Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy

The lattice Gel'fand-Dikii hierarchy was introduced by Nijhoff, Papageorgiou, Capel and Quispel in 1992 as the family of partial difference equations generalizing to higher rank the lattice Korteweg-de Vries systems, and includes in particular the lattice Boussinesq system. We present a Lagrangian for the generic member of the lattice Gel'fand-Dikii hierarchy, and show that it can be considered as a Lagrangian 2-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus the multiform structure proposed in arXiv:0903.4086v2 [nlin.SI] is extended to a multi-component system.Comment: 12 page

An integrable multicomponent quad equation and its Lagrangian formulation

We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an elementary plaquette in the 2-dimensional lattice. The system is multidimensionally consistent and a Lagrangian which respects this feature, i.e., which has the desirable closure property, is obtained.Comment: 10 page

Discrete-time Calogero-Moser system and Lagrangian 1-form structure

We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time as well as in continuous time, as a first example of a Lagrange 1-form structure in the sense of the recent paper [19]. The discrete-time model of the CM system was established some time ago arising as a pole-reduction of a semi-discrete version of the KP equation, and was shown to lead to an exactly integrable correspondence (multivalued map). In this paper we present the full KP solution based on the commutativity of the discrete-time flows in the two discrete KP variables. The compatibility of the corresponding Lax matrices is shown to lead directly to the relevant closure relation on the level of the Lagrangians. Performing successive continuum limits on both the level of the KP equation as well as of the CM system, we establish the proper Lagrange 1-form structure for the continuum case of the CM model. We use the example of the three-particle case to elucidate the implementation of the novel least-action principle, which was presented in [19], for the simpler case of Lagrange 1-forms.Comment: 37 pages, 8 figure

Ka-band (32-GHz) performance of 70-meter antennas in the Deep Space Network

Two models are provided of the Deep Space Network (DSN) 70 m antenna performance at Ka-band (32 GHz) and, for comparison purposes, one at X-band (8.4 GHz). The baseline 70 m model represents expected X-band and Ka-band performance at the end of the currently ongoing 64 m to 70 m mechanical upgrade. The improved 70 m model represents two sets of Ka-band performance estimates (the X-band performance will not change) based on two separately developed improvement schemes: the first scheme, a mechanical approach, reduces tolerances of the panels and their settings, the reflector structure and subreflector, and the pointing and tracking system. The second, an electronic/mechanical approach, uses an array feed scheme to compensate fo lack of antenna stiffness, and improves panel settings using microwave holographic measuring techniques. Results are preliminary, due to remaining technical and cost uncertainties. However, there do not appear to be any serious difficulties in upgrading the baseline DSN 70 m antenna network to operate efficiently in an improved configuration at 32 GHz (Ka-band). This upgrade can be achieved by a conventional mechanical upgrade or by a mechanical/electronic combination. An electronically compensated array feed system is technically feasible, although it needs to be modeled and demonstrated. Similarly, the mechanical upgrade requires the development and demonstration of panel actuators, sensors, and an optical surveying system

On the Lagrangian structure of 3D consistent systems of asymmetric quad-equations

Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to discrete integrable systems on Z^m. We establish Lagrangian structures and flip-invariance of the action functional for the class of discrete integrable systems involving equations for which some of the biquadratics are non-degenerate and some are degenerate. This class covers, among others, some of the above mentioned novel systems.Comment: 21 pp, pdfLaTe

Strong-field effects in the Rabi oscillations of the superconducting phase qubit

Rabi oscillations have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (qubits) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase qubit (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi frequency, and two-photon Rabi frequency are compared to measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.Comment: 4 pages, 4 figures, accepted for publication in IEEE Trans. Appl. Supercon

Comparison of coherence times in three dc SQUID phase qubits

We report measurements of spectroscopic linewidth and Rabi oscillations in three thin-film dc SQUID phase qubits. One device had a single-turn Al loop, the second had a 6-turn Nb loop, and the third was a first order gradiometer formed from 6-turn wound and counter-wound Nb coils to provide isolation from spatially uniform flux noise. In the 6 - 7.2 GHz range, the spectroscopic coherence times for the gradiometer varied from 4 ns to 8 ns, about the same as for the other devices (4 to 10 ns). The time constant for decay of Rabi oscillations was significantly longer in the single-turn Al device (20 to 30 ns) than either of the Nb devices (10 to 15 ns). These results imply that spatially uniform flux noise is not the main source of decoherence or inhomogenous broadening in these devices.Comment: 4 pages, 5 figures, accepted for publication in IEEE Trans. Appl. Supercon

Current-voltage characteristics of diluted Josephson-junction arrays: scaling behavior at current and percolation threshold

Dynamical simulations and scaling arguments are used to study the current-voltage (IV) characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where $p_c$ is the percolation threshold. For $p$ $>$ $p_c$ and zero temperature, the IV curves show power-law behavior above a disorder dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At $p_c$ and finite temperature $T$, the results show the scaling behavior of a T=0 superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to non-linearity appears at currents proportional to $$, with a thermal-correlation length exponent $\nu_T$ consistent with the corresponding value for the diluted XY model at $p_c$.Comment: Revtex, 9 postscript pages, to appear in Phys. Rev.