Connected Straight Catheter Opened Stadium Billiard System Dynamical Behavior

In the eighties of last century, it is mature in researching classical system chaos, also more and more studies and articles have been done in quantum chaos. The kicked rotor is the first model, and the billiard is another better researched model. The billiard describes that a particle moves in a restricted boundary. These days, the researches of classical and quantum chaos in the billiard are all mature, including the research of the scars of periodic orbits, the transmission of quantum scattering, and the calculation of eigenstates in quantum billiard systems. Most of Researched models are two freedoms conservative Hamilton systems. Furthermore, the majority is non-integrabel except that the minority is integrabel. The integrabel systems have regular actions, while non-integrabel systems take on chaos actions.This thesis investigates the dynamics actions of the 2-D stadium billiard system with two straight leads. In the classical system, an open stadium billiard system is a hard chaos system, and the particle moves irregularly in the cavity. While in the quantum billiard system, open stadium billiard system transits from near-integrable to non-integrable with the variety of the parameter because of quantum effect. Quantum effects can lead to that a near-integrable system presents the actions of the whole-integrable system.The first part of the thesis states the static eigen actions of the system. By using DEM(Decomposition Method),we calculated the eigenvalues and eigenstates of the system, and find the rule of the distribution of energy level spacings. Furthermore, eigenvalues of system have a trend to stability with the length of the leads added. We also summarize that the distributions of energy level spacings of system transfer from Possion to GUE with the length of straight parts added. In this thesis, we investigate the billiard system with a symmetrical straight leads in order to study conveniently and provide bases for the second part of the thesis. Through studying the eigen actions of the system, we comprehend the static actions of this kind of system elementarily.The second part of the thesis states the quantum scattering properties of the open stadium billiard with two straight leads. Through calculating the S matrix of the system, we discuss the quantum scattering and transmitting properties of our system. Moreover, we consider wigner delay times and the Landauer-Buttiker conductance for our system, and also probe the effects of the system energy spectrum on scattering properties. At last we investigate how lead placement and the shape and size of the cavity affect these conductance and time delay of the waveguide. From above, we understand this kind of waveguide more profoundly.With the development of new technology, especially with the rapid development of technology of machining micro-electronics, traditional electron-apparatus has expanded to microcosmic scale(micron,nano), and quantum effect appears little by little. In this study fields, it is not only a question to make subminiature apparatus, but also main purposes to study new-concept quantum apparatus. This thesis mainly investigates eigen actions of a billiard system with two straight leads in microcosmic scale, and the billiard system is widely researched in the quantum non-liner field in the 1980s last century. There are many works in the open billiard systems. It will be helpful to understand physical characteristic of this kind of quantum billiards and it is of great importance to improve the capacity of these apparatus and characteristic.In this thesis we mainly discuss a 2-D stadium billiard with two straight leads. Eigenvalues and eigenstates were calculated by DEM and spectrums of the nearest neighbor were investigated. Through these work, we understand static action of the system to some extent, which will benefit to study microcosmic dynamical actions more deeply. -By researching the quantum transmission of our system, we comprehend the waveguide more profoundly. It is of great significance to do researching in static actions and qua...