Spectral statistics of correlated electrons in a square-well quantum dot

The nature of correlated electrons confined in two dimensions is analyzed using the spectral statistics of three electrons confined in a square-well quantum dot. When in a small quantum dot, the spectral statistics of electrons are similar to those of Poisson distribution. As the quantum dot becomes larger, the spectral statistics approach those of Gaussian orthogonal ensemble, suggesting quantum chaotic behavior of electrons caused by electron-electron interaction. In a very large quantum dot, phonon modes from the Wigner-lattice ground state have additional effects on the spectral statistics.