Anomalous quantum chaotic behavior in nanoelectromechanical structures

TL;DR

This paper predicts that strong electron-phonon coupling in nanoelectromechanical structures induces anomalous quantum chaotic behavior, with spectral statistics shifting between GOE and GUE depending on the quantum dot's position.

Contribution

It introduces the concept of anomalous quantum chaos in nanoelectromechanical systems and links spectral statistics to the quantum dot's placement relative to symmetry axes.

Findings

Spectral statistics show GOE behavior when the quantum dot is on a symmetry axis.

Spectral statistics show GUE behavior when the quantum dot is off the symmetry axis.

Electron-phonon coupling causes the transition in spectral statistics.

Abstract

It is predicted that for sufficiently strong electron-phonon coupling an anomalous quantum chaotic behavior develops in certain types of suspended electro-mechanical nanostructures, here comprised by 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 electro-mechanic eigenenergies exhibit an anomalous behavior. If the center 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.