https://doi.org/10.1007/BF02099418
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DOI: https://doi.org/10.1007/BF02099418