Iterative treatment of the Coulomb potential in laser–atom interactions

We discuss a Faddeev-like iterative approach which allows one to consistently include the Coulomb potential in strong field phenomena through a Born series. To assess the validity of this approach, we calculate the probability of excitation to given states of atomic hydrogen exposed to radiation pulses of various frequencies, durations and peak intensities and compare our results with those obtained by solving numerically the time-dependent Schrödinger equation. We obtain excellent agreement for a range of frequencies. As the frequency decreases, many high-order terms have to be included in order to get convergence of the Born series. Our results indicate that this Faddeev-like method is particularly suitable to treat the interaction of atoms with attosecond pulses. For the lowest frequency considered ($$\omega = 0.057$$ ω = 0.057 a.u.), we study in more detail the re-collision-based frustrated tunneling process in atomic hydrogen and compare our results with those existing in the literature. Graphic Abstract

Minimizing of tunneling effect on existing infrastructure in Egypt

A set of parametric studies by using the Abaqus software is conducting to investigate the effective method to seal the CWO sewer from the tunneling process. These methods include: (i) two deep grouted walls, (ii) adjacent slurry piles, (iii) bored reinforced concrete piles assisted with slurry piles, and (iv) grouted block confining the twin tunnel wall. Based on the results of parametric studies. Most of the protective studied technique was effective on reducing the tunneling effect on the ground movements.

Tunneling-induced Talbot effect

We investigate the reforming of a plane wave into a periodic waveform in its propagation through a structural asymmetry four-level quantum dot molecule (QDM) system that is induced by an inter-dot tunneling process and present the resulting tunneling-induced Talbot effect. The tunneling process between two neighborhood dots is provided with the aid of a gate voltage. Using a periodic coupling field the response of the medium to the propagating plane probe beam becomes periodic. The needed periodic coupling field is generated with the interference of two coherent plane waves having a small angle and propagating almost parallel to the probe beam direction. In the presence of the tunneling effect of an electron between two adjacent QDs, for the probe beam propagating through the QDM system, the medium becomes transparent where the coupling fields interfere constructively. As a result, the spatial periodicity of the coupling field modulates the passing plane probe beam. We determine the minimum length of the QDM system to generate a periodic intensity profile with a visibility value equal to 1 for the probe field at the exit plane of the medium. It is also shown that by increasing the propagation length of the probe beam through the QDM medium, the profile of the maximum intensity areas becomes sharper. This feature is quantified by considering a sharpness factor for the intensity profile of the probe beam at the transverse plane. Finally, we investigate free space propagation of the induced periodic field and present the Talbot images of the tunneling-induced periodic patterns at different propagation distances for different values of the QDM medium lengths. The presented dynamically designing method of the periodic coherent intensity patterns might find applications in science and technology. For instance, in optical lithography, the need to use micro/nanofabricated physical transmission diffraction gratings, in which preparation of them is expensive and time-consuming, can be eliminated.

All waves have a zero tunneling time

Zero tunneling time and thereby a faster than light traversal velocity was calculated nearly a hundred years ago and has been observed recently. We report about experimental results and estimations, which confirm the zero time tunneling for elastic as well as for electromagnetic and Schrödinger waves. Zero time tunneling was first observed with microwaves 1992 (H. Aichmann and G. Nimtz, Found. Phys., vol. 44, p. 678, 2014; A. Enders and G. Nimtz, J. Phys. I, vol. 2, p. 169, 1992). In 2008, zero time was also observed for tunneling electrons (P. Eckle, A. N. Pfeiffer, C. Cirelli, et al., Science, vol. 322, p. 1525, 2008). Presumably, this effect took place with atoms quite recently (R. Ramos, D. Spierings, I. Racicot, and A. M. Steinberg, Nature, vol. 583, p. 529, 2020). The Einstein relation E 2 = (ħk)2 c 2 is not satisfied in the tunneling process, since the wave number k is imaginary (E is the total energy, ħ the Planck constant, and c the vacuum velocity of light), Zero time tunneling is described by virtual photons (A. Stahlhofen and G. Nimtz, Europhys. Lett., vol. 76, p. 189, 2006). The tunneling process itself violates the Special Theory of Relativity. Remarkably, Brillouin conjectured that wave mechanics is valid for all waves independent of their field (L. Brillouin, Wave Propagation in Periodic Structures, Chap. VIII, New York, Dover Publications, 1953).

GUP effect on thermodynamical properties of the noncommutative rotating BTZ black hole

In this paper, we investigated the quantum gravity effects on the thermal properties of the [Formula: see text]-dimensional noncommutative rotating Banados–Teitelboim–Zanelli (NCR-BTZ) black hole in the context of quantum tunneling of relativistic particles. These include Hawking temperature, the thermally local and global stability conditions, and the phase transitions. For this purpose, in the framework of the generalized uncertainty principle (GUP), we used the Hamilton–Jacobi approach to calculate the tunneling probability for a massive scalar, Dirac, and vector boson particles from the [Formula: see text]-dimensional NCR-BTZ black hole. We found that the modified Hawking temperature of the black hole depends on the black hole properties, on the tunneling particle properties, on the noncommutative parameter, and on the GUP parameter. Using the modified Hawking temperature, we calculated the modified heat capacity, and then we discussed the local thermodynamic stability conditions for the black hole. The black hole may undergo a first-type phase transition to become stable under the scalar particle tunneling whereas, it might undergoes both the first and the second-type phase transitions under the both Dirac and vector boson particles tunneling process. Furthermore, we calculated the Gibbs free energy of the black hole, and we investigated the global stability conditions. We observed that Hawking–Page phase transition may occur in the presence of the quantum gravity effect under the tunneling process of scalar, Dirac, and vector boson particles. In the context of quantum gravity effect, we also derived the modified equation of state to investigate the critical behavior of the commutative rotating BTZ black hole. Finally, we shown that Van der Waals-like phase transition may occur in the context of tunneling process of both Dirac and vector boson particle, whereas it may not occur for the tunneling of scalar particle.