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A random matrix model for quantum mixing. (English) Zbl 0858.58048
Quantization of the classical Hamiltonian system is carried out by means of the wave group (square root of the Laplacian stands for its generator) of a compact Riemannian manifold. The asymptotic behaviour of eigenfunctions and eigenvalues of the square root of the Laplacian reflects (semiclassically) the ergodicity and weak mixing properties of the classical geodesic flow.
Motivated by the random matrix theory approach to the quantization of classically chaotic systems, a particular kind of random matrix model is investigated. A number of open problems is listed.

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
81Q50 Quantum chaos
53D50 Geometric quantization
15B52 Random matrices (algebraic aspects)
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