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Hamiltoniens quantiques et symétries

Abstract : We study the semi-classical behavior of a quantum Hamiltonian whose Weyl symbol has some symmetries coming from a compact group G. The quantum reduction is done by restricting the operator to subspaces of L^2(R^n) called symmetry subspaces, coming from the Peter-Weyl decomposition. The restrictions are called the reduced quantum Hamiltonians. For a finite group, we give a Gutzwiller formula for the reduced Hamiltonian, involving the symmetry of periodic orbits of the energy shell. We interpret this formula in the classical reduced space when G acts freely. For a compact Lie group, we give a Weyl asymptotic formula of the eigenvalue counting function of the reduced Hamiltonian, for which we calculate the first term. Oscillations of the spectral density are also described by a Gutzwiller formula involving periodic orbits of the reduced space, corresponding to quasi-periodic orbits of the euclidian space.
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Contributor : Roch Cassanas <>
Submitted on : Friday, May 20, 2005 - 10:19:17 AM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
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  • HAL Id : tel-00009289, version 1



Roch Cassanas. Hamiltoniens quantiques et symétries. Mathématiques [math]. Université de Nantes, 2005. Français. ⟨tel-00009289⟩



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