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 s ubjected to a constant magnetic field in the perpendicular direction a re 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 fi om t he 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 s patial charge distribution indicates that the system varies from bulk Landau state to the edge state that mainly affects the transport prope rties of the stadium-shaped quantum doe. The change of the two dimensi onal charge distribution near the anticrossing point is also discussed .