Area Distribution of Elastic Brownian Motion

We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will stress on the power of self adjoint extension to investigate different possible boundary conditions for the stochastic processes.Comment: 18 pages, published versio

Universal logarithmic correction to Rényi (Shannon) entropy in generic systems of critical quadratic fermions

The R\'enyi (Shannon) entropy, i.e. $Re_{\alpha}(Sh)$, of the ground state of quantum systems in local bases normally show a volume-law behavior. For a subsystem of quantum chains at critical point there is an extra logarithmic subleading term with a coefficient which is universal. In this paper we study this coefficient for generic time-reversal translational invariant quadratic critical free fermions. These models can be parameterized by a complex function which has zeros on the unit circle. When the zeros on the unit circle do not have degeneracy and there is no zero outside of the unit circle we are able to classify the coefficient of the logarithm. In particular, we numerically calculate the R\'enyi (Shannon) entropy in configuration basis for wide variety of these models and show that there are two distinct classes. For systems with $U(1)$ symmetry the coefficient is proportional to the central charge, i.e. one half of the number of points that one can linearize the dispersion relation of the system; for all the values of $\alpha$ with transition point at $\alpha=4$. For systems without this symmetry, when $\alpha>1$ this coefficient is again proportional to the central charge. However, the coefficient for $\alpha\leq 1$ is a new universal number. Finally, by using the discrete version of Bisognano-Wichmann modular Hamiltonian of the Ising chain we show that these coefficients are universal and dependent on the underlying CFT.Comment: v2: 16 pages, 10 figures published versio

Population abundance of pomegranate aphid, Aphis punicae (Homoptera: Aphididae), predators in Southwest of Iran

Pomegranate aphid, Aphis punicae Passarini (Hom., Aphididae) is an important pest of pomegranate in Iran. Predators play critical role in natural control of the pest. In this study, seasonal population dynamics of the aphid predators were investigated during two years (2016/2017) in Ilam province, southwest of Iran. Samplings were bi-weekly performed in an experimental pomegranate orchard. Four insect predators, Coccinella septempunctata L., Oenopia congelobata L. (Col., Coccinellidae), Xanthogramma pedisseguum Haris (Dip., Syrphidae) and Chrysoperla carnea Stephens (Neu., Chryspidae) were identified as predators of A. punicae in Ilam. The natural enemies occurred during March to May in both years. The highest and the lowest densities were belong to X. pedisseguum and O. congelobata, respectively. Results of the study can be used for developing integrated pest management program of A. punicae in pomegranate orchards

Evaluation of various diets and oviposition substrates for rearing Orius albidipennis Reuter

A suitable diet and oviposition substrate are two basic needs for successful mass rearing of Orius spp. and this may reduce their production costs. The effect of various foods containing eggs of Ephestia kuehniella and Sitotroga cerealella with various pollens were investigated on the biological parameters of O. albidipennis in the laboratory. Moreover, survival, hatching rate and fecundity of the predatory bug on various natural substrates were compared. Nymphal developmental time of the bug on diets including E. kuehniella and S. cerealella varied from 13 to 14.2 and 14 to 15.3 days, respectively. The nymph and adult survival and consumption rate were not significantly affected by the dietary treatments. Because of a more rapid development with food containing eggs of E. kuehniella, they are the best nymphal diets for mass rearing of O. albidipennis. It must be noted that S. cerealella eggs are six times cheaper than E. kuehniella eggs. Therefore, the foods containing eggs of S. cerealella may be more economic for mass rearing of the bug despite a slower development of nymphs that fed on them. Also, composition of S. cerealella and date palm pollen is the most suitable diet for mass rearing of O. albidipennis adults due to a higher fecundity and longevity of the adults and lower costs of the diet. Female longevity, total eggs and hatching percentage of the predatory bug on Sedum ternatum were significantly higher than other natural substrates. These results may have practical implications for mass rearing of O. albidipennis as part of a biological control program

Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder

We investigate the explicit renormalization group for fermionic field theoretic representation of two-dimensional random bond Ising model with long-range correlated disorder. We show that a new fixed point appears by introducing a long-range correlated disorder. Such as the one has been observed in previous works for the bosonic ($\phi^4$) description. We have calculated the correlation length exponent and the anomalous scaling dimension of fermionic fields at this fixed point. Our results are in agreement with the extended Harris criterion derived by Weinrib and Halperin.Comment: 5 page

Area distribution and the average shape of a L\'evy bridge

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the area A = \sum_{m=1}^n x_B(m) under such a L\'evy bridge and show that, for large n, it has the scaling form P_B(A,n) \sim n^{-1-1/\alpha} F_\alpha(A/n^{1+1/\alpha}), with the asymptotic behavior F_\alpha(Y) \sim Y^{-2(1+\alpha)} for large Y. For \alpha=1, we obtain an explicit expression of F_1(Y) in terms of elementary functions. We also compute the average profile < \tilde x_B (m) > at time m of a L\'evy bridge with fixed area A. For large n and large m and A, one finds the scaling form = n^{1/\alpha} H_\alpha({m}/{n},{A}/{n^{1+1/\alpha}}), where at variance with Brownian bridge, H_\alpha(X,Y) is a non trivial function of the rescaled time m/n and rescaled area Y = A/n^{1+1/\alpha}. Our analytical results are verified by numerical simulations.Comment: 21 pages, 4 Figure

Integrability as a consequence of discrete holomorphicity: the Z_N model

It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the Z_N model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations. The star-triangle relation follows from the three-rhombus equation. We also show that these weights are self-dual as a consequence of discrete holomorphicity.Comment: 11 pages, 7 figures, some clarifications and a reference adde

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

Positivity, entanglement entropy, and minimal surfaces

The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in $n-1$. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of Wilson loops. Conclusions regarding entanglement entropy unchange