Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians

The quartic H\'enon-Heiles Hamiltonian $H = (P_1^2+P_2^2)/2+(\Omega_1 Q_1^2+\Omega_2 Q_2^2)/2 +C Q_1^4+ B Q_1^2 Q_2^2 + A Q_2^4 +(1/2)(\alpha/Q_1^2+\beta/Q_2^2) - \gamma Q_1$ passes the Painlev\'e test for only four sets of values of the constants. Only one of these, identical to the traveling wave reduction of the Manakov system, has been explicitly integrated (Wojciechowski, 1985), while the three others are not yet integrated in the generic case $(\alpha,\beta,\gamma)\not=(0,0,0)$. We integrate them by building a birational transformation to two fourth order first degree equations in the classification (Cosgrove, 2000) of such polynomial equations which possess the Painlev\'e property. This transformation involves the stationary reduction of various partial differential equations (PDEs). The result is the same as for the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases, a general solution which is meromorphic and hyperelliptic with genus two. As a consequence, no additional autonomous term can be added to either the cubic or the quartic Hamiltonians without destroying the Painlev\'e integrability (completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200

Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy

We use cathodoluminescence imaging spectroscopy to excite surface plasmon polaritons and measure their decay length on single crystal and polycrystalline gold surfaces. The surface plasmon polaritons are excited on the gold surface by a nanoscale focused electron beam and are coupled into free space radiation by gratings fabricated into the surface. By scanning the electron beam on a line perpendicular to the gratings, the propagation length is determined. Data for single-crystal gold are in agreement with calculations based on dielectric constants. For polycrystalline films, grain boundary scattering is identified as additional loss mechanism, with a scattering coefficient SG=0.2%

On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian

A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.Comment: 12 pages, 3 figures, NATO ARW, 15-19 september 2002, Elb

Float zone experiments in space

The molten zone/freezing crystal interface system and all the mechanisms were examined. If Marangoni convection produces oscillatory flows in the float zone of semiconductor materials, such as silicon, then it is unlikely that superior quality crystals can be grown in space using this process. The major goals were: (1) to determine the conditions for the onset of Marangoni flows in molten tin, a model system for low Prandtl number molten semiconductor materials; (2) to determine whether the flows can be suppressed by a thin oxide layer; and (3) based on experimental and mathematical analysis, to predict whether oscillatory flows will occur in the float zone silicon geometry in space, and if so, could it be suppressed by thin oxide or nitride films. Techniques were developed to analyze molten tin surfaces in a UHV system in a disk float zone geometry to minimize buoyancy flows. The critical Marangoni number for onset of oscillatory flows was determined to be greater than 4300 on atomically clean molten tin surfaces

High quality ultrafast transmission electron microscopy using resonant microwave cavities

Ultrashort, low-emittance electron pulses can be created at a high repetition rate by using a TM$_{110}$ deflection cavity to sweep a continuous beam across an aperture. These pulses can be used for time-resolved electron microscopy with atomic spatial and temporal resolution at relatively large average currents. In order to demonstrate this, a cavity has been inserted in a transmission electron microscope, and picosecond pulses have been created. No significant increase of either emittance or energy spread has been measured for these pulses. At a peak current of $814\pm2$ pA, the root-mean-square transverse normalized emittance of the electron pulses is $\varepsilon_{n,x}=(2.7\pm0.1)\cdot 10^{-12}$ m rad in the direction parallel to the streak of the cavity, and $\varepsilon_{n,y}=(2.5\pm0.1)\cdot 10^{-12}$ m rad in the perpendicular direction for pulses with a pulse length of 1.1-1.3 ps. Under the same conditions, the emittance of the continuous beam is $\varepsilon_{n,x}=\varepsilon_{n,y}=(2.5\pm0.1)\cdot 10^{-12}$ m rad. Furthermore, for both the pulsed and the continuous beam a full width at half maximum energy spread of $0.95\pm0.05$ eV has been measured

Boundary theories of critical matchgate tensor networks

Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states