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artículo con referato
"The short periodic orbit approach for Quantum Cat Maps"
E.G. Vergini, D. Schneider and A.M.F. Rivas
J. Phys. A: Math. Theor. 41(40) (2008) 405102/1-24
The short periodic orbit approach is adapted for the quantum cat maps. The main objective is to explain, in a simple abstract model, the most relevant characteristics of this method which was originally developed for Hamiltonian fluxes. In particular, we describe a semiclassical Hamiltonian formulation to evaluate eigenphases and eigenstates of quantum cat maps. The main advantage of this formulation is that each eigenstate is described in terms of a small number, N/ln N, of short periodic orbits, with N the dimension of the Hilbert space. Moreover, matrix elements can be obtained semiclassically with high accuracy in terms of a very small number, of the order of ln2N, of homoclinic and heteroclinic orbits. From the computational point of view, this approach reduces the size of matrices used to the order N/ln N.
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