The strength function spreading width as a quantitative criterion of quantum chaos

A new quantitative criterion of quantum chaoticity is discussed and applied to the quantum Henon-Heiles system. The quantum stationary bound or quasi-bound states are considered. It is shown that in this case a rather typical feature of the quantum Hamiltonian with high symmetry is the existence of the degenerate energy levels. The quantum chaoticity appears when introducing the perturbations which break the symmetries of the regular Hamiltonian and reduce the quantity of integrals of motion (good quantum numbers) in such a way that it becomes less than the number of the system degrees of freedom. The immediate and well-known consequence of such a symmetry breaking is the removal of the level degeneracies. This removal of degeneracies is the basic physical reason of the Winger level repulsion which up to now seems to be the only quantum signature of chaos. The conclusion is made that the suggested criterion of quantum chaoticity deduced from half-a-century experience of studying the compound nucleus properties works perfectly in application to Henon-Heiles problem which is one of the most typical objects of studying the transition from regularity to chaos. The most important consequence of this fact is the perspective to apply all the arsenal of theoretical methods of studying the compound nucleus accumulated in nuclear physics to the investigation of any quantum chaotic system in any field of physics