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In this paper, we combine the Hamilton-Jacobi equation with a new general tortoise coordinate transformation to study quantum tunneling of scalar particles and fermions from the non-stationary higher dimensional Vaidya-de Sitter black hole. The results show that Hamilton-Jacobi equation is a semi-classical foundation equation which can easily derived from the particles’ dynamic equations, it can helps us understand the origin of Hawking radiation. Besides, based on the dimensional analysis, we believed that the new general tortoise coordinate transformation is more reasonable than old ones.

In this article, the two-dimensional time fractional unsteady convection-diffusion system is under consideration. The convection-diffusion system of nonlinear partial differential equations has remained a uniform fascination for scientists owing to its energetic significance as well as its possession of a broad spectrum of practical and physical applications. In particular, these practicable implications include turbulence, heat transfer, fluid flow, traffic flow, and modeling of gas dynamics. The Caputo operator is applied for the fractional order derivatives and their inversion. The existence of results and uniqueness is proved by applying the fixed point theory with the help of some well-known results and theorems such as the contraction mapping theorem with Lipschitz condition, and Schauder’s fixed point theorem. Mainly, we find the exact solitary wave solutions of the underlying model. For this sake, the new extended direct algebraic method is applied and the solutions are gained in the form of dark, singular, complex, combo, trigonometric and rational solutions. Further, we draw 3D plots to show the behavior of these solutions by choosing the different values of parameters.

We introduce an interpretation of quantum superposition in predicative sequent calculus, in the framework of basic logic. Then we introduce a new predicative connective for the entanglement. Our aim is to represent quantum parallelism in terms of logical proofs.

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.

We propose some formulations of the notion of “operational independence” of two subsystems S 1,S 2 of a larger quantum system S and clarify their relation to other independence concepts in the literature. In addition, we indicate why the operational independence of quantum subsystems holds quite generally, both in nonrelativistic and relativistic quantum theory.

We propose a teleportation protocol and a dense coding protocol. In these protocols, one sender intends to send quantum states or classical bits to two receivers through two GHZ entanglement channels. The entanglement channels are locked by the sender and the communication process is supervised by a controller. In order to obtain the messages, the receivers need the controller’s permission, and must collaborate to unlock the entanglement channels.