L Benet et al 2003 J. Phys. A: Math. Gen. 36 1289 doi:10.1088/0305-4470/36/5/307
L Benet1,3, J Flores1,3, H Hernández-Saldaña1,2, F M Izrailev1,4, F Leyvraz1,3 and T H Seligman1,3
Show affiliationsQuantum–classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations of the quantum wavefunctions around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes whose width is determined by the classical shape of the eigenfunction. To compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators, we develop a rescaling method for the components. The expectations are broadly confirmed, but deviations due to scars are observed. This effect is much reduced when both Hamiltonians have chaotic dynamics.
05.45.Mt Quantum chaos; semiclassical methods
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
Issue 5 (7 February 2003)
Received 23 July 2002, in final form 3 December 2002
Published 22 January 2003
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