Asymptotic of the deuteron wave function in the coordinate representation and the charge deuteron form factor at large momentums

Numerical modeling of the deuteron wave function in the coordinate representation for the phenomenological nucleon–nucleon potential Argonne v18 has been performed. For this purpose, the asymptotic behavior of the radial wave function has been taken into account near the origin of coordinates and at infinity. The charge deuteron form factor [Formula: see text], depending on the transmitted momentums up to [Formula: see text], has been calculated employing five models for the deuteron wave function. A characteristic difference in calculations of [Formula: see text] is observed near the positions of the first and second zero. The difference between the obtained values for [Formula: see text] form factor has been analyzed using the values of the ratios and differences for the results. Obtained outcomes for charge deuteron form factor at large momentums may be a prediction for future experimental data.

Modeling of the deuteron wave function in coordinate representation and calculations of polarization characteristics

Modeling of the deuteron wave function in coordinate representation for the nucleon-nucleon potential Reid93 were performed. For this purpose, the asymptotics of the radial wave function near the origin of coordinates and at infinity are taken into account. The most simple and physical asymptotics were applied. In this case, the superfluous knots of both components of the deuteron wave function for the coordinate value r=0.301 fm were compensated. Taking into account the asymptotics of the wave function has little effect on the general behavior of the calculated polarization characteristics of t20 and Ауу. Particular points of the transmitted momentum have been identified, where the tensor deuteron polarization t20 and the tensor analyzing power Ауу show a clear difference.

Generalized penalty for circular coordinate representation

<p style='text-indent:20px;'>Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. To do that, we use a generalized penalty function instead of an <inline-formula><tex-math id="M1">\begin{document}$ L_{2} $\end{document}</tex-math></inline-formula> penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analyses to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.</p>

One-dimensional quantum mechanics with Dunkl derivative

In this paper, we consider the quantum mechanics with Dunkl derivative. We use the Dunkl derivative to obtain the coordinate representation of the momentum operator and Hamiltonian. We introduce the scalar product to find that the momentum is Hermitian under this inner product. We study the one-dimensional box problem (the spin-less particle with mass m confined to the one-dimensional infinite wall). Finally, we discuss the harmonic oscillator problem.

RKKY Interaction in Graphene at Finite Temperature

In our publication from eight years ago (Kogan, E. 2011, vol. 84, p. 115119), we calculated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities adsorbed on graphene at zero temperature. We show in this short paper that the approach based on Matsubara formalism and perturbation theory for the thermodynamic potential in the imaginary time and coordinate representation which was used then, can be easily generalized, and calculate RKKY interaction between the magnetic impurities at finite temperature.