Arithmetic quantum chaos of Maass waveforms
نویسنده
چکیده
The distribution of the eigenvalues of a quantum Hamiltonian is a central subject that is studied in quantum chaos. There are some generally accepted conjectures about the nearest-neighbor spacing distributions of the eigenvalues. Unless otherwise stated we use the following assumptions: The quantum mechanical system is desymmetrized with respect to all its unitary symmetries, and whenever we examine the distribution of the eigenvalues we regard them on the scale of the mean level spacings. Moreover, it is generically believed that after desymmetrization a generic quantum Hamiltonian possesses no degenerate eigenvalues.
منابع مشابه
On the Topography of Maass Waveforms for PSL(2, Z)
Hejhal was supported in part by NSF Grant DMS 89-10744 and by the Minnesota Supercomputer Institute (with CPU time on the Cray-2 and Cray-XMP). This paper is an expanded version of Hejhal's lecture at the Workshop on Discrete Groups, Number Theory and Ergodic Theory held at MSRI in November 1991. This article provides a glimpse into “arithmetical quantum chaos” through a study of the topography...
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