Tunneling Quantum Dynamics in Ammonia

Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.

Atomic Forces and Tunneling

This chapter presents a unified theory of tunneling phenomenon and covalent bond force, as a result of the similarity between the Bardeen theory of tunneling and the Herring-Landau theory of the covalent bond. Three general theoretical treatments are presented, which show that tunneling conductance is proportional to the square of the covalent bond interaction energy, or equivalently, the square of covalent bond force. The constant of proportionality is related to the electronic properties of the materials. For the case of a metal tip and a metal sample, an explicit equation contains only measurable physical quantities is derived. Several experimental verifications are presented. The equivalence of covalent bond energy and tunneling conductance provides a theoretical explanation of the threshold resistance observed in atom-manipulation experiments, and points to a method of predicting the threshold resistance for atom manipulation. Theory of imaging wavefunctions with AFM is discussed.

Tunneling Phenomenon

This chapter presents basic experimental methods and the basic theory of tunneling. The classical metal-insulator-metal tunneling junction experiment of Giaever, designed to verify the Bardeen-Cooper-Schrieffer theory of superconductivity, is the motivation for Bardeen to invent his perturbation theory of tunneling. That Bardeen theory then became the starting point of the most useful models of STM. Section 2.2 presents the Bardeen tunneling theory from time-dependent perturbation theory of quantum mechanics, starting from a one-dimensional case, then proceeds to three-dimensional version with wave-function corrections. The Bardeen theory in second-quantization format, the transfer-Hamiltonian formalism, is also presented. As extensions of the original Bardeen theory, the theories and experiments of inelastic tunneling and spin-polarized tunneling are discussed in depth.

Stability Analysis of Charged Rotating Black Ring

We study the electromagnetic field equation along with the WKB approximation. The boson tunneling phenomenon from charged rotating black ring (CRBR) is analyzed. It is examined that reserve radiation consistent with CRBR can be computed in general by neglecting back reaction and self-gravitational of the radiated boson particle. The calculated temperature depends upon quantum gravity and CRBR geometry. We also examine the corrected tunneling rate/probability of boson particles by assuming charge as well as energy conservation laws and the quantum gravity. Furthermore, we study the graphical behavior of the temperature and check the stability and instability of CRBR.

Effect of the GUP on the Hawking radiation of black hole in 2 + 1 dimensions with quintessence and charged BTZ-like magnetic black hole

In this paper, we investigate the Hawking radiation process by using the quantum tunneling phenomenon of massive spin-1 (W-bosons) and spin-0 particles by the black hole in 2 + 1 dimensions surrounded by quintessence as well as charged BTZ-like magnetic black hole. First of all, by using Hamilton–Jacobi ansatz and WKB approximation to the field equation of massive vector particles, we get the required tunneling rate of emitted particles and obtain the corresponding Hawking temperature [Formula: see text] for the black hole (BH) surrounded by quintessence. In order to study the quantum gravity effects, we utilize the generalized Proca and Klein–Gordan equations incorporating the generalized uncertainty principle (GUP) for these BHs and recover their modified tunneling probability as well as accompanying quantum corrected temperatures [Formula: see text].

Effect of Quintessential and Magnetic Field on GUP Modified Hawking Radiation

In this paper, we investigate the Hawking radiation process by using the quantum tunneling phenomenon of massive spin-1 (W-bosons) and spin-0 particles from (2+1) dimensional Black Hoke with quintessential and magnetic field. For this purpose, using Hamilton-Jacobi ansatz, we apply the WKB approximation to the field equations of massive charged vector particles. We get the required tunneling rate of radiated particles and obtain their corresponding Hawking temperature $T_h$. In order to study the quantum gravity effects, we utilize the generalized Proca and Klein-Gordan equations incorporating the generalized uncertainty principle (GUP) and recover the accompanying quantum corrected temperature $T'_{h}$.

Charged vector particles tunneling from black ring and 5D black hole

In this paper, we have investigated the Hawking radiation process as a semiclassical quantum tunneling phenomenon from black ring and 5D Myers–Perry black holes. Using Lagrangian of Glashow–Weinberg–Salam model with background electromagnetic field (for charged W-bosons) and the Wentzel–Kramers–Brillouin approximation, we have evaluated the tunneling rate or probability of charged vector particles at through the horizons by taking into account the electromagnetic vector potential. Moreover, we have calculated the corresponding Hawking temperature via Boltzmann factor for both types of considered background and analyzed the whole spectrum generally.