96-249 Zelditch, S.

Index and dynamics of quantized contact transformations (129K, TeX) Jun 5, 96

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Abstract. We study the Toeplitz quantization of contact transformations as unitary operators. For instance, symplectic torus automorphisms lift to contact transformations of a Heisenberg nil-manifold and quantize to give the Hermite-Jacobi transformation laws on theta functions. The focus is on the quantum dynamics of quantized contact transformations, e.g. ergodicity and mixing, in the semi-classical limit.

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