41,701 research outputs found

    Scattering in PT\cal PT and RT\cal RT Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension

    Full text link
    We extend the generalize conservation law of light propagating in a one-dimensional PT\cal PT-symmetric system, i.e., T1=RLRR|T-1|=\sqrt{R_LR_R} for the transmittance TT and the reflectance RL,RR_{L,R} from the left and right, to a multimode waveguide with either PT\cal PT or RT\cal RT symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first time, how a multimode PT\cal PT-symmetric waveguide can be used to observe spontaneous symmetry breaking of the scattering matrix, which typically requires tuning the non-hermiticity of the system (i.e. the strength of gain and loss). Here the advantage of using a multimode waveguide is the elimination of tuning any system parameters: the transverse mode order mm plays the role of the symmetry breaking parameter, and one observes the symmetry breaking by simply performing scattering experiment in each waveguide channel at a single frequency and fixed strength of gain and loss.Comment: 8 pages, 6 figure

    [Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

    Full text link
    We study the Hopf algebra structure and the highest weight representation of a multiparameter version of Uqgl(2)U_{q}gl(2). The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal R{\cal R} matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic qq, the other for qq being a root of unity. When applying the representation theory to the multiparameter universal R{\cal R} matrix, the so called standard and nonstandard colored solutions R(μ,ν;μ,ν)R(\mu,\nu; {\mu}', {\nu}') of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

    VConv-DAE: Deep Volumetric Shape Learning Without Object Labels

    Full text link
    With the advent of affordable depth sensors, 3D capture becomes more and more ubiquitous and already has made its way into commercial products. Yet, capturing the geometry or complete shapes of everyday objects using scanning devices (e.g. Kinect) still comes with several challenges that result in noise or even incomplete shapes. Recent success in deep learning has shown how to learn complex shape distributions in a data-driven way from large scale 3D CAD Model collections and to utilize them for 3D processing on volumetric representations and thereby circumventing problems of topology and tessellation. Prior work has shown encouraging results on problems ranging from shape completion to recognition. We provide an analysis of such approaches and discover that training as well as the resulting representation are strongly and unnecessarily tied to the notion of object labels. Thus, we propose a full convolutional volumetric auto encoder that learns volumetric representation from noisy data by estimating the voxel occupancy grids. The proposed method outperforms prior work on challenging tasks like denoising and shape completion. We also show that the obtained deep embedding gives competitive performance when used for classification and promising results for shape interpolation

    Resistivity phase diagram of cuprates revisited

    Full text link
    The phase diagram of the cuprate superconductors has posed a formidable scientific challenge for more than three decades. This challenge is perhaps best exemplified by the need to understand the normal-state charge transport as the system evolves from Mott insulator to Fermi-liquid metal with doping. Here we report a detailed analysis of the temperature (T) and doping (p) dependence of the planar resistivity of simple-tetragonal HgBa2_2CuO4+δ_{4+\delta} (Hg1201), the single-CuO2_2-layer cuprate with the highest optimal TcT_c. The data allow us to test a recently proposed phenomenological model for the cuprate phase diagram that combines a universal transport scattering rate with spatially inhomogeneous (de)localization of the Mott-localized hole. We find that the model provides an excellent description of the data. We then extend this analysis to prior transport results for several other cuprates, including the Hall number in the overdoped part of the phase diagram, and find little compound-to-compound variation in (de)localization gap scale. The results point to a robust, universal structural origin of the inherent gap inhomogeneity that is unrelated to doping-related disorder. They are inconsistent with the notion that much of the phase diagram is controlled by a quantum critical point, and instead indicate that the unusual electronic properties exhibited by the cuprates are fundamentally related to strong nonlinearities associated with subtle nanoscale inhomogeneity.Comment: 22 pages, 5 figure
    corecore