In this theoretical study, based on a nonlinear wave equation describing the interaction of fields of an X-ray laser beam with relativistic quantum plasma, modulation instability and formation of solitary waves are investigated. Analytical expressions are derived for the growth rate of modulation instability and electromagnetic envelope solitons. The frequency interval of instability and the dependence of the growth rate on some physical parameters such as the initial laser beam amplitude and frequency are considered. Additionally, the effect of the laser amplitude on the solitary waves is studied. It is shown that quantum effects lead to the reduction of nonlinearity of plasma.

In this theoretical study, the problem of self-focusing of an X-ray intense laser beam in the thermal quantum plasma is studied. Using a relativistic fluid model and taking into account the hydrodynamic pressure of degenerate electrons in the zero temperature limit, the nonlinear momentum equation of electrons is solved by means of a perturbative method and the nonlinear current density of the relativistic degenerate electrons is obtained. Saving only the third-order nonlinearity of the laser beam amplitude, a nonlinear equation describing the interaction of a laser beam with the quantum plasma is derived. It is shown that considering the nonlinearity of the system through solving the nonlinear equation of the degenerate electron leads to the originally different wave equation in comparison to outcomes of the approach in which the permittivity of longitudinal waves of quantum plasma is problematically extended to the relativistic case. The evolution of the laser beam spot size with the Gaussian profile is considered, and the effect of quantum terms on the self-focusing quality is studied. It is shown that considering quantum effects leads to the decrease in the self-focusing property and the effect of Bohm tunneling potential is more dominant than the degenerate electron pressure term.

The quantum diffraction and symmetry effects on the entanglement fidelity (EF) of different elastic electron-electron, ion-ion and electron-ion interactions are investigated in non-ideal dense plasmas. The partial wave analysis, an effective screened interaction potential including quantum mechanical diffraction and symmetry effects are employed to obtain the EF in a nonideal dense plasma. We show that collision energy and temperatures of electron and ion have destructive effects on the entanglement in the system. In fact, by decreasing the temperature of plasma particles, the quantum effects become more prominent and the entanglement is elevated. Also, increase in the density of plasma leads to the enhancement of entanglement ratio. Additionally, some important characteristic parameters of the scattering such as differential, transport and total cross sections are calculated.

We consider new generalized statistics based on the generalization of statistical weight. We work out the thermodynamic curvature of an ideal gas with particles obeying such generalized statistics. For different values of generalization parameters; p and q, we observe that both attractive and repulsive intrinsic statistical interaction is expected. As long as p q, the thermodynamic curvature is positive in full physical range. We show that for p < q, generally dominant behavior in high temperature is Fermi-like while in low temperature, the thermodynamic curvature is positive and the systems behaves such as bosons. Also, by more decreasing of the temperature, the system transits to the condensate phase. In fact, the attractive statistical interaction is related to parameter p, while by increasing the value of q, the repulsive interaction is induced. Explicitly, the specified fugacity (z = z * p,q ) of the system, where the sign of thermodynamic curvature is changed and for z < z * p,q (z > z * p,q ) the statistical behavior is fermion like (boson like ), is explored. Also, we extract the variation of statistical behavior of the system for different values of generalization parameters with respect

Using subdivision potential approach and mean-field theory for a ferromagnetic cluster, we obtained nanothermodynamic properties for a ferromagnetic nanocluster in the presence and also the absence of the magnetic field. The subdivision potential and the magnetic field both makes Gibbs and Helmholtz free energies of the ferromagnetic nanocluster stand at a lower level compared to those of the ferromagnetic cluster. Our main conclusion is that the presence of the magnetic field leads to decrease in the amount of specific heat capacity for the ferromagnetic cluster. On the other hand, this effect leads to increase in the amount of specific heat capacity for the ferromagnetic nanocluster.