Different numerical methods offer for solving wave equation with diverse boundary conditions. In these methods given partial (Differential Equation: DE) change to a normal DE system using equation separating in terms of time variable method. Pade Approximation is used for appreciative calculation of exponential matrix function which is created in response of normal DE. Furthermore, its error and stability are investigated by separating method, parallel algorithm is proposed for solving normal Differential Equation and numbers of function in serial and parallel methods are compared.

The aim of this study is to investigate dynamical properties of a two-mode f-deformed cavity- field ‎coupled to an effective two-level atom with and without the rotating wave Approximation. The first ‎section discusses the theoretical model of the interaction between a two-mode cavity-field and an ‎effective two-level atom within the framework of an f-DJCM without the rotating wave ‎Approximation. After that, we obtain the reduced density matrix of the cavity-field with and without ‎the rotating-wave Approximation. Then, we have investigated the effect of the counter-rotating ‎terms on temporal evolution of various non-classical properties of the cavity-field, i.e., photon-‎counting statistics, the cross correlation between the modes of the field, and the quantum ‎fluctuations of the quadrature components. Particularly, we compare the numerical result for three ‎different values of the deformation parameter q (q=1, q=1.1, q=0.9) with and without applying the rotating ‎wave Approximation. By using of the numerical method, we concluded that even under the ‎condition in which the RWA is considered to be valid, there are the significant effects of virtual-‎photon field on the photon-counting statistics, the cross correlation between the modes of the ‎field, and the quantum fluctuations of the quadrature components‎.

The aim of this paper is to investigate dynamical properties of a harmonic oscillator coupled to a non-equilibrium bath without the rotating wave Approximation. At first, we investigate the theory of this model and obtain the Heisenberg equations of motion for the oscillator and bath annihilation operators in the absence and in the presence of a rotating wave Approximation. Then, we obtain the fluctuation and fluctuation-dissipation relations in the absence and in the presence of a rotating wave Approximation for the non-equilibrium bath annihilation operator, respectively. After that, we study the decay of system modes using the Wigner-Weisskopf Approximation. Finally, we calculate the time-dependent spectrum of a cavity field mode coupled to a non-equilibrium reservoir. We show that even under the condition in which the RWA is considered to be valid (weak interaction), there are significant effects of virtual-photon field on the diffusion coefficient, the energy density, line width and the shift frequency.

The aim of this study is to investigate an effective two-level atom coupled to a twomode f-deformed cavity field with and without the rotating wave Approximation. The first section discusses the theoretical model of the interaction between a two-mode cavity-field and an effective two-level atom within the framework of an f-DJCM without the rotating wave Approximation. After that, we obtain the reduced density matrix of the atom with and without the rotating-wave Approximation. Then, we have investigated the effect of the counterterm on temporal evolution of various nonclassical properties of the atom, i. e., atomic population inversion, atomic dipole squeezing and atom-field entanglement. Particularly, we compare the numerical result for three different values of the deformation parameter q (q=1, q=1. 1, q=1) with and without the rotating wave Approximation.

In this paper a novel Long-wavelength infrared (IR) photodetector based on Electromagneticlly induced transparency (EIT) is proposed. This kind of photo-detectors is suitable for operation in room temperature and terahertz range (low level signal) detection. Main idea for operation in the room temperature is related to convert the incoming Long-wave length IR signal to short-wave length or visible probe field through EIT phenomena. Realization of the idea implemented with using atomic states (that can be simulated by introducing quantum wells or dots). In the proposed structure Long-wave length IR signal dose not directly interact with electrons, but affects the absorption characteristic of short-wave length or visible probe field. Therefore; the introduced structure reduces and/or cancels out the thermionic dark current component and can operate as a Long-wave length photo detector

This study aims to discuss and illustrate the role of insoluble surfactants on the stability analysis of a shearimposed free surface motion down an oblique heated substrate. The couple effects of temperature and surfactant concentration gradient on the surface tension are assessed, in which the surface tension of the fluid is assumed to vary linearly on surfactant concentration and the temperature. The exact analytical solutions for the Stokes flow and the Long-wave Approximation are derived, depending on the linear stability theory, and hence the neutral curves are plotted and discussed. Due to the presence of the surfactant, there are two different modes that impact the stability process of a shear-imposed inclined flow. The current study recovers some limiting cases upon the selected data. The system parameters governing the liquid layer and the substrate geometry have a strong effect on the wave forms and so the stability of the free surface. The influences of various parameters such as Marangoni, Biot, elasticity, surfactant Pé clet number and Reynolds numbers, besides the angle of inclination are considered. It is found that, the Reynolds and the surfactant Pé clet numbers and the angle of inclination have destabilizing effects.