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 spect rum of a two-dimensional (2D) hydrogenic impurity in a parabolic quant um wire in a magnetic field. The problem is mapped into the problem of interacting nonlinear harmonic oscillators. The evolution of the ener gy levels and level statistics from a 2D to a ID effective hydrogen at om is investigated in the quantum and clinically chaotic regimes. The ground-state energy reflects a delicate balance between a blueshift du e 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-know n problem of quantum chaos in a 3D hydrogen atom in a magnetic field i n a zero angular-momentum channel. The presence of a magnetic field in the wire breaks the scaling behavior inherent in the 3D hydrogen prob lem.