Soft-pulse dynamical decoupling in a cavity

Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails pumping energy into the system, which can be especially dangerous when it has sharp spectral features like a cavity mode close to resonance. In this work we show that such an effect can be avoided with properly constructed refocusing sequences. To this end we construct the average Hamiltonian expansion for the system evolution operator associated with a single ``soft'' pi-pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be turned to zero by shaping. We express the effective Hamiltonians for several pulse sequences in terms of these parameters, and use the results to analyze the structure of error operators for controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly-suppressed oscillator heating.Comment: 9pages, 5eps figure

Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface.Comment: 56 pages, 4 eps figures, LaTeX, uses eps

A proof of factorization for B -> D pi

We prove that the matrix elements of four fermion operators mediating the decay B^0 -> D^+ \pi^- and B^- -> D^0 \pi^- factor into the product of a form factor describing the B -> D transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in alpha_s, up to corrections suppressed by factors of 1/mb, 1/mc, and 1/E_pi. It is not necessary to assume that the pion state is dominated by the q-qbar Fock state.Comment: 4 pages, 3 figs, PRL versio

Microscopic calculation of the phonon dynamics of Sr2_{2}RuO4_{4} compared with La2_{2}CuO4_{4}

The phonon dynamics of the low-temperature superconductor Sr$_{2}$RuO$_{4}$ is calculated quantitatively in linear response theory and compared with the structurally isomorphic high-temperature superconductor La$_{2}$CuO$_{4}$. Our calculation corrects for a typical deficit of LDA-based calculations which always predict a too large electronic $k_{z}$-dispersion insufficient to describe the c-axis response in the real materials. With a more realistic computation of the electronic band structure the frequency and wavevector dependent irreducible polarization part of the density response function is determined and used for adiabatic and nonadiabatic phonon calculations. Our analysis for Sr$_{2}$RuO$_{4}$ reveals important differences from the lattice dynamics of $p$- and $n$-doped cuprates. Consistent with experimental evidence from inelastic neutron scattering the anomalous doping related softening of the strongly coupling high-frequency oxygen bond-stretching modes (OBSM) which is generic for the cuprate superconductors is largely suppressed or completely absent, respectively, depending on the actual value of the on-site Coulomb repulsion of the Ru4d orbitals. Also the presence of a characteristic $\Lambda_{1}$-mode with a very steep dispersion coupling strongly with the electrons is missing in Sr$_{2}$RuO$_{4}$. Moreover, we evaluate the possibility of a phonon-plasmon scenario for Sr$_{2}$RuO$_{4}$ which has been shown recently to be realistic for La$_{2}$CuO$_{4}$. In contrast to La$_{2}$CuO$_{4}$ in Sr$_{2}$RuO$_{4}$ the very low lying plasmons are overdamped along the c-axis.Comment: 30 pages, 16 figures, 4 tables, 33 reference

Nonsequential Double Recombination in Intense Laser Fields

A second plateau in the harmonic spectra of laser-driven two-electron atoms is observed both in the numerical solution of a low-dimensional model helium atom and using an extended strong field approximation. It is shown that the harmonics well beyond the usual cut-off are due to the simultaneous recombination of the two electrons, which were emitted during different, previous half-cycles. The new cut-off is explained in terms of classical trajectories. Classical predictions and the time-frequency analysis of the ab initio quantum results are in excellent agreement. The mechanism corresponds to the inverse single photon double ionization process in the presence of a (low frequency) laser field.Comment: 4 pages, RevTeX, v2 with an extended strong field approximation treatment of the process; instead, v1 describes an attosecond control scheme to enhance the proces

Spectral estimates of solar radiation intercepted by corn canopies

Reflectance factor data were acquired with a Landsat band radiometer throughout two growing seasons for corn (Zea mays L.) canopies differing in planting dates, populations, and soil types. Agronomic data collected included leaf area index (LAI), biomass, development stage, and final grain yields. The spectral variable, greenness, was associated with 78 percent of the variation in LAI over all treatments. Single observations of LAI or greenness have limited value in predicting corn yields. The proportions of solar radiation intercepted (SRI) by these canopies were estimated using either measured LAI or greenness. Both SRI estimates, when accumulated over the growing season, accounted for approximately 65 percent of the variation in yields. Models which simulated the daily effects of weather and intercepted solar radiation on growth had the highest correlations to grain yields. This concept of estimating intercepted solar radiation using spectral data represents a viable approach for merging spectral and meteorological data for crop yield models

Runtime Verification of Temporal Properties over Out-of-order Data Streams

We present a monitoring approach for verifying systems at runtime. Our approach targets systems whose components communicate with the monitors over unreliable channels, where messages can be delayed or lost. In contrast to prior works, whose property specification languages are limited to propositional temporal logics, our approach handles an extension of the real-time logic MTL with freeze quantifiers for reasoning about data values. We present its underlying theory based on a new three-valued semantics that is well suited to soundly and completely reason online about event streams in the presence of message delay or loss. We also evaluate our approach experimentally. Our prototype implementation processes hundreds of events per second in settings where messages are received out of order.Comment: long version of the CAV 2017 pape

Phase Transitions in a Two-Component Site-Bond Percolation Model

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.Comment: RevTeX, 5 pages, 5 eps-figure