New Frontiers in Physical Science Research Vol. 3

We present an extension of General Relativity governed by a scalar Lagrangian density, function of all the independent invariant scalars one is able to build by the powers of the Ricci tensor. The new terms arising in the generalized Einstein filed equations, in the viewpoint of usual General Relativity, may be interpreted as dark matter and dark energy contributions. Metricity condition fulfilled by a new tensor different than the usual metric tensor is also obtained. More it is shown that Schwarzschild-De Sitter, Robertson-Walker-De Sitter and Kerr-De Sitter metrics are exact solutions to the new field equations. Remarkably the form of the equation of the geodesic trajectories of particle motions across space-time remains the same as in Einstein General Relativity unless the cosmological constant \(\Lambda\) is no longer a constant becoming a function of the space-time co-ordinates.

ZnO is naturally an n-type semiconductor with the wide direct band gap of 3.37 eV and the material is naturally abundant in the earth’s crust. Owing to its low toxicity ZnO finds application in devices like solar cells, flat panel displays and thin film transistors. It is a prominent wide bandgap material with appreciable transparency which is widely utilized in transparent conducting oxide layer applications. However, metal doping on ZnO reports was extensively investigated for tuning the electrical properties. This article is focused on pulsed laser deposition of ZnO-Y₂O₃ (YZO) thin films with various concentrations of Y₂O₃ (0-5%) as a dopant in ZnO. X-ray diffraction spectrum of the YZO thin films exhibits the presence of hexagonal wurtzite structure with a preferential orientation along the (002) plane. Morphology aspects of the film abide with XRD results which shows a uniform distribution till 2 wt% and resulted in grain growth with increasing wt% of Y₂O_3. The influence of Y₂O₃ concentration on the optical transmittance of ZnO is investigated by UV- Vis spectroscopy. The electrical resistivity of the deposited films is in the order \(\sim\)10^-4 which was on par with the earlier reports suitable for TCO applications.

A fresh illustration of a Jacobi elliptic potential-related quasi-exactly solvable 2 × 2 matrix Hamiltonian is developed.  In order for the Jacobi Hamiltonian to have a finite dimensional invariant vector space, we must satisfy three necessary and sufficient criteria, which we compute algebraically using the QES analytic approach.  It is referred to as being "quasi-exactly solvable" for the matrix Jacobi Hamiltonian.

We give a two-dimensional analysis of the classical conservation theorem-derived two-electron problem, from which we derive a particular form of the Dirac equation for the helium atom. Although in theory this problem can be solved analytically, approximate solutions for it are given using two different approaches. One approach is a Hylleraas-type variational approach, the execution of which is postponed until a subsequent communication. The set of equations in the alternative method will be divided into its angular and radial components for a more thorough study. Additionally, just for the fundamental state of the atom, an accurate solution for the angular component and an approximative solution for the radial component will be shown.

This chapter is devoted to the theoretical and practical aspects of the application of chaos theory. The objects of research are multidimensional nonlinear information systems. Methods for studying the behavior of multidimensional nonlinear information systems operating within the framework of the Open System are presented. It should be noted that the physics of open systems develops a unified approach to the description of a wide variety of non-linear phenomena. Using the achievements of such scientific fields as chaos theory, thermodynamics, visual thinking and artificial intelligence, it is possible to discover hidden patterns and additional knowledge when studying such complex systems. In studies of the dynamics of complex systems, various characteristic indicators are used. To study the development processes of a dynamic system in time, Poincare return times, Lyapunov exponents, Tsallis entropy, fractal dimensions of the system, stability parameters, etc. are used. In the final part of the chapter, all these informative characteristic indicators of the system under study are proposed to be used for the input layer of the Recurrent Neural Network of the Deep Learning Artificial Intelligence algorithm. The issues of visualization of measurement results and information processing using the "Visual Thinking" technology are considered. In the examples given, due attention is paid to the issues of modern visualization, which is the basis for the implementation of the "Visual Thinking" technology in research activities. The analysis of visual information characterizing the dynamics of the parameters of the system under study will increase the speed of assessing its behavior, as well as the validity of the decisions made on its control.

This chapter is continuation of application of a newly developed generalized formula for capacitor i.e. charge as a function of time, which is convolution operation of a time varying capacity function and a time-varying voltage function (different from capacitance multiplied by voltage to get charge stored in a capacitor). This chapter gives a theoretical validity test i.e. analytically obtained in several applications for this new formulation. This chapter will be useful in various super-capacitor studies, dielectric relaxation experiments, and impedance spectroscopy for various material developments for electrical energy storage missions. This new generalized formula is also verified experimentally. Here we use this new expression and apply to various types of input excitation voltages those are-sinusoidal, constant step, ramp voltage We analyze and interpret the effects, like the charge, the current, the loss-tangent and the memory effects, memorizing shape of input voltage and extend this to evaluate impedance function of a classical capacitor as well as a fractional capacitor. We also derive by using this new formula to get value of equivalent Farads for a fractional capacitor having units in fractional order elaborated on the Nyquist’s diagram.  However, this concept is yet to be used to its full potential.

Neutrinos can interact with photons in a thermal medium or an external electromagnetic field via the associated charged leptons (real or virtual). Neutrinos in a medium pick up an effective charge, which in the electroweak standard model originates from the vector type vertex of weak interaction. In a magnetized plasma, the axial vector part also start contributing to the effective charge of a neutrino dominantly to order \(\frac{eB}{m^2}\) for eB < m², when B is the magnetic field.We conclude by inferring the magnetic field dependent contribution to the neutrino charge from the vector type vertex.

The Extended Wigner’s Friend thought experiment, which involves a quantum system with an agent who draws conclusions based on the results of a measurement of a quantum state provided in two nonorthogonal versions by another agent, led its designers to the conclusion that quantum theory cannot consistently explain the use of itself. It has also been suggested that this thought experiment is equivalent to entangled state (Bell-type) experiments. This study indicates that the assumption of the first Wigner's friend's freedom of choice, regarding how to prepare a quantum state in one of the two available nonorthogonal versions, invalidates such equivalence. A no-go theorem for superposed actions is derived on this basis. It is also argued that modeling Wigner-type experiments under the principle of locality, i.e., using enclosed containers modeled as composite, many-body quantum states, is fundamentally wrong as it neglects quantum nonlocality.

The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. According to the special relativity theory, the group velocity with which the overall envelope shape of the wave, namely the related particle’s propagation and information convey speed is changeable with its energy and related wavelength, among which only the energy exceeds over the minimum value, the propagation can be starting and the velocity is not allowed to surpass the maximum value i.e. the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 8.187×10^-l4 J and the related wavelength is shorter than around 5.316×10^-3nm, the matter wave with information can start to propagate.

Microbe behavior can be characterized using the framework of non-equilibrium statistical mechanics because discontinuous activity is dependent on surrounding dynamics, which are a function of interactions with the environment. Microbial motion is typically thought to be Brownian, however when perturbations in the environment alter the fluctuations in the randomness of motion, the general situation resolves to a particular instance of Multi-Fractal Brownian motion. Bacterial cells dwell in an environment with a low Reynolds number, which makes inertia in their motion irrelevant. The use of the Fokker-Planck and Lotka-Volterra expressions yields both qualitative and quantitative findings. In this chapter, we have taken the best possible measures to define a complicated biological system using a physicsbased methodology.