On the Convergence to Ergodic Behaviour of Quantum Wave Functions

Details On the Convergence to Ergodic Behaviour of Quantum Wave Functions On the Convergence to Ergodic Behaviour of Quantum Wave Functions

1996-10-15

arxiv.org/abs/chao-dyn/9610014v1

Nonlinear Sciences

Chaotic Dynamics

13 pages Latex, 5 figures

Scientific paper

10.1088/0305-4470/30/9/011

We study the decrease of fluctuations of diagonal matrix elements of observables and of Husimi densities of quantum mechanical wave functions around their mean value upon approaching the semi-classical regime ($\hbar \rightarrow 0$). The model studied is a spin (SU(2)) one in a classically strongly chaotic regime. We show that the fluctuations are Gaussian distributed, with a width $\sigma^2$ decreasing as the square root of Planck's constant. This is consistent with Random Matrix Theory (RMT) predictions, and previous studies on these fluctuations. We further study the width of the probability distribution of $\hbar$-dependent fluctuations and compare it to the Gaussian Orthogonal Ensemble (GOE) of RMT.

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