General features of quantum chaos and its relevance to nuclear physics

Some general features of the eigenenergies and the eigenwave functions of a chaotic quantum system are investigated by level dynamics in connection with nuclear physics. It is shown that the chaotic property of the eigensolutions is due to a large number of avoided level crossings. The critical strength of the perturbation for onset of quantum chaos is that the average value of the matrix elements of the perturbation equals the average level spacing of the unperturbed Hamiltonian tin the so-called strong mixing limit in nuclear physics). This kind of critical perturbation makes each level experience 4-5 avoided level crossings, and produces a spreading width of 16-32 on average. The extreme sensitivity of eigenenergies and eigenwave functions to a small change of the perturbation also originates from the avoided level crossings. The analytical expressions for a measured sensitivity are derived. More general expressions for the probability distribution (or strength function) and the spreading width of a perturbed state over a regular basis are obtained, which generalize the previous results: the strength function is still in the form of a Lorentzian function but with a spreading width consisting of the regular level contribution (the width being given by the so-called picket-fence model) and the avoided-level crossing contribution (width from level fluctuations). The relation between two chaotic bases is peculiar and the corresponding strength function shows a remarkable discontinuity, which is new and due to the statistical independence of different chaotic bases. The decay properties of nuclear ergodic collective states are discussed and explained in terms of the above results. Extensive results of computer simulations are presented to verify the level dynamical predictions.