The Cauchy Operator for Basic Hypergeometric Series

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator $T(bD_q)$. Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the $q$-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big $q$-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic

Extremely Correlated Fermi Liquid Description of Normal State ARPES in Cuprates

The normal state single particle spectral function of the high temperature superconducting cuprates, measured by the angle resolved photoelectron spectroscopy (ARPES), has been considered both anomalous and crucial to understand. Here we show that an unprecedentedly detailed description of the data is provided by a spectral function arising from the Extremely Correlated Fermi Liquid state of the t-J model proposed recently by Shastry. The description encompasses both laser and conventional synchrotron ARPES data on optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, and also conventional synchrotron ARPES data on the La$_{1.85}$Sr$_{0.15}$CuO$_4$ materials. {\em It fits all data sets with the same physical parameter values}, satisfies the particle sum rule and successfully addresses two widely discussed "kink" anomalies in the dispersion.Comment: Published version, 5 figs; published 29 July (2011

Phase sensitive detection of dipole radiation in a fiber-based high numerical aperture optical system

We theoretically study the problem of detecting dipole radiation in an optical system of high numerical aperture in which the detector is sensitive to \textit{field amplitude}. In particular, we model the phase sensitive detector as a single-mode cylindrical optical fiber. We find that the maximum in collection efficiency of the dipole radiation does not coincide with the optimum resolution for the light gathering instrument. The calculated results are important for analyzing fiber-based confocal microscope performance in fluorescence and spectroscopic studies of single molecules and/or quantum dots.Comment: 12 pages, 2 figure

Relations between Neutrino and Charged Fermion Masses

We find an intriguing relation between neutrino and charged fermion masses, $|m_{\nu_3^{}}^2- m_{\nu_1^{}}^2| : (m_{\nu_2^{}}^2- m_{\nu_1^{}}^2):: V_{tb}^4 m_\tau^2 m_b^2/m_t^2 : V_{cs}^4 m_\mu^2 m_s^2/m_c^2$. We further indicate this relation can be predicted by a left-right symmetric model.Comment: 4 pages, 1 figure. Model is slightly corrected. Title is changed. Journal versio

Super Mario's prison break -- a proposal of object-intelligent-feedback-based classical Zeno and anti-Zeno effects

Super Mario is imprisoned by a demon in a finite potential well. He can escape from the well with the help of a flight of magic stairs floating in the space. However, the hateful demon may occasionally check his status. At that time, he has to make a judgement of either jumping to the inside ground immediately in order to avoid the discovery of his escape intention, or speeding up his escape process. Therefore, if the demon checks him too frequently such that there is no probability for him to reach the top of the barrier, he will be always inside the well, then a classical Zeno effect occurs. On the other hand, if the time interval between two subsequent checks is large enough such that he has a higher probability of being beyond the demon's controllable range already, then the demon's check actually speeds up his escape and a classical anti-Zeno effect takes place.Comment: 4 pages, 4 figure