Vibrations and Berry Phases of Charged Buckminsterfullerene

A simple model of electron-vibron interactions in buckminsterfullerene ions is solved semiclassically. Electronic degeneracies of C$_{60}$$^{n-}$ induce dynamical Jahn-Teller distortions, which are unimodal for $n\!\ne\!3$ and bimodal for $n\!=\!3$. The quantization of motion along the Jahn-Teller manifold leads to a symmetric-top rotator Hamiltonian. I find Molecular Aharonov-Bohm effects where electronic Berry phases determine the vibrational spectra, zero point fluctuations, and electrons' pair binding energies. The latter are relevant to superconductivity in alkali-fullerenes.Comment: Latex 11 pages. IIT-00

Camera motion estimation through planar deformation determination

In this paper, we propose a global method for estimating the motion of a camera which films a static scene. Our approach is direct, fast and robust, and deals with adjacent frames of a sequence. It is based on a quadratic approximation of the deformation between two images, in the case of a scene with constant depth in the camera coordinate system. This condition is very restrictive but we show that provided translation and depth inverse variations are small enough, the error on optical flow involved by the approximation of depths by a constant is small. In this context, we propose a new model of camera motion, that allows to separate the image deformation in a similarity and a ``purely'' projective application, due to change of optical axis direction. This model leads to a quadratic approximation of image deformation that we estimate with an M-estimator; we can immediatly deduce camera motion parameters.Comment: 21 pages, version modifi\'ee accept\'e le 20 mars 200

Spin-squeezed Ground States in the Bilayer Quantum Hall Ferromagnet

A "squeezed-vacuum" state considered in quantum optics is shown to be realized in the ground-state wavefunction for the bilayer quantum Hall system at the total Landau level filling of $\nu=1/m$ (m: odd integer). This is derived in the boson approximation, where a particle-hole pair creation across the symmetric-antisymmetric gap, $\Delta_{SAS}$, is regarded as a boson. In terms of the pseudospin describing the layers, the state is a spin-squeezed state, where the degree of squeezing is controlled by the layer separation and $\Delta_{SAS}$. An exciton condensation, which amounts to a rotated spin-squeezed state, has a higher energy due to the degraded SU(2) symmetry for $\Delta_{SAS} \neq 0$.Comment: 4 pages, revtex, one figure, to appear in PRB Rapid Communicatio

Chaos and its quantization in dynamical Jahn-Teller systems

We investigate the $E_g \otimes e_g$ Jahn-Teller system for the purpose to reveal the nature of quantum chaos in crystals. This system simulates the interaction between the nuclear vibrational modes and the electronic motion in non-Kramers doublets for multiplets of transition-metal ions. Inclusion of the anharmonic potential due to the trigonal symmetry in crystals makes the system nonintegrable and chaotic. Besides the quantal analysis of the transition from Poisson to Wigner level statistics with increasing the strength of anharmonicity, we study the effect of chaos on the electronic orbital angular momentum and explore the magnetic $g$-factor as a function of the system's energy. The regular oscillation of this factor changes to a rapidly-decaying irregular oscillation by increasing the anharmonicity (chaoticity).Comment: 8 pages, 6 figure

Fermi Surface Measurements on the Low Carrier Density Ferromagnet Ca1-xLaxB6 and SrB6

Recently it has been discovered that weak ferromagnetism of a dilute 3D electron gas develops on the energy scale of the Fermi temperature in some of the hexaborides; that is, the Curie temperature approximately equals the Fermi temperature. We report the results of de Haas-van Alphen experiments on two concentrations of La-doped CaB6 as well as Ca-deficient Ca1-dB6 and Sr-deficient Sr1-dB6. The results show that a Fermi surface exists in each case and that there are significant electron-electron interactions in the low density electron gas.Comment: 4 pages, 5 figures, submitted to PR

Development of an approximate method for quantum optical models and their pseudo-Hermicity

An approximate method is suggested to obtain analytical expressions for the eigenvalues and eigenfunctions of the some quantum optical models. The method is based on the Lie-type transformation of the Hamiltonians. In a particular case it is demonstrated that $E\times \epsilon$ Jahn-Teller Hamiltonian can easily be solved within the framework of the suggested approximation. The method presented here is conceptually simple and can easily be extended to the other quantum optical models. We also show that for a purely imaginary coupling the $E\times \epsilon$ Hamiltonian becomes non-Hermitian but $P\sigma _{0}$-symmetric. Possible generalization of this approach is outlined.Comment: Paper prepared fo the "3rd International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics" June 2005 Istanbul. To be published in Czechoslovak Journal of Physic