Cayley-Type Conditions for Billiards within kk Quadrics in RdR^d

The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by $k$ quadrics in $R^d$ and for the billiard ordered game within $k$ ellipsoids in $R^d$ are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in $R^d$ is obtained.Comment: 10 pages, some corractions are made in Section

Laboratory simulations of astrophysical jets and solar coronal loops: new results

An experimental program underway at Caltech has produced plasmas where the shape is neither fixed by the vacuum chamber nor fixed by an external coil set, but instead is determined by self-organization. The plasma dynamics is highly reproducible and so can be studied in considerable detail even though the morphology of the plasma is both complex and time-dependent. A surprising result has been the observation that self-collimating MHD-driven plasma jets are ubiquitous and play a fundamental role in the self-organization. The jets can be considered lab-scale simulations of astrophysical jets and in addition are intimately related to solar coronal loops. The jets are driven by the combination of the axial component of the J×B force and the axial pressure gradient resulting from the non-uniform pinch force associated with the flared axial current density. Behavior is consistent with a model showing that collimation results from axial non-uniformity of the jet velocity. In particular, flow stagnation in the jet frame compresses frozen-in azimuthal magnetic flux, squeezes together toroidal magnetic field lines, thereby amplifying the embedded toroidal magnetic field, enhancing the pinch force, and hence causing collimation of the jet

A few things I learnt from Jurgen Moser

A few remarks on integrable dynamical systems inspired by discussions with Jurgen Moser and by his work.Comment: An article for the special issue of "Regular and Chaotic Dynamics" dedicated to 80-th anniversary of Jurgen Mose

Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family

We show that the continuous limit of a wide natural class of the right-invariant discrete Lagrangian systems on the Virasoro group gives the family of integrable PDE's containing Camassa-Holm, Hunter-Saxton and Korteweg-de Vries equations. This family has been recently derived by Khesin and Misiolek as Euler equations on the Virasoro algebra for $H^1_{\alpha,\beta}$-metrics. Our result demonstrates a universal nature of these equations.Comment: 6 pages, no figures, AMS-LaTeX. Version 2: minor changes. Version 3: minor change

Contact complete integrability

Complete integrability in a symplectic setting means the existence of a Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we describe complete integrability in a contact set-up as a more subtle structure: a flag of two foliations, Legendrian and co-Legendrian, and a holonomy-invariant transverse measure of the former in the latter. This turns out to be equivalent to the existence of a canonical $\R\ltimes \R^{n-1}$ structure on the leaves of the co-Legendrian foliation. Further, the above structure implies the existence of $n$ contact fields preserving a special contact 1-form, thus providing the geometric framework and establishing equivalence with previously known definitions of contact integrability. We also show that contact completely integrable systems are solvable in quadratures. We present an example of contact complete integrability: the billiard system inside an ellipsoid in pseudo-Euclidean space, restricted to the space of oriented null geodesics. We describe a surprising acceleration mechanism for closed light-like billiard trajectories

Geodesic Flow on the Normal Congruence of a Minimal Surface

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ${\Bbb{R}}^3$ and relate it to the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure

Classical-to-stochastic Coulomb blockade cross-over in aluminum arsenide wires

We report low-temperature differential conductance measurements in aluminum arsenide cleaved-edge overgrown quantum wires in the pinch-off regime. At zero source-drain bias we observe Coulomb blockade conductance resonances that become vanishingly small as the temperature is lowered below $250 {\rm mK}$. We show that this behavior can be interpreted as a classical-to-stochastic Coulomb blockade cross-over in a series of asymmetric quantum dots, and offer a quantitative analysis of the temperature-dependence of the resonances lineshape. The conductance behavior at large source-drain bias is suggestive of the charge density wave conduction expected for a chain of quantum dots.Comment: version 2: new figure 4, refined discussio

The electronic structure of the high-symmetry perovskite iridate Ba2IrO4

We report angle-resolved photoemission (ARPES) measurements, density functional and model tight-binding calculations on Ba$_2$IrO$_4$ (Ba-214), an antiferromagnetic ($T_N=230$ K) insulator. Ba-214 does not exhibit the rotational distortion of the IrO$_6$ octahedra that is present in its sister compound Sr$_2$IrO$_4$ (Sr-214), and is therefore an attractive reference material to study the electronic structure of layered iridates. We find that the band structures of Ba-214 and Sr-214 are qualitatively similar, hinting at the predominant role of the spin-orbit interaction in these materials. Temperature-dependent ARPES data show that the energy gap persists well above $T_N$, and favour a Mott over a Slater scenario for this compound.Comment: 13 pages, 9 figure

Pseudo-boundaries in discontinuous 2-dimensional maps

It is known that Kolmogorov-Arnold-Moser boundaries appear in sufficiently smooth 2-dimensional area-preserving maps. When such boundaries are destroyed, they become pseudo-boundaries. We show that pseudo-boundaries can also be found in discontinuous maps. The origin of these pseudo-boundaries are groups of chains of islands which separate parts of the phase space and need to be crossed in order to move between the different sub-spaces. Trajectories, however, do not easily cross these chains, but tend to propagate along them. This type of behavior is demonstrated using a ``generalized'' Fermi map.Comment: 4 pages, 4 figures, Revtex, epsf, submitted to Physical Review E (as a brief report