Physics

This paper presents the over view of concepts and theorems on crystal vibrations and thermal conductivity of solids. By considering the elastic vibrations of crystals where the elastic response of the force a linear function of crystal displacement, X and the potential energy due to side ways vibrations is quadratic function of displacement.
Here, the frequency of Phonon is visualized for both short and long wave length limit. In this paper, the Skittle equation is completely specified for a long wave length limit by defining the natural frequency of an elastic crystal vibration. A comparison of classical and Modern theory of heat capacity at constant volume is discussed.

In this paper, a distinctions between the crystalline and amorphous solid is discussed. By explaining the periodicity of lattice points their lattice structure is clarified. As the paper presents, the 2D and 3D crystal structures are reviewed.In addition, the 3 cubic systems namely, simple cubic, body centered cubic and face centered cubic crystal structures are studied with respect to their primitive axis, number of atoms per primitive cell and their coordination numbers. the discussion of this concept is then extended to ionic solids, carbons and diluted magnetic semiconductors, namely, NaCl, CsCl, diamond, ZnS, ZnO and CdTe, GdO and their compounds doped with transitions(Mn, Fe, Co, Ni, Cu, etc.) and rare Earth metals( La, Eu, Er, Sr, Dy, etc.)

Many quantum mechanics, modern physics, solid state physics, condensed matter physics, statistical Physics and nanoscale physics experts are familier with physical theorems. These theorems inevitably solve the change of physical world in approximately or nearly equaivalently to the real nature. In deepth physical body, analysis it appear more challenging and regorus to manupulate exactly the intrinsic properties of quantum world including quantum nanostructures, atomic, sub atomic, molecular and particulate  matter. In this circumstance, it is important to  turn our vision toward the determinations intrinsic behavior of matter such as microstates, density of states, and spin states following the probabilistic approach. This envokes most theoretical scientist to veiw in deepth analysis of nanoscale matter. Hence, the quantum mechanical approaches including Bell's theorems become a virtual fingur print to solve spin systems and their physical behavior by enumerating states and probability by applying the fundamental postulates of probability called equal a priori Postulate". Here, the 3rd part of Bell's theorem and its implication in determining its probability of spin 1/2 systems such as electron is presented.

In this paper, the detailed inseparability criteria of entanglement quantification of correlated two-mode light generated by a three-level laser with a coherently driven parametric amplifier and coupled to a two-mode vacuum reservoir is thoroughly analyzed. Using the master equation, we obtain the stochastic differential equation and the correlation properties of the noise forces associated with the normal ordering. Next, we study the squeezing and the photon entanglement by considering different inseparability criteria. The various criteria of entanglement used in this paper show that the light generated by the quantum optical system is entangled and the amount of entanglement is amplified by introducing the parametric amplifier into the laser cavity and manipulating the linear gain coefficient.

In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. Particularly, the enhancement of squeezing and the amplification of photon entanglement of the two-mode cavity light are investigated. It is found that the two cavity modes are strongly entangled and the degree of entanglement is directly related to the two-mode squeezing. Despite the fact that the entanglement and squeezing decrease with the increment of the mean photon number of the thermal reservoir, strong amount of these nonclassical properties can be generated for a considerable amount of thermal noise with the help of the nonlinear crystal introduced into the laser cavity. Moreover, the squeezing and entanglement of the cavity radiation enhance with the rate of atomic injection.

The quantum and statistical properties of light generated by an external classical field in a correlated emission laser with a parametric amplifier and coupled to a squeezed vacuum reservoir are investigated using the combination of the master and stochastic differential equations. First, the solutions of the cavity-mode variables and correlation properties of noise forces associated to the normal ordering are obtained. Next, applying the resulting solutions, the mean photon number of the separate cavity modes and their crosscorrelation, smallest eigenvalue of the symplectic matrix, mean photon number, intensity difference fluctuation, photon number variance, and intensity correlation are derived for the cavity-mode radiation. The entanglement produced is studied employing the logarithmic negativity criterion. It is found that pumping atoms from the lower energy state to excited state, introducing the nonlinear crystal into the cavity and coupling the system to a biased noise fluctu...

In this paper, the quantum properties of a two-level atom interaction with squeezed vacuum reservoir is throughly analyzed. With the aid of the interaction Hamiltonian and the master equation, we obtain the time evolution of the expectation values of the atomic operators. Employing the steady-state solution of these equations, we calculate the power spectrum and the second-order correlation function for the interaction of two-level atom with squeezed vacuum reservoir. It is found that the half width of the power spectrum of the light increases with the squeeze parameter, . Furthermore, in the absence of decay constant and interaction time, it enhances the probability for the atom to be in the upper level.

We have analyzed the squeezing and statistical properties of the cavity light beam produced by a coherently driven degenerate three-level laser with a degenerate parametric amplifier (DPA) in an open cavity and coupled to a vacuum reservoir via a single-port mirror. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equation for the cavity mode operator, the mean photon number and the quadrature squeezing of the cavity light are calculated. And a large part of the mean photon number is confined in a relatively small frequency interval. Furthermore, we also obtain the antinormally ordered characteristic function defined in the Heisenberg picture. With the aid of the resulting characteristic function, we determine the function which is then used to calculate the photon number distribution.

We analyse the entanglement of the light produced by a three-level laser whose cavity contains a parametric amplifier, with the cavity mode driven by the coherent light and coupled to a squeezed vacuum reservoir. Employing stochastic differential equations associated with the normal ordering resulted from the pertinent master equation, the quadrature variances and entanglement of the two-mode light are obtained and photon statistics of the two-light modes is discussed. It is found that the three-level laser generates squeezed light under certain conditions, with maximum intracavity squeezing being 89.7% below the coherent state level. We also show that the parametric amplifier enhances the mean photon number and photon number correlation.