Reduced Gutzwiller formula with symmetry: Case of a Lie group |
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Authors: | Roch Cassanas |
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Affiliation: | Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2, Rue de la Houssinière, BP92208 F-44322, Nantes Cedex 3, France |
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Abstract: | We consider a classical Hamiltonian H on R2d, invariant by a Lie group of symmetry G, whose Weyl quantization is a selfadjoint operator on L2(Rd). If χ is an irreducible character of G, we investigate the spectrum of its restriction to the symmetry subspace of L2(Rd) coming from the decomposition of Peter-Weyl. We give semi-classical Weyl asymptotics for the eigenvalues counting function of in an interval of R, and interpret it geometrically in terms of dynamics in the reduced space R2d/G. Besides, oscillations of the spectral density of are described by a Gutzwiller trace formula involving periodic orbits of the reduced space, corresponding to quasi-periodic orbits of R2d. |
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Keywords: | Symmetry reduction Gutzwiller formula Coherent states Semi-classical analysis |
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