Microscopic Spectral Density of the Dirac Operator in Quenched QCD

Measurements of the lowest-lying eigenvalues of the staggered fermion Dirac operator are made on ensembles of equilibrium gauge field configurations in quenched SU(3) lattice gauge theory. The results are compared with exact analytical predictions in the microscopic finite-volume scaling regime.Comment: 8 pages, LaTeX, with 2 ps figure

Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order

We calculate the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order using the supersymmetry method in the formulation without a singlet particle. We include a nonzero imaginary chemical potential and show that the finite-volume corrections to the low-energy constants $\Sigma$ and $F$ for the partially quenched partition function, and hence for spectral correlation functions of the Dirac operator, are the same as for the unquenched partition function. We briefly comment on how to minimize these corrections in lattice simulations of QCD. As a side result, we show that the zero-momentum integral in the formulation without a singlet particle agrees with previous results from random matrix theory.Comment: 19 pages, 4 figures; minor changes, to appear in JHE

Effect of Elymus repens on yield of winter wheat, spring barley and faba bean in an organic crop rotation experiment

The impact of crop rotation, nutrient levels and use of catch crops on effect of E. repens on a sandy soil at Jyndevad on yield of winter wheat (2006), spring barley (2007-2008) and faba bean (2006-2008) was studied in an existing organic crop rotation experiment (Olesen et al., 2000; Rasmussen et al., 2006). Some of the objectives were to determine the yield loss at different levels of infestation of the weed, and to determine whether this relationship was influenced by the treatments. For all crops, the treatments had a high impact on the yield. The two treatments that had no manure applied for up to 12 years consistently had the lowest yields. In spring barley, the two treatments with manure and with catch crops consistently had the highest yields. In faba bean, the treatment with manure and without catch crops had the highest yields. As for the effect of E. repens shoots on yield, in spring barley, there was a larger decrease in the system without grass clover. The same tendency was seen for winter wheat. For spring barley and faba bean, within each system (with or without grass clover), the yield in treatments without manure was less influenced by E. repens than in treatments with manure

Exact Vacuum Energy of Orbifold Lattice Theories

We investigate the orbifold lattice theories constructed from supersymmetric Yang-Mills matrix theories (mother theories) with four and eight supercharges. We show that the vacuum energy of these theories does not receive any quantum correction perturbatively.Comment: 14 pages, no figure, LaTeX2e, typos corrected, errors in references corrected, comments adde

Individual Eigenvalue Distributions for the Wilson Dirac Operator

We derive the distributions of individual eigenvalues for the Hermitian Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac Operator DW. The framework we provide is valid in the epsilon regime of chiral perturbation theory for any number of flavours Nf and for non-zero low energy constants W6, W7, W8. It is given as a perturbative expansion in terms of the k-point spectral density correlation functions and integrals thereof, which in some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at fixed chirality nu this expansion truncates after at most nu terms for small lattice spacing "a". Explicit examples for the distribution of the first and second eigenvalue are given in the microscopic domain as a truncated expansion of the Fredholm Pfaffian for quenched D5, where all k-point densities are explicitly known from random matrix theory. For the real eigenvalues of quenched DW at small "a" we illustrate our method by the finite expansion of the corresponding Fredholm determinant of size nu.Comment: 20 pages, 5 figures; v2: typos corrected, refs added and discussion of W6 and W7 extende

Universal and non-universal behavior in Dirac spectra

We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.Comment: LATTICE98(confine), 9 pages, 11 figure

Spectral Properties of the Overlap Dirac Operator in QCD

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the \epsilon-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE

Nutrient allocations and metabolism in two collembolans with contrasting reproduction and growth strategies

Physiological mechanisms such as allocation and release of nutrients are keys to understanding an animal\u27s adaptation to a particular habitat. This study investigated how two detrivores with contrasting life‐history traits allocated carbon (C) and nitrogen (N) to growth, reproduction and metabolism. As model organisms we used the collembolans, Proisotoma minuta (Tullberg 1871) and Protaphorura fimata (Gisin 1952). To estimate allocations of C and N in tissue, we changed the isotopic composition of the animal\u27s yeast diets when they became sexually mature and followed isotope turnover in tissue, growth and reproduction for 28 days. In addition, we measured the composition of C, N and phosphorus (P) to gain complementary information on the stoichiometry underlying life‐history traits and nutrient allocation. For P. minuta, the smallest and most fecund of the two species, the tissue turnover of C and N were 13% and 11% day−1, respectively. For P. fimata, the equivalent rates were 5% and 4% d−1, respectively. Protaphorura fimata had the lowest metabolic rate relative to total body mass but the highest metabolic rates relative to reproductive investment. Adult P. fimata retained approximately 17% of the nutrient reserves acquired while a juvenile and adult P. minuta about 11%. N and P contents of total tissue were significantly higher in P. minuta than in P. fimata, suggesting that tissue turnover was correlated with high protein‐N and RNA‐P. Our results suggest that the lower metabolism and nutritional requirements by P. fimata than P. minuta is an adaptation to the generally low availability and quality of food in its natural habitat. The methodological approach we implemented tracking mass balance, isotope turnover and elemental composition is promising for linking nutrient budgets and life‐history traits in small invertebrates such as Collembola

Comments on the Covariant Sp(2)-Symmetric Lagrangian BRST Formalism

We give a simple geometrical picture of the basic structures of the covariant $Sp(2)$ symmetric quantization formalism -- triplectic quantization -- recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the appearance of an even Poisson bracket is not a particular property of triplectic quantization. Rather, any solution of the classical master equation generates on a Lagrangian surface of the antibracket an even Poisson bracket. Also other features of triplectic quantization can be identified with aspects of conventional Lagrangian BRST quantization without extended BRST symmetry.Comment: 9 pages, LaTe

Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio