Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

We study the q-dependent susceptibility chi(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of chi(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic-antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen.Comment: LaTeX2e, 26 pages, 9 figures (27 eps files). v2: Misprints correcte

Bethe Ansatz solutions for Temperley-Lieb Quantum Spin Chains

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version of the coordinate Bethe Ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed non-local boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed non-local cases the models are quantum group invariant as well as periodic in a certain sense.Comment: 28 pages, plain LaTex, no figures, to appear in Int. J. Mod. Phys.

Reaction-Diffusion Processes as Physical Realizations of Hecke Algebras

We show that the master equation governing the dynamics of simple diffusion and certain chemical reaction processes in one dimension give time evolution operators (Hamiltonians) which are realizations of Hecke algebras. In the case of simple diffusion one obtains, after similarity transformations, reducible hermitian representations while in the other cases they are non-hermitian and correspond to supersymmetric quotients of Hecke algebras.Comment: Latex, 6 pages, BONN-HE-93.1

Dynamic properties of the spin-1/2 XY chain with three-site interactions

We consider a spin-1/2 XY chain in a transverse (z) field with multi-site interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan-Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and hence the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First we consider the zz dynamic structure factor reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors which are signatures for the presence of the three-site interactions.Comment: 28 pages, 10 fugure

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

Finite dimensional representations of Uq(C(n+1))U_q(C(n+1)) at arbitrary qq

A method is developed to construct irreducible representations(irreps) of the quantum supergroup $U_q(C(n+1))$ in a systematic fashion. It is shown that every finite dimensional irrep of this quantum supergroup at generic $q$ is a deformation of a finite dimensional irrep of its underlying Lie superalgebra $C(n+1)$, and is essentially uniquely characterized by a highest weight. The character of the irrep is given. When $q$ is a root of unity, all irreps of $U_q(C(n+1))$ are finite dimensional; multiply atypical highest weight irreps and (semi)cyclic irreps also exist. As examples, all the highest weight and (semi)cyclic irreps of $U_q(C(2))$ are thoroughly studied.Comment: 21 page

The anisotropic XY model on the inhomogeneous periodic chain

The static and dynamic properties of the anisotropic XY-model $(s=1/2)$ on the inhomogeneous periodic chain, composed of $N$ cells with $n$ different exchange interactions and magnetic moments, in a transverse field $h,$ are determined exactly at arbitrary temperatures. The properties are obtained by introducing the Jordan-Wigner fermionization and by reducing the problem to a diagonalization of a finite matrix of $nth$ order. The quantum transitions are determined exactly by analyzing, as a function of the field, the induced magnetization 1/n\sum_{m=1}^{n}\mu_{m}\left ($j$ denotes the cell, $m$ the site within the cell, $\mu_{m}$ the magnetic moment at site $m$ within the cell) and the spontaneous magnetization $1/n\sum_{m=1}^{n}\left< S_{j,m}^{x},\right>$ which is obtained from the correlations $\left< S_{j,m}^{x}S_{j+r,m}^{x}\right>$ for large spin separations. These results, which are obtained for infinite chains, correspond to an extension of the ones obtained by Tong and Zhong(\textit{Physica B} \textbf{304,}91 (2001)). The dynamic correlations, $\left< S_{j,m}^{z}(t)S_{j^{\prime},m^{\prime}}^{z}(0)\right>$, and the dynamic susceptibility, $\chi_{q}^{zz}(\omega),$ are also obtained at arbitrary temperatures. Explicit results are presented in the limit T=0, where the critical behaviour occurs, for the static susceptibility $\chi_{q}^{zz}(0)$ as a function of the transverse field $h$, and for the frequency dependency of dynamic susceptibility $\chi_{q}^{zz}(\omega)$.Comment: 33 pages, 13 figures, 01 table. Revised version (minor corrections) accepted for publiction in Phys. Rev.

The structure of quotients of the Onsager algebra by closed ideals

We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio

Association of Anticholinergic Burden with Cognitive Impairment and Health Care Utilization Among a Diverse Ambulatory Older Adult Population

Study Objective To determine the association between Anticholinergic Cognitive Burden (ACB) score and both cognitive impairment and health care utilization among a diverse ambulatory older adult population. Design Retrospective cohort study. Data Source Medication exposure and other clinical data were extracted from the Regenstrief Medical Record System (RMRS), and cognitive diagnosis was derived from a dementia screening and diagnosis study. Patients A total of 3344 community-dwelling older adults (age 65 yrs and older) who were enrolled in a previously published dementia screening and diagnosis study; of these, 3127 were determined to have no cognitive impairment, and 217 were determined to have cognitive impairment. Measurements and Main Results The study followed a two-phase screening and comprehensive neuropsychiatric examination to determine a cognitive diagnosis, which defined cognitive impairment as dementia or mild cognitive impairment. The ACB scale was used to identify anticholinergics dispensed in the 12 months prior to screening. A total daily ACB score was calculated by using pharmacy dispensing data from RMRS; each anticholinergic was multiplied by 1, 2, or 3 consistent with anticholinergic burden defined by the ACB scale. The sum of all ACB medications was divided by the number of days with any medication dispensed to achieve the total daily ACB score. Health care utilization included visits to inpatient, outpatient, and the emergency department, and it was determined by using visit data from the RMRS. The overall population had a mean age of 71.5 years, 71% were female, and 58% were African American. Each 1-point increase in mean total daily ACB score was associated with increasing risk of cognitive impairment (odds ratio [OR] 1.13, 95% confidence interval [CI] 1.004–1.27, p=0.043). Each 1-point increase in mean total daily ACB score increased the likelihood of inpatient admission (OR 1.11, 95% CI 1.02–1.29, p=0.014) and number of outpatient visits after adjusting for demographic characteristics, number of chronic conditions, and prior visit history (estimate 0.382, standard error [SE] 0.113; p=0.001). The number of visits to the emergency department was also significantly different after similar adjustments (estimate 0.046, SE 0.023, p=0.043). Conclusion Increasing total ACB score was correlated with an increased risk for cognitive impairment and more frequent health care utilization. Future work should study interventions that safely reduce ACB and evaluate the impact on brain health and health care costs

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models.Comment: 17 pages, RevTe