Eigenvalues and Eigenfunctions of a Stadium-Shaped Quantum Dot Subjected to a Perpendicular Magnetic Field

The eigenvalues and eigenfunctions of the stadium-shaped quantum dot subjected to a constant magnetic field in the perpendicular direction are computed by a simple and efficient method. With the magnetic field increasing, the nearest-neighour-energy-level-spacing distribution of the stadium-shaped quantum dot is found to transform gradually from the Wigner distribution to the Poisson distribution. The transition of the nearest-neighour-energy- level-spacing distribution indicates that system changes from quantum chaotic to regular. The variation of the spatial charge distribution indicates that the system varies from bulk Landau state to the edge state that mainly affects the transport properties of the stadium-shaped quantum dot. The change of the two dimensional charge distribution near the anticrossing point is also discussed.