Interaction-induced chaos in a two-electron quantum dot system

A quasi-one-dimensional quantum dot containing two interacting electrons is analyzed in search of signatures of chaos. The two-electron energy spectrum is obtained by diagonalization of the Hamiltonian including the exact Coulomb interaction. We find that the level-spacing fluctuations closely follow a Wigner-Dyson distribution, which indicates the emergence of quantum signatures of chaos due to the Coulomb interaction in an otherwise nonchaotic system. In general, the Poincaré maps of a classical analog of this quantum-mechanical problem can exhibit a mixed classical dynamics. However, for the range of energies involved in the present system, the dynamics is strongly chaotic, aside from small regular regions. The system we study models a realistic semiconductor nanostructure, with electronic parameters typical of gallium arsenide.