In this study, we have investigated the influence of an external electric field on the electronic properties of the ground and excited states and studied the linear and the third-order nonlinear optical properties (i.e., absorption coefficients and refractive indices) in a spherical semiconductor quantum dot of a parabolic confinement with an on-center shallow hydrogenic impurity. In the calculations, a variational procedure was employed within the effective-mass approximation. We found that the binding energies of the ground and excited states, the absorption coefficients, and the refractive index changes of 0s-1p and 1p-2d transitions depend on the applied electric field. The results show that the existence of the electric field has great influence on the optical absorption coefficients and the refractive index changes. Also, we have found that the magnitudes of the absorption coefficient and the refractive index change of the spherical quantum dot increase for transitions between higher levels.
We investigate the critical lines of polymer mixtures in the presence of their vapor phase at the mathematical double point, where two critical lines meet and exchange branches, and its environment. The model used combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory. The critical line structure is displayed for various combinations of the chain length and system parameters in the pressure (P)-temperature (T) plane, as is usually done with experimental results. This type of work sheds light on the essential transition mechanism involved in the phase diagram's change of character, such as multi-critical points and mathematical double points, which are of great practical importance in supercritical fluid extraction processes. The P, T diagrams are discussed in accordance with the Scott and van Konynenburg binary phase diagram classification. We found that our P, T plots were in agreement with type II, type III, or type IV phase diagram behaviors. We also found that some of our phase diagrams represent the liquid-liquid equilibria in polymer solutions and mixtures.
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