Hydrogenic impurity in a parabolic quantum wire in a magnetic field: Quantum chaos and optical properties

We investigate electronic states and the far-infrared absorption spectrum of a two-dimensional (2D) hydrogenic impurity in a parabolic quantum wire in a magnetic field. The problem is mapped into the problem of interacting nonlinear harmonic oscillators. The evolution of the energy levels and level statistics from a 2D to a 1D effective hydrogen atom is investigated in the quantum and classically chaotic regimes. The ground-state energy reflects a delicate balance between a blueshift due to confinement and a redshift due to an increase in binding energy. In the absence of a magnetic field, the model reduces to the well-known problem of quantum chaos in a 3D hydrogen atom in a magnetic field in a zero angular-momentum channel. The presence of a magnetic field in the wire breaks the scaling behavior inherent in the 3D hydrogen problem.