Quantum Corral Simulations And Calculations

With the development of new science and micro-electronics techniques, the traditional electron device can be made more and more smaller, even into the micro-cosmic field. The quantum effect generally stands out in such circumstance and can not be ignored. Sometimes this problem is not an important embarrassment which the manufacturer should over come but a interest research domain. In May of 1993, the Crommie and his group use STM equipment fix several iron atomics on the Cu (III) surface with help of liquid nitrogen. These iron atomics get together in a circle which made it like a barrier, and then the scientist found the visible diffraction design in it which made by the electron. This system is called quantum corral because the electron was confined in a tiny barrier construct by the inner iron's electrons. It is a forcefully evidence which can prove the micro-article's fluctuate property.In theory, we can use a quantum billiard system to simulate .quantum corrals and the distribution of wave function can be regarded as the distribution of electron in quantum corrals. In this paper, the Boundary-Integral Method (short for BIM), which is a powerful method for solve the eigen problem of quantum billiard system, is adopted and some improvements were introduced to enhance the numerical efficiency and accuracyn. By using new defined quantization measure for BIM, eigen-energies can be determined accurately and quickly. In this paper, a simple and efficient definition, correlation function about wave function, is introduced to determine the degenerate degree of eigen-states. These new improvements can provide a new accesses for the future work in this field.By use the new quantization measure for BIM, the writer simulate two kinds of billiards system: the Sinai billiard and the 1/4 Sinai billiard. The past work believed that both of the Sinai billiard and the 1/4 Sinai billiard have the same physics property. But our result suggest, there are existed some eigen-states in the Sinai billiard system which are not eigen-states in the 1/4 Sinai billiard. The set of all eigen-states of 1/4 Sinai billiard is only the subset of Sinai billiard. The reason should be the difference of spatial symmetry between two systems. that is to say, we can't simply regard the 1/4 Sinai billiard as the 1/4 part cutted from Sinai billiard. In addition, the write find that the Sinai billiard's wave function of high eigen-state is more complex than the 1/4 Sinai billiard.In the 4th sector of this paper, the author use BIM to calculate the electron-wave distribution respectively in circle quantum barrier and ellipse quantum corral, the numerical result matches well with the published experimental result. But the result of simulation in the ellipse quantum corral with a small circle wall on its right focus point is not the expected one of published experiments. Maybe it is caused by using a small circle wall to approximate a atom at the focus, the approximate is rough. In the following, we will replace the small circle wall with a circle finite stepped potential, we expect to find the atom's"quantum ghost"at another focus, the phenomena has been found in published experiment.