Connected Straight Catheter Opened Stadium Billiard System Dynamical Behavior

The history of research of classical chaos , which we can trace back to the end of 19th century, began at H.Poincare's research of three-body movement. The research of classical chaos became mature since 8th decade last century. Meanwhile, the study of quantum chaos was mature too.2-D billiards which contain Sinai billiard, stadium billiard and so on are the models which often used to study quantum chaos. The opened 2-D stadium billiard model ,which was connected with two straight leads, were studied in the thesis.In chapter one and two, we introduce the background of classical chaos, quantum chaos and some research of stadium billiard model previously. In chapter three we investigate the classical scatter properties in the stadium billiard. By projecting particles from a guide at different angles, we can investigate the properties of its transmission and reflectibity and calculate its distribution. While the length of lines were gradually increased from zero, the system will change from a integrable one to a non-integrable one and the distribution of scattered angle also changes from regularity to chaos. Especially when system is an non integrable one, the distribution of scattered angles is an irregular fractal. We calculate the dimension of the fractal. Our result shown that the short periodic orbits greatly affect the structure of the fractal.Chapter four is about the calculation of eigenstate for the system. By using DEM (Decomposition Method), the eigenvalues and eigenfunctions of the system at different energy were numerically calculated. Especially for high energy, the quantum scar was shown obviously. The distributions of classical orbits on the opened billiard were studied and were contrast with the distributions of some eigenfunctions on the opened billiard. There are similar distributions for the two different case.Chapter five is about the scattering properties of the opened stadium billiard with two straight leads. We use the Green's theory to calculate the coefficient of the...