Transition from chaotic to regular behavior of electrons in a stadium-shaped quantum dot in a perpendicular magnetic field

The energy spectrum, wave functions, and field-induced currents in a two-dimensional isolated stadium-shaped dot are calculated in the presence of a perpendicular magnetic field. By means of the magnetic field one can explore the dynamics of this type of system, from quantum chaotic to regular behavior. The distribution of energy-level spacings is found to transform gradually from a Wigner (Gaussian orthogonal ensemble) distribution at zero field to a Poisson distribution as the magnetic field increases. The spatial distributions of the currents and charge densities are used in elucidating and visualizing the gradual formation of bulk Landau states and edge states at high magnetic fields.