Autocorrelation function of eigenstates in chaotic and mixed systems

Details Autocorrelation function of eigenstates in chaotic and mixed systems Autocorrelation function of eigenstates in chaotic and mixed systems

2001-06-13

arxiv.org/abs/nlin/0106018v1

J. Phys. A 35 (2002) 539-564

Nonlinear Sciences

Chaotic Dynamics

30 pages, 12 figures. Some of the pictures are included in low resolution only. For a version with pictures in high resolution

Scientific paper

10.1088/0305-4470/35/3/307

We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation length. For localized states, like bouncing ball modes or states living on tori, a simple model using only classical input gives good agreement with the exact result. In particular, a prediction for irregular eigenfunctions in mixed systems is derived and tested. For chaotic systems, the expansion of the autocorrelation function can be used to test quantum ergodicity on different length scales.

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