Scattering states of a particle, with position-dependent mass, in a PT{\cal{PT}} symmetric heterojunction

The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian ${\cal{PT}}$ symmetric systems --- viz., left / right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed.Comment: 12 pages, including 6 figures; Journal of Physics A : Math. Theor. (2012

Temporal evolution of carbon stocks, fluxes and carbon balance in pedunculate oak chronosequence under close-to-nature forest management

Under current environmental changes, forest management is challenged to foster contrasting benefits from forests, such as continuous wood supply while preserving biomass production, biodiversity conservation, and contribution to climate change mitigation through atmospheric carbon sequestration. Although being found as globally important, estimates of long-term forest C balance are still highly uncertain. In this context, the chronosequence experiments (space-for-time substitution) might fill this gap in even-aged forests, as they represent an approach that enables the assessment of forest net C balance in the long term. In this research, we explored the dynamics of C stocks and fluxes in different forest pools throughout the rotation period (140 years) of a Pedunculate oak (Quercus robur L.) forest in Croatia. For this purpose, we selected a chronosequence that was made up of seven forest stands with different age (5, 13, 38, 53, 68, 108, and 138 years). To address the issues of uncertainty in C balance estimates, we compared net ecosystem carbon balance (NECB) estimated while using two different approaches, which we name pool-change (from C stocks) approach and component-flux (from C fluxes) approach. Overall, the pool-change approach showed higher NECB estimate, with the greatest difference being observed in younger stands (<50 years). Component-flux approach showed significantly higher uncertainty. Throughout the rotation period, managed pedunculate oak stands become a C sink early in their development phase, between the age of 13 and 35 years according to pool-change and component-flux approach, respectively. During the 140 years, oak forest provided 187.2 Mg C ha−1 (604 m3 ha−1) through thinnings and 147.9 Mg C ha−1 (477 m3 ha−1) in the final cut, while preserving, on average, 88.9 Mg C ha−1 in mineral soil down to 40 cm, 18.2 Mg C ha−1 in dead wood, and 6.0 Mg C ha−1 in the forest floor. Soil C stocks in our chronosequence did not show any age-related trend, indicating that current management practice has no negative effect on soil C stocks. Finally, under current close-to-nature forest management, Pedunculate oak forest showed to be sustainable in providing both economic and ecological ecosystem services

Exact Spin and Pseudo-Spin Symmetric Solutions of the Dirac-Kratzer Problem with a tensor potential via Laplace Transform Approach

Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectra is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agrement with the ones given in literature. The numerical results are also given in a table for different parameter values.Comment: 8 page

Psychosocial Characteristics of Patients with Bronchial Asthma and Coronary Disease: Similarities and Differences

The authors compare two groups of subjects: patients with bronchial asthma and those with coronary disease, with regard to some social characteristics, abilities and perception of factors which they conceive are important in the etiology of their disease. Data were obtained by means of a questionnaire based on a known calibrated scale. A group of 100 patients with bronchial asthma and a group of 102 patients with coronary disease were examined. The significance of the difference was tested by c 2, t-test, Wilcoxon’s test and multivariate discriminative analysis. The results showed statistically significant differences between the patients with bronchial asthma and those with coronary disease in some social and psychological characteristics and also with regard to perception of potential etiological factors of their disease. However, no difference was found in life style and habits between the coronary and asthmatic patients

Effective-mass Klein-Gordon Equation for non-PT/non-Hermitian Generalized Morse Potential

The one-dimensional effective-mass Klein-Gordon equation for the real, and non-\textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. The energy eigenvalues, and the corresponding eigenfunctions are obtained. They are also calculated for the constant mass case.Comment: 14 page

Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthen Potential by the Nikiforov-Uvarov Method

The one-dimensional spinless Salpeter equation has been solved for the PT-symmetric generalized Hulth\'{e}n potential. The Nikiforov-Uvarov {NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthen potentials.Comment: 24 page

OPE for Super Loops

We extend the Operator Product Expansion for Null Polygon Wilson loops to the Mason-Skinner-Caron-Huot super loop, dual to non MHV gluon amplitudes. We explain how the known tree level amplitudes can be promoted into an infinite amount of data at any loop order in the OPE picture. As an application, we re-derive all one loop NMHV six gluon amplitudes by promoting their tree level expressions. We also present some new all loops predictions for these amplitudes.Comment: 16 pages + appendices; 5 figure

Wilson Loops @ 3-Loops in Special Kinematics

We obtain a compact expression for the octagon MHV amplitude / Wilson loop at 3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed coefficients. We do this by making use of the cyclic and parity symmetry of the amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as in the leading term in the expansion away from this limit. We also make a natural and quite general assumption about the functional form of the result, namely that it should consist of weight 6 polylogarithms whose symbol consists of basic cross-ratios only (and not functions thereof). We also describe the uplift of this result to 10 points.Comment: 26 pages. Typos correcte

Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities

We examine the gluon scattering amplitude in N=4 super Yang-Mills at finite temperature with nonzero R-charge densities, and in Non-Commutative gauge theory at finite temperature. The gluon scattering amplitude is defined as a light-like Wilson loop which lives at the horizon of the T-dual black holes of the backgrounds we consider. We study in detail a special amplitude, which corresponds to forward scattering of a low energy gluon off a high energy one. For this kinematic configuration in the considered backgrounds, we find the corresponding minimal surface which is directly related to the gluon scattering amplitude. We find that for increasing the chemical potential or the non-commutative parameter, the on-shell action corresponding to our Wilson loop in the T-dual space decreases. For all of our solutions the length of the short side of the Wilson loop is constrained by an upper bound which depends on the temperature, the R-charge density and the non-commutative parameter. Due to this constraint, in the limit of zeroth temperature our approach breaks down since the upper bound goes to zero, while by keeping the temperature finite and letting the chemical potential or the non-commutative parameter to approach to zero the limit is smooth.Comment: 30 pages, 16 figures, minor corrections (plus improved numerical computation for the non-commutative case

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral \Omega^{(2)}, also plays a key role in a new representation of the remainder function R_6^{(2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) \times (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) \times (parity even) part. The second non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)}, characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo correction