The present study focuses on the examination of the propagation of plane surface waves on a coated half-space, which is accompanied by the magnetic field force, and the normal mechanical loading, due to Winkler’s elastic foundation. The study is based upon the application of the analytical and asymptotic integration procedures to acquire and further analyze the aspiring secular equation. Asymptotically, the influence of the coating layer is suppressed by deploying apposite effective boundary conditions that are ingrained on a long-wave approximation condition, to obtain the resulting pseudo-differential operator of the reduced equation of surface motion. In fact, the comparison between the two approaches yielded considerable agreement through the dependency plots, featuring the scaled velocity $v/v_R$ versus the dimensionless wavenumber $K.$ Moreover, certain well-known results in the literature are obtained as liming circumstances of the present examination. Additionally, an insightful finding about the vanishing possibility of the coating layer is illustratively highlighted.

In the present paper, we examine the quantum entanglement for more general states of two-qubit system in the context of spin coherent states (SCSs). We consider the concurrence as a quantifier of entanglement and express it in terms of SCSs. We determine new set of maximally entangled conditions that provide the maximal amount of entanglement for certain values of the amplitudes of SCSs for the case of pure states. Finally, we examine the entanglement of a class of mixed states of the two qubits and provide the range in which the entanglement value is maximal with respect to the values of the amplitudes of SCSs.

Some dynamical features of two- and three-level atoms interacting locally with an ideal cavity field are investigated. These dynamical features are introduced by employing the statistical atomic inversion, entropy squeezing, and tomographic entropy. Our results show that the initial setting states play an essential role in the temporal evolution of the three quantities. The sensitivity of the two-level atomic state is less than that depicted by the three-level atom. The initial state has a small impact on the two types of entropies for the two-level atom. However, it has an appreciable effect in the case of the three-level atom for different regulations of the initial atomic state.

In this framework, the effect of a Kerr-like medium and the coupling function dependent on the number of photons operator on the interaction between a two-level atom and a non-linear field is studied. A relation between the Kerr-like medium parameter and the field-atom coupling parameter is used to obtain a simplified formula for Rabi frequency. The wave function of the proposed model is obtained, followed by the derivation of the phase distribution and from which the wehrl entropy formula is calculated. The effect of the initial state and the non-linear func­tion dependent on the number of photons operator and the Kerr-like medium on entanglement is calculated through the Wehrl entropy formula, wehrl distribution and the behaviour of photons by studying the correlation function. The entangle­ment decreases when the function dependent on the number of photons operator is taken into account, while the entanglement gradually improves when the squeezed state is considered, and the entanglement decreases significantly when considering the Kerr medium. An oscillatory distribution is formed between the classical and non-classical in the coherent state. The non-classical distribution disappears when considering the squeezed state and the Kerr-like medium.