Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

It has been shown in earlier works that for Q=0 and L a multiple of N, the ground state sector eigenspace of the superintegrable tau_2(t_q) model is highly degenerate and is generated by a quantum loop algebra L(sl_2). Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2 algebras. For Q not equal 0, we shall show here that the corresponding eigenspace of tau_2(t_q) is still highly degenerate, but splits into two spaces, each containing 2^{r-1} independent eigenvectors. The generators for the sl_2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q=0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q not equal 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages, uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added, improvements and minor corrections made, erratum to paper 2 included. Version 3: Small paragraph added in introductio

Biological relationships of mites associated with insects

Thesis (M.A.)--Boston University, 1950Our knowledge of Acarina is limited. Life histories have not been studied because it is difficult to rear these mites in the laboratory. Of the two-hundred or more identified mite larvae known in 1946, only twelve are known as nymphs or adults. However, this lack of knowledge in taxonomy does not appear to hinder the work on the biological relationships of mites associated with insects. Mites attacking members of the order, Orthoptera, were described by Lawrence (1940), Howard (1918), Hamilton (1914), Wehrle and Welch (1925), and Radford (1946). The mites attacked mainly the grasshoppers and locueta. These mites belonged to four families: Trombidiidae, Erythraeidae, Tarsonemidae, and Tyroglyphidae. Walsh (1868), Shimer (1868), Lignieres (1893), Riley (1873), and Ewing (1912) gave accounts of mites attacking the scale insect eggs and adults. These mites, which play an important part in the natural control of scale insects, include: Hemisarcoptes malus (Shimer), Monieziella entomophaga Laboulbene, Tydeus cocoophagus Ewing, Bdells cardinalis Banks, Cyta brevipalpa Ewing, Anystis agilis Banks, Eupalus sp., Tetranychus telariue Linne, and Oribata sp.. Of the mites which are parasitic on members of the order Hymenoptera, the most important one is Acarapis woodi (Rennie) which is the causative agent of the well-known Isle of Wight disease of honey bees. The mites infest the tracheal system of the bees and cause death due to the possible secretion of a toxic substance by the mite. White (1921), who reported on this acarine disease, experimented with healthy bees in an attempt to secure information on the mechanical effects of obstruction of the honey bee's tracheal system. The transmission of this disease was reported on by Burnside, Sturtevant, and Halst (1949). Other mites associated with hymenopterans were commensals. The Gamasid mites of the genus, Antennophorus, were described by Wheeler (1910) and Michael (1891, 1894). A certain biological specificity in the relationships with ants wes shown by these mites. One species of Gamasid mite usually was found with only one or two species of ants. LeVeque (1930, 1931) worked extensively on the mites belonging to the genus, Dinogamasus, Kramer. She described several new species of this genus and listed the different groups in whioh the species of Dinogamasus were placed. The groups listed were the perkinsi group, the alfkeni group, the ootoconus group, and the braunsi group. Descriptions of oommon features of the members of the groups and keys for distinguishing between the various species were also included. Marshall (1938), Shapiro, Saliternik, and Belferman (1944) reported the finding of larvae of bydrachnid mites as external parasites on adult mosquitoes. Other records of these water-mite larval parasites were made by Wolcott (1905) and Soar and Williamson (1925). The larvae of Hydrachna (Mulller) Latreille live parasitically on aquatic insects, larvae of Limnoohares Latreille live parasitically on water-bugs, larvae of Eylais Latreille are parasites on insects which leave the water and became aerial, and larvae of the family Hydryphantidae leave the water and live parasitically on aerial fnsects. Mites found on Buprestid beetles and Cerambycid beetles attack in particular in the ventral joints and sutures of the host insect. Lawrence (1940a) described a mite, Pysmephorus crassipes, which was found on the beetles. Anothe mite parasite of beetles, Uropoda vegetans de Geer, reported on by Riley (1877), developed an adaptive organ for attachment. The organ was an extensile organ which issued from the anal vent just beneath the extremity of the body and stuck to the beetle by means of a flattened disc. The mite parasite, Pediculoides ventricosus Newport, which attacks the grain moth, Sitotroga oereallela Oliv. is beneficial to man. It acts as a natural control for the destruction of the grain moth. More recently in 1948 mites of the genus Leptus were found parasitic on species of Corythucha. This discussion given on mite-insect relationship is not by any means complete, but it does point to the fact that investigations have been carried out and that there are great opportunities tor any researcher who may be interested in this field of study

Duality and Symmetry in Chiral Potts Model

We discover an Ising-type duality in the general $N$-state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N=2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small $k'$) to those of another chiral Potts model at a high temperature (of $k'^{-1}$). The $\tau^{(2)}$-model and chiral Potts model on the dual lattice are established alongside the dual chiral Potts models. With the aid of this duality relation, we exact a precise relationship between the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts model and the $sl_2$-loop-algebra symmetry of its associated spin-$\frac{N-1}{2}$ XXZ chain through the identification of their eigenstates.Comment: Latex 34 pages, 2 figures; Typos and misprints in Journal version are corrected with minor changes in expression of some formula

Bayesian Updating of Nonlinear Model Predictions using Markov Chain Monte Carlo Simulation

The usual practice in system identification is to use system data to identify one model from a set of possible models and then to use this model for predicting system behavior. In contrast, the present robust predictive approach rigorously combines the predictions of all the possible models, appropriately weighted by their updated probabilities based on the data. This Bayesian system identification approach is applied to update the robust reliability of a dynamical system based on its measured response time histories. A Markov chain simulation method based on the Metropolis-Hastings algorithm and an adaptive scheme is proposed to evaluate the robust reliability integrals. An example for updating the reliability of a Duffing oscillator is given to illustrate the proposed method

Nonequilibrium Forces Between Neutral Atoms Mediated by a Quantum Field

We study all known and as yet unknown forces between two neutral atoms, modeled as three dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center of mass motion of the atom, its internal degrees of freedom and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first principle, systematic and unified description including the intrinsic field fluctuations and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces -- London, van der Waals and Casimir-Polder forces -- between neutral atoms in the long-time limit but also discover the existence of two new types of interatomic forces. The first, a `nonequilibrium force', arises when the field and atoms are not in thermal equilibrium, and the second, which we call an `entanglement force', originates from the correlations of the internal degrees of freedom of entangled atoms.Comment: 16 pages, 2 figure

On τ(2)\tau^{(2)}-model in Chiral Potts Model and Cyclic Representation of Quantum Group Uq(sl2)U_q(sl_2)

We identify the precise relationship between the five-parameter $\tau^{(2)}$-family in the $N$-state chiral Potts model and XXZ chains with $U_q (sl_2)$-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover an one-parameter family of $L$-operators in terms of the quantum group $U_q (sl_2)$. When $N$ is odd, the $N$-state $\tau^{(2)}$-model can be regarded as the XXZ chain of $U_{\sf q} (sl_2)$ cyclic representations with ${\sf q}^N=1$. The symmetry algebra of the $\tau^{(2)}$-model is described by the quantum affine algebra $U_{\sf q} (\hat{sl}_2)$ via the canonical representation. In general for an arbitrary $N$, we show that the XXZ chain with a $U_q (sl_2)$-cyclic representation for $q^{2N}=1$ is equivalent to two copies of the same $N$-state $\tau^{(2)}$-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal versio

Spin operator matrix elements in the superintegrable chiral Potts quantum chain

We derive spin operator matrix elements between general eigenstates of the superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by R.Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum chain in a transverse field (N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the Separation of Variables Method.Comment: 24 pages, 1 figur