On theK-property of some planar hyperbolic billiards

TheK-property is demonstrated for a class of planar billiards satisfying Wojtkowski's principles. Their boundary may consist of convex-scattering, concave and linear pieces. Earlier Wojtkowski showed that these billards had non-zero Lyapunov exponents.     

On the equilibria of finely discretized curves and surfaces

Our goal is to identify the type and number of static equilibrium points of solids arising from fine, equidistant n-discretizations of smooth, convex surfaces. We assume uniform gravity and a frictionless, horizontal, planar support. We show that as n approaches infinity these numbers fluctuate around specific values which we call the imaginary equilibrium indices associated with the approximated smooth surface. We derive simple formulae for these numbers in terms of the principal curvatures and the radial distances of the equilibrium points of the solid from its center of gravity. Our results are illustrated on a discretized ellipsoid and match well the observations on natural pebble surfaces.     

Spacetime Interpretation of Torsion in Prismatic Bodies

A non-linear theory for the plastic deformation of prismatic bodies is constructed which interpolates between Prandtl??s linear soap-film approximation and Nádai??s sand-pile model. Geometrically Prandtl??s soap film and Nádai??s wavefront are unified into a single smooth surface of constant mean curvature in three-dimensional Minkowski spacetime.     

Baryon-number-induced Chern-Simons couplings of vector and axial-vector mesons in holographic QCD

We show that holographic models of QCD predict the presence of a Chern-Simons coupling between vector and axial-vector mesons at finite baryon density. In the Anti de Sitter/Conformal Field Theory dictionary, the coefficient of this coupling is proportional to the baryon number density and is fixed uniquely in the five-dimensional holographic dual by anomalies in the flavor currents. For the lightest mesons, the coupling mixes transverse rho and a1 polarization states. At sufficiently large baryon number densities, it produces an instability, which causes the rho and a1 mesons to condense in a state breaking both rotational and translational invariance.     

Collective cooling and self-organization of atoms in a cavity

We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.     

Solution Sensitivity of Variational Inequalities

Our goal is to show that the continuity of the solutions of monotone variational inequalities with respect to perturbations is independent from the geometrical properties of reflexive Banach spaces.     

Wave packet realization of lightlike states

We construct a new realization of lightlike particle states. The realization considered corresponds to objects which form partially localized wave packets in the space dimensions transverse to the direction of the lightlike momentum. The states of the transverse motion are classified by the representations of an algebraSU(1, 1) constructed of the generators of the conformal group. It is conjectured that this realization is suitable for the formulation of the parton-model of hadrons.Research supported in part by the U.S. Atomic Energy Commission under Contract No. AT(30-1)-4076.     

Orthogonal transformations for feature extraction in chemical pattern recognition

A crucial point in pattern recognition methods is the extraction of features to determine the pattern vectors. Orthogonal transformations, e.g., Fourier, Walsh and Haar, are investigated as preprocessing methods for feature extraction. The theoretical considerations and conclusions are compared with computational results obtained by applying different pattern recognition methods to two different but similar collections of low-resolution mass spectra.     

Entanglement assisted fast reordering of atoms in an optical lattice within a cavity at T = 0

Laser-illuminated atoms in an optical resonator exhibit a phase transition between the homogenous distribution and two possible ordered configurations in the optical lattice formed by the cavity and pump fields. At zero temperature, atom-field entanglement plays a crucial role in the spatial reordering of the atoms from a homogeneous towards the two ordered states, where all atoms occupy either only even or only odd lattice sites. Concurrent with the buildup of atom-field entanglement, the homogeneous atomic cloud evolves immediately into the superposition of the two stable patterns entangled with opposite cavity field amplitudes. This possibility is absent in a factorized (classical) treatment of atoms and field and should be generic for spontaneous symmetry breaking in quantum phase transitions in optical potentials.