On the convergence to ergodic behaviour of quantum wavefunctions

Ph Jacquod, J-P Amiet
1997 Journal of Physics A: Mathematical and General  
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 (ħ→ 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 σ^2 decreasing as the square root of Planck's constant. This is consistent with Random Matrix Theory (RMT) predictions, and
more » ... studies on these fluctuations. We further study the width of the probability distribution of ħ-dependent fluctuations and compare it to the Gaussian Orthogonal Ensemble (GOE) of RMT.
doi:10.1088/0305-4470/30/9/011 fatcat:arc5ugbgynhtnhqchnks75q6h4