Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials

A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coefficients of certain bivariate dual-Hahn polynomials. For a specific choice of the parameters, perfect state transfer and fractional revival are shown to take place.Comment: 14pages, 3 figure

Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems

Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)-dimensional case, the corresponding system can be extended to 2x2 matrix form. The factorization theorem of the Christoffel kernel for skew orthogonal polynomials in random matrix theory is presented as a by-product of these transformations

Sub-Arcsecond Near-Infrared Images of Massive Star Formation Region NGC 6334 V

We present high spatial resolution (0\farcs3) polarimetric images in the $H$ and $K$ bands and direct images in the $L'$ and $M'$ bands of the NGC 6334 V infrared nebulae. The images show complex structures including the multi-shells and various knots in the nebulae. The appearances and colors of the eastern and western nebulae differ considerably. Our polarization images also show differences between the illuminating sources of the nebulae: the eastern nebula is illuminated by a deeply embedded mid-infrared source, KDJ 4, and the western nebula by our newly detected near-infrared source, WN-A1. The degree of polarization of the nebulae is very large, up to 70% at $K$ and 60% at $H$, which is consistent with a single scattering of near-infrared radiation from each source at the walls of the mass outflows