Anomalous behavior of control pulses in presence of noise with singular autocorrelation

We report on the anomalous behavior of control pulses for spins under spin-spin relaxation and subject to classical noise with a singular autocorrelation function. This behavior is not detected for noise with analytic autocorrelation functions. The effect is manifest in the different scaling behavior of the deviation of a real pulse to the ideal, instantaneous one. While a standard pulse displays scaling $\propto \tau_\mathrm{p}^1$, a first-order refocusing pulse normally shows scaling $\propto \tau_\mathrm{p}^2$. But in presence of cusps in the noise autocorrelation the scaling $\propto \tau_\mathrm{p}^{3/2}$ occurs. Cusps in the autocorrelation are characteristic for fast fluctuations in the noise with a spectral density of Lorentzian shape. We prove that the anomalous exponent cannot be avoided; it represents a fundamental limit. On the one hand, this redefines the strategies one has to adopt to design refocusing pulses. On the other hand, the anomalous exponent, if found in experiment, provides important information on the noise properties.Comment: 11 pages, 8 figure

Average Degree in the Interval Graph of a Random Boolean Function

We consider an n-ary random Boolean function f such that for and study its geometric model, the so called interval graph. The interval graph of a Boolean function was introduced by Sapozhenko and has been used in construction of schemes realizing Boolean functions. Using this model, we estimate the number of maximal intervals intersecting a given maximal interval of a random Boolean function and prove that the asymptotic bound on the logarithm of the number is , where ?(n) ? 0 as

Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides

Recent neutron scattering studies revealed the three dimensional character of the magnetism in the iron pnictides and a strong anisotropy between the exchange perpendicular and parallel to the spin stripes. We extend studies of the J1-J2-Jc Heisenberg model with S = 1 using self-consistent spin-wave theory. A discussion of two scenarios for the instability of the columnar phase is provided. The relevance of a biquadratic exchange term between in-plane nearest neighbors is discussed. We introduce mean-field decouplings for biquadratic terms using the Dyson-Maleev and the Schwinger boson representation. Remarkably their respective mean-field theories do not lead to the same results, even at zero temperature. They are gauged in the N'eel phase in comparison to exact diagonalization and series expansion. The J1-J2-Jc model is analyzed under the influence of the biquadratic exchange Jbq and a detailed description of the staggered magnetization and of the magnetic excitations is given. The biquadratic exchange increases the renormalization of the in-plane exchange constants which enhances the anisotropy between the exchange parallel and perpendicular to the spin stripes. Applying the model to iron pnictides, it is possible to reproduce the spin-wave dispersion for CaFe2As2 in the direction perpendicular to the spin stripes and perpendicular to the planes. Discrepancies remain in the direction parallel to the spin stripes which can be resolved by passing from S = 1 to S = 2. In addition, results for the dynamical structure factor within the self-consistent spin-wave theory are provided.Comment: 18 pages, 12 figures. Updated version, several references adde

Three dimensional generalization of the J1J_1-J2J_2 Heisenberg model on a square lattice and role of the interlayer coupling JcJ_c

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg $J_1$-$J_2$ model has been actively discussed recently. However, recent neutron scattering data has shown that the pnictides have a relatively large spin wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the $J_1$-$J_2$-$J_c$ model that is the three dimensional generalization of the $J_1$-$J_2$ Heisenberg model for $S = 1/2$ and S = 1. Using self-consistent spin wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling $J_c$ suppresses the quantum fluctuations and strengthens the long range ordering. In the $J_1$-$J_2$-$J_c$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable upon increasing $J_1$. Either the magnetization or one of the spin wave velocities vanishes. For $S = 1/2$ renormalization due to quantum fluctuations is significantly stronger than for S=1, in particular close to the quantum phase transition. Our findings for the $J_1$-$J_2$-$J_c$ model are of general theoretical interest, however, the results show that it is unlikely that the model is relevant to undoped pnictides.Comment: 11 pages, 10 figures. Updated version, several references adde

Effects of a Short Term, Short Duration, High Intensity Exercise Intervention on Body Composition and Intra-Abdominal Fat

Short-term high intensity interval training (HIIT) has been shown to significantly improve body composition and intraabdominal fat stores. Studies have shown Tabata, a protocol using repeated rounds of 20-sec of work and 10-sec of rest, to be a valid protocol for HIIT. The purpose of this study was to determine the effectiveness of a short term, short duration, HIIT intervention using a Tabata protocol, on intra-abdominal fat and body composition. Fourteen participants performed eight rounds of Tabata body weight jump squats, at maximal effort each Monday, Wednesday, and Friday for three weeks. There were no significant differences in body composition. The amount of intra-abdominal fat did significantly decrease, p ≤ 0.05. The decrease in intra-abdominal fat suggest that short term, short duration, HIIT can reduce health risks associated with high amounts of intra-abdominal fat, such as cardiovascular disease and the metabolic syndrome. Future research should utilize lower impact body weight exercises, control for outside physical activity, and include a larger population size

SDSS1133: An Unusually Persistent Transient in a Nearby Dwarf Galaxy

While performing a survey to detect recoiling supermassive black holes, we have identified an unusual source having a projected offset of 800 pc from a nearby dwarf galaxy. The object, SDSS J113323.97+550415.8, exhibits broad emission lines and strong variability. While originally classified as a supernova (SN) because of its nondetection in 2005, we detect it in recent and past observations over 63 yr and find over a magnitude of rebrightening in the last 2 years. Using high-resolution adaptive optics observations, we constrain the source emission region to be <12 pc and find a disturbed host-galaxy morphology indicative of recent merger activity. Observations taken over more than a decade show narrow [O III] lines, constant ultraviolet emission, broad Balmer lines, a constant putative black hole mass over a decade of observations despite changes in the continuum, and optical emission-line diagnostics consistent with an active galactic nucleus (AGN). However, the optical spectra exhibit blueshifted absorption, and eventually narrow Fe II and [Ca II] emission, each of which is rarely found in AGN spectra. While this peculiar source displays many of the observational properties expected of a potential black hole recoil candidate, some of the properties could also be explained by a luminous blue variable star (LBV) erupting for decades since 1950, followed by a Type IIn SN in 2001. Interpreted as an LBV followed by a SN analogous to SN 2009ip, the multi-decade LBV eruptions would be the longest ever observed, and the broad Halpha emission would be the most luminous ever observed at late times (>10 yr), larger than that of unusually luminous supernovae such as SN 1988Z, suggesting one of the most extreme episodes of pre-SN mass loss ever discovered.Comment: Accepted for publication in MNRA