2005/10/14 by André Gusso, Andre Gusso, M. G. E. da Luz +2
Mathematics · Physics and Astronomy · #Classical mechanics #Condensed matter physics #Eigenvalues and eigenvectors #Gaussian #Hamiltonian (control theory) #Mathematics #Nonlinear Photonic Systems #Phonon #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dot #Quantum dynamics #Quantum mechanics #Random matrix #Statistical physics #cond-mat.mes-hall #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevb.73.035436
14 pages, two columns
arxiv created 2005/10/14 · openalex publication_date 2006/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate's surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian orthogonal ensemble or the Gaussian unitary ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.