Gravitational Tunneling Radiation

The isolated black hole radiation of both Hawking and Zel'dovich are idealized abstractions as there is always another body to distort the potential. This is considered with respect to both gravitational tunneling, and black hole "no-hair" theorems. The effects of a second body are to lower the gravitational barrier of a black hole and to give the barrier a finite rather than infinite width so tha a particle can escape by tunneling (as in field emission) or over the top of the lowered barrier (as in Schottky emission). Thus radiation may be emitted from black holes in a process differing from that of Hawking radiation, P SH, which has been undetected for over 24 years. The radiated power from a black hole derived here is PR e ^2__ PSH, where e ^2__ is he ransmission probability for radiation through the barrier. This is similar to electric field emission of electrons from a metal in that the emission can in principle be modulated and beamed. The temperature and entropy of black holes are reexamined. Miniscule black holes herein may help explain the missing mass of the universe, accelerated expansion of the universe, and anomalous rotation of spiral galaxies. A gravitational interference effect for black hole radiation similar to the Aharonov-Bohm effect is also examined.Comment: 29 pages, 4 figures Keywords: Hawking-Zel'dovich Radiation, black holes, gravitational tunneling, universe expansion, galaxy rotation, Aharonov-Bohm effect, hairy black holes, entrop

On the Use of Multipole Expansion in Time Evolution of Non-linear Dynamical Systems and Some Surprises Related to Superradiance

A new numerical method is introduced to study the problem of time evolution of generic non-linear dynamical systems in four-dimensional spacetimes. It is assumed that the time level surfaces are foliated by a one-parameter family of codimension two compact surfaces with no boundary and which are conformal to a Riemannian manifold C. The method is based on the use of a multipole expansion determined uniquely by the induced metric structure on C. The approach is fully spectral in the angular directions. The dynamics in the complementary 1+1 Lorentzian spacetime is followed by making use of a fourth order finite differencing scheme with adaptive mesh refinement. In checking the reliability of the introduced new method the evolution of a massless scalar field on a fixed Kerr spacetime is investigated. In particular, the angular distribution of the evolving field in to be superradiant scattering is studied. The primary aim was to check the validity of some of the recent arguments claiming that the Penrose process, or its field theoretical correspondence---superradiance---does play crucial role in jet formation in black hole spacetimes while matter accretes onto the central object. Our findings appear to be on contrary to these claims as the angular dependence of a to be superradiant scattering of a massless scalar field does not show any preference of the axis of rotation. In addition, the process of superradiance, in case of a massless scalar field, was also investigated. On contrary to the general expectations no energy extraction from black hole was found even though the incident wave packets was fine tuned to be maximally superradiant. Instead of energy extraction the to be superradiant part of the incident wave packet fails to reach the ergoregion rather it suffers a total reflection which appears to be a new phenomenon.Comment: 49 pages, 11 figure

Physics-informed Reduced-Order Learning from the First Principles for Simulation of Quantum Nanostructures

Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices, etc. In large-scale nanostructures, extensive computational effort needed in DNS may become prohibitive due to the high degrees of freedom (DoF). This study employs a reduced-order learning algorithm, enabled by the first principles, for simulation of the Schr\"odinger equation to achieve high accuracy and efficiency. The proposed simulation methodology is applied to investigate two quantum-dot structures; one operates under external electric field, and the other is influenced by internal potential variation with periodic boundary conditions. The former is similar to typical operations of nanoelectronic devices, and the latter is of interest to simulation and design of nanostructures and materials, such as applications of density functional theory. Using the proposed methodology, a very accurate prediction can be realized with a reduction in the DoF by more than 3 orders of magnitude and in the computational time by 2 orders, compared to DNS. The proposed physics-informed learning methodology is also able to offer an accurate prediction beyond the training conditions, including higher external field and larger internal potential in untrained quantum states.Comment: 18 pages, 11 figures. An additional demonstration using Fourier-based plan waves in the revised versio

Developing Exchange-Correlation and Kinetic Energy Functional Approximations for Density Functional Theory

A nearly endless amount of technology relies on the understanding of the properties of matter and materials. Because the properties emerge from the motion of the electrons within matter, deepest and most accurate understanding can only be achieved by measuring or simulating the electronic structure. This thesis considers the computational simulation aspect, and currently the most popular way of conducting these simulations on a computer is density functional theory (DFT). The accuracy of the DFT calculations mostly depends on a small, but very important, component of the total energy — the exchange-correlation (XC) energy. The exact form of the XC energy term is not known and therefore always has to be approximated. When calculating very big systems also the kinetic energy term has to approximated in an orbital-free manner, because computing the electronic orbitals is too expensive for the big systems. Firstly, a new gradient-level XC approximation calledQNAis presented, and it is designed for the calculation of metallic bulk alloys. QNA exploits the subsystem functional scheme to address the issue of inconsistent performance that current gradient-level approximations have with many alloys. QNA is shown to produce more accurate binary alloy formation energies, and the good accuracy of formation energies is very important in alloy theory. Secondly, a new method of computing the kinetic energy without orbitals is presented and tested in practice. This method allows one, in principle, to perform orbital-free calculations for spherically symmetric systems at the high accuracy level of orbital DFT. A succesful orbital-free solution for the electronic structure of the Be atom is presented. One of the ultimate goals in DFT research is to combine the high accuracy of orbital DFT with the excellent computational speed of orbital-free DFT, and the proofof-concept solution for the Be atom is a step in this direction.Tiheysfunktionaaliteoriaa varten kehitetyt vaihtokorrelaatio- ja liike-energia –approksimaatiot Lähes lukematon määrä teknologiaa nojautuu aineen ja materiaalien ominaisuuksien ymmärtämiseen. Koska nämä ominaisuudet kumpuavat aineen koossapitävästä elektronirakenteesta, syvällisin ja kaikista tarkin ymmärrys voidaan saavuttaa ainoastaan mittaamalla tai simuloimalla kyseistä elektronirakennetta. Tämä väitöskirja käsittelee jälkimmäistä vaihtoehtoa, eli elektronirakenteen mallintamista tietokoneella tehtävien laskujen avulla. Nykyään suosituin tällaisista laskentamenetelmistä on tiheysfunktionaalimenetelmä. Tiheysfunktionaaliteoriaan pohjautuvien laskujen tarkkuus riippuu pääasiassa yhdestä pienestä, mutta erittäin tärkeästä kokonaisenergian komponentista—vaihto-korrelaatioenergiasta. Vaihto-korrelaatioenergian tarkkaa matemaattista muotoa ei tunneta, joten sille on aina käytettävä jotakin approksimaatiota. Kun halutaan mallintaa erittäin kookkaita systeemejä, myös liike-energia on approksimoitava orbitaalivapaalla tavalla, sillä orbitaalien laskeminen kookkaille systeemeille on liian aikaavievää. Ensimmäiseksi tässä tutkielmassa esitetään uusi gradientti-tason vaihto- korrelaatioapproksimaatio QNA, joka on suunniteltu metalliseosten laskemiseen.QNA hyödyntää alisysteemifunktionaaleja (subsystem functional scheme) parantamaan laskujen tarkkuutta metalliseoksille verrattuna nykyisiin gradienttitason funktionaaleihin. Nykyiset gradienttitason funktionaalit eivät useinkaan pysty mallintamaan kaikkia seoksen komponentteja (puhtaat alkuaineet) tarkasti, minkä tässä väitöskirjassa osoitetaan johtavan epätarkkoihin tuloksiin itse seokselle. QNA-approksimaatiossa kukin seoksen komponentti mallinnetaan erillisen alisysteemifunktionaalin avulla, jolloin kukin komponentti ja itse seos voidaan laskea tarkasti. Käytännön laskuilla osoitetaan, että QNA tuottaa erittäin tarkkoja muodostumisenergioita kaksikomponenttisille metalliseoksille, mikä on erittäin tärkeä seikka metalliseosten teoriassa

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD

Perturbative Semiclassical Trace Formulae for Harmonic Oscillators

In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting $\mathrm{U}(D)$ to $\mathrm{O}(D)$ symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative ($\hbar \rightarrow 0$) trace formula. We then show how to apply the results to even order polynomial potentials, possibly including mean-field terms. We have drawn the conclusion that the gross structure of the quantum spectrum is determined from only classical circular- and diameter-orbits for this class of systems.Comment: Added a comparison with Einstein-Brillouin-Keller theory. To appear in Reports on Mathematical Physic

Nicholas Charles Handy. 17 June 1941 - 2 October 2012

Nicholas Handy made significant contributions in the applications of quantum mechanics to molecules. In an academic career at Cambridge University he was involved with many advances in the computational methods that have turned quantum chemistry into a central tool for understanding modern molecular science

Ground state properties of a weakly-bound three-body halo system

In this dissertation, we investigate the role of the nucleon-nucleon (nn) and threebody interactions on the ground-state structure of the 22C! 20C + n + n borromean system. We start by outlining the theoretical formulation of a three-body bound-state problems, starting with the fundamentals of two-body bound and scattering states. The different steps leading to the transformation of the three-body Schrödinger equation into a one-dimensional set of coupled differential equations are shown. These equations are numerically solved to obtain the three-body groundstate binding energy. The analysis of the numerical results show that even in the absence of the nn interaction, the system remains bound, provided the three-body interaction becomes more attractive. Similarly, the system remains bound in the absence of the three-body interaction, provided the nn interaction becomes more attractive. The ground-state binding energy is also found to be a continuous function of the strengths and ranges of both interactions, meaning that when these parameters increase, the binding energy increases as well, making the system to be more compact. The study presented in this dissertation highlights the interplay of the nn and three-body interactions in the dynamics of the three-body neutron-halo system. These results have been published in the Brazilian Journal of Physics (2022) 52, 193. DOI: https://doi.org/10.1007/s13538-022-01194-5. Using the ground-state binding energy, various thermodynamic properties such as the mean energy, the free energy, the entropy as well as the specific heat capacity of this system are also calculated.Physic