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Gaussian representation of extended quantum states |
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| Authors: | A.R.R. Carvalho A. KenfackF. Toscano J.M. RostA.M. Ozorio de Almeida |
| Affiliation: | a Centre for Quantum Computation and Communication Technology, Department of Quantum Sciences, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia b Physikalische und Theoretische Chemie, Institut für Chemie und Biochemie, Freie Universität Berlin, D-14195 Berlin, Germany c Instituto de Física, Universidade Federal do Rio de Janeiro, Cx. P. 68528, 21941-972 Rio de Janeiro, RJ, Brazil d Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany e Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil |
| Abstract: | Excited energy eigenstates and their superpositions typically exhibit a fine oscillatory structure near caustics. Semiclassical theory accesses these, but depends on detailed geometrical knowledge of the caustics. Here we show that a finite placement of coherent states on the classical region efficiently fits such extended states, reproducing structures that are much finer than the Gaussian width of the basis states. An extended state, evolved such that it becomes fully distinguishable from the original state, can also be faithfully reproduced by this finite basis. The ideal fitting follows from the projection of the extended state on the finite Hilbert space spanned by the Gaussians, rather than any discretization of the continuous (overcomplete) coherent state representation. |
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