Hyperspherical theory of anisotropic exciton

A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the perturbation theory. The binding energies, wave functions and oscillator strengths of elongated as well as flattened excitons are obtained numerically. It is shown that with an increase of the anisotropy degree the oscillator strengths are markedly redistributed between optically active and formerly inactive states, making the latter optically active. An approximate analytical solution of the anisotropic exciton problem taking into account the angular momentum conserving terms is obtained. This solution gives the binding energies of moderately anisotropic exciton with a good accuracy and provides a useful qualitative description of the energy level evolution.Comment: 23 pages, 8 figure

Deformed Fermi Surface Theory of Magneto-Acoustic Anomaly in Modulated Quantum Hall Systems Near /nu=1/2/nu=1/2

We introduce a new generic model of a deformed Composite Fermion-Fermi Surface (CF-FS) for the Fractional Quantum Hall Effect near $/nu=1/2$ in the presence of a periodic density modulation. Our model permits us to explain recent Surface Acoustic Wave observations of anisotropic anomalies [1,2] in sound velocity and attenuation- appearance of peaks and anisotropy - which originate from contributions to the conductivity tensor due to regions of the CF-FS which are flattened by the applied modulation. The calculated magnetic field and wave vector dependence of the CF conductivity,velocity shift and attenuation agree with experiments.Comment: Revised manuscript (cond-mat/9807044) 23 September 1998; 10 page

Strong contraction of the representations of the three dimensional Lie algebras

For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof

Quantum Versus Mean Field Behavior of Normal Modes of a Bose-Einstein Condensate in a Magnetic Trap

Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles shows the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode and N. The corresponding time values have been derived analytically under certain approximation and numerically for the parabolic atomic trap. The revival of the mode at time of several seconds, as a direct evidence of the effect, can occur, if the normal component is significantly suppressed. We also discuss alternative means to verify the proposed mechanism.Comment: minor corrections are introduced into the tex