  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 follow closely a
Wigner-Dyson distribution, which indicates the emergence of quantum signatures
of chaos due to the Coulomb interaction in an otherwise non-chaotic system. In
general, the Poincar\'e 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.
