10,060 research outputs found

    Electric field distortions in structures of the twist bend nematic (NTB) phase of a bent-core liquid crystal

    Full text link
    Dielectric spectroscopy of a twist bend nematic phase of an achiral bent core liquid crystalline compound under DC bias is used to investigate its response to electric field. Two collective relaxation processes are revealed, these are assigned to distortions of helicoidal structure by the external bias field. Frequency of the mode depends primarily on the helicoidal angle and has anomalous, softening- like behaviour at the nematic to the twist bend nematic transition. A coupling of dielectric anisotropy with electric field gives rise to a new equilibrium periodic structure in the time scale involved. The modulus of the wave vector gradually vanishes on increasing the bias field (except for the initial behaviour, which is just the opposite). Transition from the twist bend to the splay bend structure is clearly observed by a sudden drop in the frequency of this mode, which decreases almost linearly with increasing field. Results agree with predictions from current models for the periodically distorted a twist bend nematic phase.Comment: 14 PAGES, 7 FIGURES, submitted to Physical Review Letter

    Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors

    Get PDF
    We provide an alternative proof of Wallman's [Quantum 2, 47 (2018)] and Proctor's [Phys. Rev. Lett. 119, 130502 (2017)] bounds on the effect of gate-dependent noise on randomized benchmarking (RB). Our primary insight is that a RB sequence is a convolution amenable to Fourier space analysis, and we adopt the mathematical framework of Fourier transforms of matrix-valued functions on groups established in recent work from Gowers and Hatami [Sbornik: Mathematics 208, 1784 (2017)]. We show explicitly that as long as our faulty gate-set is close to some representation of the Clifford group, an RB sequence is described by the exponential decay of a process that has exactly two eigenvalues close to one and the rest close to zero. This framework also allows us to construct a gauge in which the average gate-set error is a depolarizing channel parameterized by the RB decay rates, as well as a gauge which maximizes the fidelity with respect to the ideal gate-set

    The Predictive Validity of Mathematics Curriculum-Based Measurement on Smarter Balanced Assessment Consortium Mathematics Scores

    Full text link
    The purpose of this study was to examine the predicative validity of computation curriculumbased measurement (CBM) on mathematics Smarter Balanced Assessment Consortium scores (SBAC). This study looked at one cohort consisting of 2,741 participants in third, fourth, and fifth grade during the 2017-2018 school year in one school district in Oregon. This study used a hierarchical multiple regression to examine the relationship between CBM and mathematics SBAC. Additionally, this study looked at the extent to which gender, ethnicity, special education status (SPED) and English language learner (ELL) status interacted with CBM scores to predict end-of-year mathematics SBAC scores. The findings of this study indicate that CBM scores predict math SBAC scores in third, fourth, and fifth grade to a modest extent. The findings also indicate that taken together, CBM scores, gender, ethnicity, special education status, and English language learner status predict math SBAC scores to a moderate extent
    • 

    corecore