A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Signed zeros of Gaussian vector fields-density, correlation functions and curvature

We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and two-point functions. The zeros of a two-dimensional Gaussian vector field model the distribution of topological defects in the high-temperature phase of two-dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear in J. Phys.

Geometry of One-Dimensional Wave Propagation

We investigate the geometrical features of one-dimensional wave propagation, whose dynamics is described by the (2+1)-dimensional Lorentz group. We find many interesting geometrical ingredients such as spinorlike behavior of wave amplitudes, gauge transformations, Bloch-type equations, and Lorentz-group Berry phases. We also propose an optical experiment to verify these effects.Comment: RevTeX, 16 pages, 6 postscript figure

Electron--Vibron Interactions and Berry Phases in Charged Buckminsterfullerene: Part I

A simple model for electron-vibron interactions on charged buckminsterfullerene C$_{60}^{n-}$, $n=1,\ldots 5$, is solved both at weak and strong couplings. We consider a single $H_g$ vibrational multiplet interacting with $t_{1u}$ electrons. At strong coupling the semiclassical dynamical Jahn-Teller theory is valid. The Jahn-Teller distortions are unimodal for $n$=1,2,4,5 electrons, and bimodal for 3 electrons. The distortions are quantized as rigid body pseudo--rotators which are subject to geometrical Berry phases. These impose ground state degeneracies and dramatically change zero point energies. Exact diagonalization shows that the semiclassical level degeneracies and ordering survive well into the weak coupling regime. At weak coupling, we discover an enhancement factor of $5/2$ for the pair binding energies over their classical values. This has potentially important implications for superconductivity in fullerides, and demonstrates the shortcoming of Migdal--Eliashberg theory for molecular crystals.Comment: 29 pages (+7 figures, 3 available upon request), LATEX, report-number: BM515

Microscopic modelling of doped manganites

Colossal magneto-resistance manganites are characterised by a complex interplay of charge, spin, orbital and lattice degrees of freedom. Formulating microscopic models for these compounds aims at meeting to conflicting objectives: sufficient simplification without excessive restrictions on the phase space. We give a detailed introduction to the electronic structure of manganites and derive a microscopic model for their low energy physics. Focussing on short range electron-lattice and spin-orbital correlations we supplement the modelling with numerical simulations.Comment: 20 pages, 10 figs, accepted for publ. in New J. Phys., Focus issue on Orbital Physic

Acoustic Energy and Momentum in a Moving Medium

By exploiting the mathematical analogy between the propagation of sound in a non-homogeneous potential flow and the propagation of a scalar field in a background gravitational field, various wave ``energy'' and wave ``momentum'' conservation laws are established in a systematic manner. In particular the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed co- and contravariant energy-momentum tensor, while the exchange of relative energy between the wave and the mean flow mediated by the radiation stress tensor, first noted by Longuet-Higgins and Stewart in the context of ocean waves, appears as the covariant conservation of the doubly contravariant form of the same energy-momentum tensor.Comment: 25 Pages, Late

Born-Oppenheimer Approximation near Level Crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette

Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field

The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs heterostructures is studied in the case where the two-dimensional electron gas (2DEG) is subject to a strong magnetic field and a smooth random potential with correlation length Lambda and amplitude Delta. The electron wave functions are described in a quasiclassical picture using results of percolation theory for two-dimensional systems. In accordance with the experimental situation, Lambda is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to electrons occupying extended trajectories of fractal structure. Both piezoelectric and deformation potential interactions of surface acoustic phonons with electrons are considered and the corresponding interaction vertices are derived. These vertices are found to differ from those valid for three-dimensional bulk phonon systems with respect to the phonon wave vector dependence. We derive the appropriate dielectric function varepsilon(omega,q) to describe the effect of screening on the electron-phonon coupling. In the low temperature, high frequency regime T << Delta (omega_q*Lambda /v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q) are independent of temperature. The classical percolation indices give alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW occurs is found to be given by the scaling law |Delta \bar{\nu}| approx (omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon coupling and the screening due to the 2DEG on the filling factor leads to a double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad

Bandgaps in the propagation and scattering of surface water waves over cylindrical steps

Here we investigate the propagation and scattering of surface water waves by arrays of bottom-mounted cylindrical steps. Both periodic and random arrangements of the steps are considered. The wave transmission through the arrays is computed using the multiple scattering method based upon a recently derived formulation. For the periodic case, the results are compared to the band structure calculation. We demonstrate that complete band gaps can be obtained in such a system. Furthermore, we show that the randomization of the location of the steps can significantly reduce the transmission of water waves. Comparison with other systems is also discussed.Comment: 4 pages, 3 figure