We prove a tropical mirror symmetry theorem for descendant Gromov-Witten invariants of the elliptic curve, generalizing Hurwitz numbers Theorem 2.20 in [B\"ohm J., Bringmann K., Buchholz A., Markwig H., J. Reine Angew. Math. 732 (2017), 211-246, arXiv:1309.5893]. For case version holds on fine level and easily implies equality generating series curve to Feynman integrals. To curves, we investig...

Let $\Theta$ be the Wigner time reversal operator for spin half and let $\phi$ a Weyl spinor. Then, left-transforming $\phi$, construct $\zeta_\lambda \Theta \phi^\ast$ yields right-transforming If instead, is spinor, then $\zeta _\rho results in spinor ($\zeta_{\lambda,\rho}$ are phase factors). This allows us to introduce two sets of four-component spinors. Setting $\zeta_\lambda$ $\zeta_\rho...

We demonstrate a new method to generate second-harmonic Talbot effect through degenerate Cherenkov radiation in one-dimension anomalous-dispersion-like nonlinear photonic crystals. In anomalous-dispersion-like medium, the degenerated nonlinear Cherenkov radiation can be achieved and is parallel to domain walls, of which the intensity is adjusted by the second-order nonlinear coefficient. In thi...