Anomalous quantum chaotic behaviour in suspended electromechanical nanostructures

It is predicted that for sufficiently strong electron-phonon coupling an anomalous quantum chaotic behaviour develops in certain types of suspended electromechanical nanostructures, here comprised of a thin cylindrical quantum dot (billiard) on a suspended rectangular dielectric plate. The deformation potential and piezoelectric interactions are considered. As a result of the electron-phonon coupling between the two systems the spectral statistics of the electromechanical eigenenergies exhibit an anomalous behaviour. If the centre of the quantum dot is located at one of the symmetry axes of the rectangular plate, the energy level distributions correspond to the Gaussian orthogonal ensemble (GOE), otherwise they belong to the Gaussian unitary ensemble (GUE), even though the system is time-reversal invariant. (letter to the editor)