Quantum diffusion and generalized Rényi dimensions of spectral measures
Barbaroux, Jean-Marie ; Germinet, François ; Tcheremchantsev, Serguei
Journées équations aux dérivées partielles, (2000), p. 1-16 / Harvested from Numdam
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We estimate the spreading of the solution of the Schrödinger equation asymptotically in time, in term of the fractal properties of the associated spectral measures. For this, we exhibit a lower bound for the moments of order p at time T for the state ψ defined by [1 T∫ 0 T ∥|X| p/2 e -itH ψ∥ 2 dt]. We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure μ ψ associated to the hamiltonian H and the state ψ. We especially concentrate on continuous models.

Publié le : 2000-01-01
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     author = {Barbaroux, Jean-Marie and Germinet, Fran\c cois and Tcheremchantsev, Serguei},
     title = {Quantum diffusion and generalized R\'enyi dimensions of spectral measures},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2000},
     pages = {1-16},
     mrnumber = {2001f:81042},
     zbl = {01808691},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2000____A1_0}
}

Barbaroux, Jean-Marie; Germinet, François; Tcheremchantsev, Serguei. Quantum diffusion and generalized Rényi dimensions of spectral measures. Journées équations aux dérivées partielles,  (2000), pp. 1-16. http://gdmltest.u-ga.fr/item/JEDP_2000____A1_0/

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