Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

Affine Hall-Littlewood Functions for A(1)((1)) And Some Constant Term Identities of Cherednik-Macdonald-Mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A(1)((1)). We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.

Effective action and adiabatic expansions for the 1-D and 2-D hubbard models at half-filling

We analyze here the occurrence of antiferromagnetic (AFM) correlations in the half-filled Hubbard model in one and two space dimensions using a natural fermionic representation of the model and a newly proposed way of implementing the half-filling constraint. We find that our way of implementing the constraint is capable of enforcing it exactly already at the lowest levels of approximation. We discuss how to develop a systematic adiabatic expansion for the model and how Berry's phase contributions arise quite naturally from the adiabatic expansion. At low temperatures and in the continuum limit the model gets mapped onto an O(3) nonlinear sigma model (NLsigma). A topological, Wess-Zumino term is present in the effective action of the ID NLsigma as expected, while no topological terms are present in 2D. Some specific difficulties that arise in connection with the implementation of an adiabatic expansion scheme within a thermodynamic context are also discussed, and we hint at possible solutions.

Why is there a short-term increase in global precipitation in response to diminished CO2 forcing?

Recently, it was found that a reduction in atmospheric CO2 concentration leads to a temporary increase in global precipitation. We use the Hadley Center coupled atmosphere-ocean model, HadCM3L, to demonstrate that this precipitation increase is a consequence of precipitation sensitivity to changes in atmospheric CO2 concentrations through fast tropospheric adjustment processes. Slow ocean cooling explains the longer-term decrease in precipitation. Increased CO2 tends to suppress evaporation/precipitation whereas increased temperatures tend to increase evaporation/precipitation. When the enhanced CO2 forcing is removed, global precipitation increases temporarily, but this increase is not observed when a similar negative radiative forcing is applied as a reduction of solar intensity. Therefore, transient precipitation increase following a reduction in CO2-radiative forcing is a consequence of the specific character of CO2 forcing and is not a general feature associated with decreases in radiative forcing. Citation: Cao, L., G. Bala, and K. Caldeira (2011), Why is there a short-term increase in global precipitation in response to diminished CO2 forcing?, Geophys. Res. Lett., 38, L06703, doi:10.1029/2011GL046713.

Long-term Accelerated Weathering of Outdoor Silicone Rubber Insulators

Multistress aging/weathering of outdoor composite polymeric insulators has been a topic of interest for power transmission research community in the last few decades. This paper deals with the long-term accelerated weathering of full-scale distribution class silicone rubber composite insulators. To evaluate the long-term synergistic effect of electric stress, temperature and UV radiation on insulators, they were subjected to accelerated weathering in a specially designed multistress-aging chamber for 30,000 h. All the insulators were subjected to the same level of electrical and thermal stresses but different UV radiation levels. Chemical, physical and electrical changes due to degradation have been assessed using various techniques. It was found that there was a monotonous reduction of the content of low molecular weight (LMW) molecules with the duration of the weathering. Further, due to oxidation and weathering there is an appreciable increase in surface roughness and atomic percentage of oxygen. There is no change in the leakage current of new and aged insulators under both wet and dry conditions at the end of the aging. The results also indicate that there is no influence of UV radiation on the silicone rubber for the durations and conditions under which the studies were made.

Long term monitering of vegetation in a tropical deciduous forest in Mudumalai,southern India

As part of an international network of large plots to study tropical vegetation dynamics on a long-term basis, a 50-hectare permanent plot was set up during 1988-89 in the deciduous forests of Mudumalai, southern India. Within this plot 25,929 living woody plants (71 species) above 1 cm DBH (diameter at breast height) were identified, measured, tagged and mapped. Species abundances corresponded to the characteristic log-normal distribution. The four most abundant species (Kydia calycina, Lagerstroemia microcarpa, Terminalia crenulata and Helicteres isora) constituted nearly 56% of total stems, while seven species were represented by only one individual each in the plot. Variance/mean ratios of density showed most species to have clumped distributions. The population declined overall by 14% during the first two years, largely due to elephant and fire-mediated damage to Kydia calycina and Helicteres isora. In this article we discuss the need for large plots to study vegetation dynamics.

Photolysis of arene chromium tricarbonyl complexes in presence of amine-boranes: Observation of sigma-borane complexes in solution

Activation of the B-H sigma-bond of amine-boranes on the chromium(0) center of arene chromium tricarbonyl complexes (eta(6)-arene) Cr(CO)(3) (arene = fluorobenzene, 1a; benzene, 1b and mesitylene, 1c) has been studied. Photolysis of 1b in presence of ammonia-borane (H3N center dot BH3, AB) and tert-butylamine-borane ((BuH2N)-Bu-t center dot BH3, TBAB) resulted in H-2 evolution and precipitation of a BNHx polymer. On the other hand, photolysis in the presence of trimethylamine-borane (Me3N center dot BH3, TMAB) resulted in the formation of a sigma-borane complex (2) along with Cr(CO)(5)(eta(1)-HBH2 center dot NMe3) (3). The sigma-borane complexes (eta(6)-arene) Cr-( CO)(2)(eta(1)-HBH2 center dot NMe3) (arene = fluorobenzene, 2a; benzene, 2b and mesitylene, 2c) were characterized in solution by H-1, B-11, and C-13 NMR spectroscopy. Electron withdrawing substituents on the arene ring provide the more stable sigma-borane moiety in this series of complexes. (C) 2011 Elsevier B.V. All rights reserved.

Magnetism in MnPSe3: a layered 3d(5) antiferromagnet with unusually large XY anisotropy

The anisotropic magnetic susceptibilities of single crystals of the isostructural layered antiferromagnets, MnPS3 (T-N = 78 K) and MnPSe3 (T-N = 74 K), have been measured as functions of temperature. In both compounds, divalent manganese is present in the high-spin S = 5/2 state. The anisotropies in the susceptibilities of the two are, however, very different; while the susceptibility of MnPS3 is isotropic, that of MnPSe3 shows a large XY anisotropy, unusual for a manganese compound. The anisotropic susceptibilities are described by the zero-field spin Hamiltonian: H = DSiz2 - Sigma J(ij).(S) over right arrow (S) over right arrow(j) with the quadratic single-ion anisotropy term introducing anisotropy in an otherwise isotropic situation. The exchange J and the single-ion zero-field-splitting (ZFS) parameter D were evaluated using the correlated effective-field theory of Lines. For MnPSe3, J/k = -5.29 K and D/k = 26.6 K, while for isotropic MnPS3, J/k = -8.1 K. It is suggested that the large value of the ZFS parameter for MnPSe3 as compared to MnPS3 could be due to the large ligand spin-orbit contribution of the heavier selenium.

Assessment of conditional moment closure models of turbulent autoignition using DNS data

A systematic assessment of the submodels of conditional moment closure (CMC) formalism for the autoignition problem is carried out using direct numerical simulation (DNS) data. An initially non-premixed, n-heptane/air system, subjected to a three-dimensional, homogeneous, isotropic, and decaying turbulence, is considered. Two kinetic schemes, (1) a one-step and (2) a reduced four-step reaction mechanism, are considered for chemistry An alternative formulation is developed for closure of the mean chemical source term , based on the condition that the instantaneous fluctuation of excess temperature is small. With this model, it is shown that the CMC equations describe the autoignition process all the way up to near the equilibrium limit. The effect of second-order terms (namely, conditional variance of temperature excess sigma(2) and conditional correlations of species q(ij)) in modeling is examined. Comparison with DNS data shows that sigma(2) has little effect on the predicted conditional mean temperature evolution, if the average conditional scalar dissipation rate is properly modeled. Using DNS data, a correction factor is introduced in the modeling of nonlinear terms to include the effect of species fluctuations. Computations including such a correction factor show that the species conditional correlations q(ij) have little effect on model predictions with a one-step reaction, but those q(ij) involving intermediate species are found to be crucial when four-step reduced kinetics is considered. The "most reactive mixture fraction" is found to vary with time when a four-step kinetics is considered. First-order CMC results are found to be qualitatively wrong if the conditional mean scalar dissipation rate is not modeled properly. The autoignition delay time predicted by the CMC model compares excellently with DNS results and shows a trend similar to experimental data over a range of initial temperatures.

Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in 2+2epsilon dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an epsilon expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in 2+2epsilon dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action (theta term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as nu and p, control not only the scaling behavior of the conductances sigma(xx) and sigma(xy) at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat (c(v)proportional toT(p)). To extract the numerical values of nu and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.

An extended Cahn-Hilliard model for interfaces with cubic anisotropy

For studying systems with a cubic anisotropy in interfacial energy sigma, we extend the Cahn-Hilliard model by including in it a fourth-rank term, namely, gamma (ijlm) [partial derivative (2) c/(partial derivativex(i) partial derivativex(j))] [partial derivative (2) c/(partial derivativex(l) partial derivativex(m))]. This term leads to an additional linear term in the evolution equation for the composition parameter field. It also leads to an orientation-dependent effective fourth-rank coefficient gamma ([hkl]) in the governing equation for the one-dimensional composition profile across a planar interface. The main effect of a non-negative gamma ([hkl]) is to increase both sigma and interfacial width w, each of which, upon suitable scaling, is related to gamma ([hkl]) through a universal scaling function. In this model, sigma is a differentiable function of interface orientation (n) over cap, and does not exhibit cusps; therefore, the equilibrium particle shapes (Wulff shapes) do not contain planar facets. However, the anisotropy in the interfacial energy can be large enough to give rise to corners in the Wulff shapes in two dimensions. In particles of finite sizes, the corners become rounded, and their shapes tend towards the Wulff shape with increasing particle size.

Continous Time Sigma-Delta Modulator Employing a Novel Comparator Architecture

A novel comparator architecture is proposed for speed operation in low voltage environment. Performance comparison with a conventional regenerative comparator shows a speed-up of 41%. The proposed comparator is embedded in a continuous time sigma-delta ADC so as to reduce the quantizer delay and hence minimizes the excess loop delay problem. A performance enhancement of 1dB in the dynamic range of the ADC is achieved with this new comparator. We have implemented this ADC in a standard single-poly 8-Metal 0.13 mum UMC process. The entire system operates at 1.2 V supply providing a dynamic range of 32 dB consuming 720 muW of power and occupies an area of 0.1 mm2.

A homobimetallic complex of chromium(0) with a sigma-borane component

The synthesis, characterization, and reactivity of a chromium(0) complex bearing an amine-borane moiety (eta(6)-C(6)H(5)CH(2)NMe(2)center dot BH(3))Cr(CO)(3) (2) is reported. Photolysis of complex 2 results in the elimination of a CO ligand followed by the formation of an intramolecular sigma-borane complex (eta(1)-(eta(6)- C(6)H(5)CH(2)NMe(2)center dot BH(2)-H))Cr(CO)(2) (3). This species was characterized in solution by NMR spectroscopy. Reaction of complex 2 with photochemically generated (OC)(5)Cr(THF) affords a novel homobimetallic sigma-borane complex (OC)(3)Cr(eta(6)-C(6)H(5)CH(2)NMe(2)center dot BH(2)-H-Cr(CO)(5)) (4), wherein one of the BH moieties is bound to the chromium center in an eta(1)-fashion. The sigma-borane complex 4 was isolated in moderate to good yield (72%). The BH(3) fragment in the complexes 3 and 4 are highly dynamic involving exchange of the BH hydrogen bound to the metal with the terminal BH hydrogen atoms. The dynamics has been studied using variable-temperature NMR spectroscopy. Complexes 2 and 4 have been characterized by X-ray crystallography.

Long term stability studies of particle storage rings using polynomial Maps

Long-term stability studies of particle storage rings can not be carried out using conventional numerical integration algorithms. We require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the sym-plectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is used to perform long term integration on a particle storage ring.