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

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ 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 $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

Black Holes, Entropy Bound and Causality Violation

The gravity/gauge theory duality has provided us a way of studying QCD at short distances from straightforward calculations in classical general relativity. Among numerous results obtained so far, one of the most striking is the universality of the ratio of the shear viscosity to the entropy density. For all gauge theories with Einstein gravity dual, this ratio is \eta/s=1/4\pi. However, in general higher-curvature gravity theories, including two concrete models under discussion - the Gauss-Bonnet gravity and the (Riemann)^2 gravity - the ratio \eta/s can be smaller than 1/4\pi (thus violating the conjecture bound), equal to 1/4\pi or even larger than 1/4\pi. As we probe spacetime at shorter distances, there arises an internal inconsistency in the theory, such as a violation of microcausality, which is correlated with a classical limit on black hole entropy.Comment: 8 pages, no figures; Invited contribution to appear in the Proceedings of the 75 Years since Solvay, Singapore, Nov 2008, (World Scientific, Singapore, 2009

Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model

Integrable Kondo impurities in two cases of the one-dimensional $t-J$ model are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse scattering method. The boundary $K$ matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.Comment: 14 pages, RevTe

Pump-induced Exceptional Points in Lasers

We demonstrate that the above-threshold behavior of a laser can be strongly affected by exceptional points which are induced by pumping the laser nonuniformly. At these singularities, the eigenstates of the non-Hermitian operator which describes the lasing modes coalesce. In their vicinity, the laser may turn off even when the overall pump power deposited in the system is increased. Such signatures of a pump- induced exceptional point can be experimentally probed with coupled ridge or microdisk lasers.Comment: 4.5 pages, 4 figures, final version including additional FDTD dat

A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

Stochastic Physics, Complex Systems and Biology

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibrium, spontaneous random "mutations" and "adaptations". On an evlutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.Comment: 10 page

Theory of the spatial structure of non-linear lasing modes

A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a linear wave equation and not in terms of resonances of the cold cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found to have non-trivial spatial structure even in the single-mode limit. In the multi-mode regime spatial hole-burning and mode competition is treated exactly. The formalism generalizes to complex, chaotic and random laser media.Comment: 4 pages, 3 figure

First High Contrast Imaging Using a Gaussian Aperture Pupil Mask

Placing a pupil mask with a gaussian aperture into the optical train of current telescopes represents a way to attain high contrast imaging that potentially improves contrast by orders of magnitude compared to current techniques. We present here the first observations ever using a gaussian aperture pupil mask (GAPM) on the Penn State near-IR Imager and Spectrograph (PIRIS) at the Mt. Wilson 100$^{\prime\prime}$ telescope. Two nearby stars were observed, $\epsilon$ Eridani and $\mu$ Her A. A faint companion was detected around $\mu$ Her A, confirming it as a proper motion companion. Furthermore, the observed H and K magnitudes of the companion were used to constrain its nature. No companions or faint structure were observed for $\epsilon$ Eridani. We found that our observations with the GAPM achieved contrast levels similar to our coronographic images, without blocking light from the central star. The mask's performance also nearly reached sensitivities reported for other ground based adaptive optics coronographs and deep HST images, but did not reach theoretically predicted contrast levels. We outline ways that could improve the performance of the GAPM by an order of magnitude or more.Comment: 8 pages, 4 figures, accepted by ApJ letter

Holographic fermions in charged Gauss-Bonnet black hole

We study the properties of the Green's functions of the fermions in charged Gauss-Bonnet black hole. What we want to do is to investigate how the presence of Gauss-Bonnet coupling constant $\alpha$ affects the dispersion relation, which is a characteristic of Fermi or non-Fermi liquid, as well as what properties such a system has, for instance, the Particle-hole (a)symmetry. One important result of this research is that we find for $q=1$, the behavior of this system is different from that of the Landau Fermi liquid and so the system can be candidates for holographic dual of generalized non-Fermi liquids. More importantly, the behavior of this system increasingly similar to that of the Landau Fermi liquid when $\alpha$ is approaching its lower bound. Also we find that this system possesses the Particle-hole asymmetry when $q\neq 0$, another important characteristic of this system. In addition, we also investigate briefly the cases of the charge dependence.Comment: 22 pages, 6 figures; version published in JHE