Behavior of the Hamiltonian's Eigenstates Around the Avoided Level Crossing11The project supported by National Basic Research Project “Nonlinear Science” of China and National Natural Science Foundation of China

Abstract

We numerically show the changing of eigenstates of the Hamiltonian as a function of a control parameter governing the strength of a non-integrable 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 distribution, especially for those which can be 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 broken down locally at this kind of avoided level crossings.