In this paper, using the concept of mutual information, we consider the Schwingers effect on an entangled state of a qubit and a bosonic mode coupled with the electric field. The system is initially prepared in the N00N state. Due to the Schwinger production of particle-antiparticle pairs, we observe the variation of the entanglement of the initial NOON state.

In this paper , the space-time fractional advection-diffusion equation (STFADE) is considered in the finite domain that the time and space derivatives are the Caputo fractional derivative . At first , a quadratic interpolation with convergence order is applied to obtain the semi-discrete in the time variable . Then , the Chebyshev collocation method of the fourth kind has been used to approximate the spatial fractional derivative . Finally , the accuracy of the numerical method is analyzed and showed that our method is much more accurate than existing techniques .

Hydrogen atom is always applicable for obtaining data from the other atoms. Revision of the algebraic approach in studying the radial part of the Hydrogen atom and using the Tilting transformation is a good guidance to discuss the alkali atoms. The characteristic property between Alkali atoms and Hydrogen is the screening effect in Alkali atoms which causes the net charge of the atom decreased and more freedom of the highest electron. By using the Lie algebra the energy levels of both bound and excited states and corresponding wave functions are obtained.

Here, we are going to study the existence of radial solutions of an elliptic problem with Neumann boundary condition on 𝛺 which is the unite Korányi ball in the Heisenberg group and the coefficients are satisfying in some suitable conditions. To prove this result, we apply a variational principle and mountain pass theorem.

We introduce semi-doubly stochastic operators, which is between doubly stochastic operators and Markov operators on the space of integrable functions and as an application of our result in quantum information theory, we use it for the problem of entanglement transformation. In fact, if we have target pure state we can identify the set of initial states that can be converted to by local operations and classical communication channel (LOCC channel).