BEHAVIOR OF THE HAMILTONIAN EIGENSTATES AROUND THE AVOIDED LEVEL-CROSSING

We numerically show the changing of eigenstates of the Hamiltonian as a function of a control parameter governing the strength of a non-inte grable perturbation. The eigenstates change abruptly at avoided level crossing. After the avoided level crossing, they tend to restore their original form before the avoided level crossing, and exchange their d istribution, especially for those which can he treated as isolated two -body collisions. But in general, the eigenstates have some changings after the avoided crossing, and the symmetries of the system are broke n down locally at this kind of avoided level crossings.