Vanadium dioxide (VO2) have attracted tremendous interest in recent years due to their semiconductor-metal transition near room temperature. In this work, we report numerical simulation of the optical properties of VO2 thin layers which include the index of refraction, the coefficient of extinction, the reflectance and the transmittance. In this sense, we used the Model of Drude-Lorentz for calculating coefficients at from the optical parameters n and k using the determination of the dielectric constant ε (ω, T). Knowing that the semiconductor-metal transition temperature of VO2 is 68 °C, the thickness effect on the optical properties of VO2 thin films has been studied by transmittance simulations. Our results revealed a significant changes in optical properties of VO2 thin layers, which produces many interesting applications especially for smart windows.

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In this paper, we performed an adapted canonical transformation, and we analysed the phase space topology and the bifurcation of Liouville tori of the Hydrogen atom subjected to three static external fields: Van der Waals potential, electric and magnetic fields. In particular, for all values of the parameters of the system under consideration, the bifurcation diagrams of the momentum mapping are constructed, bifurcations of the common level sets of the first integrals are described and the all-generic bifurcations are computed for all singular points of the bifurcation diagrams. However no author has combined these three fields and studied their behavior. Numerical investigations are performed for the integrable case by means of Poincaré surfaces of section and the phase space trajectories method, and we observed the chaos-order-chaos transition

In this article, we studied the problem of the Colombian potential perturbed by van der Waals potential interacting with combined electric and magnetic fields, known as Stark and Zeeman effects, and we determined new integrable cases by using the Painlevé analysis for 2D integrability. This analysis contains three steps: Leading-order behaviors, resonances, and evaluation of arbitrary constants. We also determined the associated second integrals of motion. We verified the integrability of the problem in 3D, with determination of the integrals of motion. We justified the results by numerical investigations using the Poincaré surfaces of the section, and we observed the transition chaos-order-chaos when we varied one of the system parameters.