Distribution of matrix elements of a classically chaotic system

The statistics of matrix elements of a perturbation of a classically chaotic quartic oscillator system are investigated. Our numerical results confirm that the local variance of the matrix elements can be obtained from a classical correlation function. The probability distribution of the matrix elements (normalised using their local variance) was investigated. This is expected to be a Gaussian distribution in the semi-classical (high-energy) limit. The expected Gaussian form emerges slowly as the energy is increased. The form of the distribution at lower energies is identified.