Structure and evolution of strange attractors in non-elastic triangular billiards

We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\lambda < 1$ smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter $\lambda$ is varied. For $\lambda$ in the interval (0, 1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of $\lambda$ the billiard dynamics gives rise to nonaccessible regions in phase space. For $\lambda$ close to 1, the attractor splits into three transitive components, the basins of attraction of which have fractal basin boundaries.Comment: 12 pages, 10 figures; submitted for publication. One video file available at http://sistemas.fciencias.unam.mx/~dsanders

Fixed points of dynamic processes of set-valued F-contractions and application to functional equations

The article is a continuation of the investigations concerning F-contractions which have been recently introduced in [Wardowski in Fixed Point Theory Appl. 2012:94,2012]. The authors extend the concept of F-contractive mappings to the case of nonlinear F-contractions and prove a fixed point theorem via the dynamic processes. The paper includes a non-trivial example which shows the motivation for such investigations. The work is summarized by the application of the introduced nonlinear F-contractions to functional equations

Butterfly Hysteresis and Slow Relaxation of the Magnetization in (Et4N)3Fe2F9: Manifestations of a Single-Molecule Magnet

(Et4N)3Fe2F9 exhibits a butterfly--shaped hysteresis below 5 K when the magnetic field is parallel to the threefold axis, in accordance with a very slow magnetization relaxation in the timescale of minutes. This is attributed to an energy barrier Delta=2.40 K resulting from the S=5 dimer ground state of [Fe2F9]^{3-} and a negative axial anisotropy. The relaxation partly occurs via thermally assisted quantum tunneling. These features of a single-molecule magnet are observable at temperatures comparable to the barrier height, due to an extremely inefficient energy exchange between the spin system and the phonons. The butterfly shape of the hysteresis arises from a phonon avalanche effect.Comment: 18 pages, 5 eps figures, latex (elsart

Chiral perturbation theory for lattice QCD including O(a^2)

The O(a^2) contributions to the chiral effective Lagrangian for lattice QCD with Wilson fermions are constructed. The results are generalized to partially quenched QCD with Wilson fermions as well as to the "mixed'' lattice theory with Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 3 pages, Lattice2003 (spectrum

Quantum tunneling in a three dimensional network of exchange coupled single-molecule magnets

A Mn4 single-molecule magnet (SMM) is used to show that quantum tunneling of magnetization (QTM) is not suppressed by moderate three dimensional exchange coupling between molecules. Instead, it leads to an exchange bias of the quantum resonances which allows precise measurements of the effective exchange coupling that is mainly due to weak intermolecular hydrogen bounds. The magnetization versus applied field was recorded on single crystals of [Mn4]2 using an array of micro-SQUIDs. The step fine structure was studied via minor hysteresis loops.Comment: 4 pages, 4 figure

Lattice Gauge Fixing as Quenching and the Violation of Spectral Positivity

Lattice Landau gauge and other related lattice gauge fixing schemes are known to violate spectral positivity. The most direct sign of the violation is the rise of the effective mass as a function of distance. The origin of this phenomenon lies in the quenched character of the auxiliary field $g$ used to implement lattice gauge fixing, and is similar to quenched QCD in this respect. This is best studied using the PJLZ formalism, leading to a class of covariant gauges similar to the one-parameter class of covariant gauges commonly used in continuum gauge theories. Soluble models are used to illustrate the origin of the violation of spectral positivity. The phase diagram of the lattice theory, as a function of the gauge coupling $\beta$ and the gauge-fixing parameter $\alpha$, is similar to that of the unquenched theory, a Higgs model of a type first studied by Fradkin and Shenker. The gluon propagator is interpreted as yielding bound states in the confined phase, and a mixture of fundamental particles in the Higgs phase, but lattice simulation shows the two phases are connected. Gauge field propagators from the simulation of an SU(2) lattice gauge theory on a $20^4$ lattice are well described by a quenched mass-mixing model. The mass of the lightest state, which we interpret as the gluon mass, appears to be independent of $\alpha$ for sufficiently large $\alpha$.Comment: 28 pages, 14 figures, RevTeX

Quasiparticle and Cooper Pair Tunneling in the Vortex State of Bi-2212

From measurements of the c-axis I-V characteristics of intrinsic Josephson junctions in Bi_2Sr_2CaCu_2O_{8+delta} (Bi-2212) mesas we obtain the field dependence (H || c) of the quasiparticle (QP) conductivity, sigma_q(H,T), and of the Josephson critical current density, J_c(H,T). The quasiparticle conductivity sigma_q(H) increases sharply with H and reaches a plateau at 0.05 T <H< 0.3 T. We explain such behavior by the dual effect of supercurrents around vortices. First, they enhance the QP DOS, leading to an increase of sigma_q with H at low H and, second, they enhance the scattering rate for specular tunneling as pancakes become disordered along the c-axis at higher H, leading to a plateau at moderate H.Comment: 4 pages, 4 figure