The development of theories on the nature of light.

Thesis (M.A.)--Boston UniversityIn this thesis I plan to trace man's thoughts on the nature of light from earliest times up to the present. I shall select those highlights which will reveal the growth and development of each theory out of the experiences and speculations of the past. The chief contributors of the Greek and Roman period are Anaxagoras, Empedocles, Aristotle, Lucretius, and Euclid. The philosophers and scientists of this period had noted the rectilinear propagation of light, the equality of angles for incident and reflected rays at plane and concave surfaces, and the change of direction of a ray on entering a different medium. But only the first two of these properties could be explained by means of the current emission theories. The rainbow and mirage were quite familiar to the ancients. [TRUNCATED

Quantum collision theory with phase-space distributions

Quantum-mechanical phase-space distributions, introduced by Wigner in 1932, provide an intuitive alternative to the usual wave-function approach to problems in scattering and reaction theory. The aim of the present work is to collect and extend previous efforts in a unified way, emphasizing the parallels among problems in ordinary quantum theory, nuclear physics, chemical physics, and quantum field theory. The method is especially useful in providing easy reductions to classical physics and kinetic regimes under suitable conditions. Section II, dealing in detail with potential scattering of a spinless nonrelativistic particle, provides the background for more complex problems. Following a brief description of the two-body problem, the authors address the N-body problem with special attention to hierarchy closures, Boltzmann-Vlasov equations, and hydrodynamic aspects. The final section sketches past and possibly future applications to a wide variety of problems

Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference

We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. In this spirit, we provide a complete English translation of the original proceedings (lectures and discussions), and give background essays on the three main interpretations presented: de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schroedinger's wave mechanics. We provide an extensive analysis of the lectures and discussions that took place, in the light of current debates about the meaning of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a "quantum mechanics" apparently lacking in wave function collapse or fundamental time evolution. We hope that the book will contribute to the ongoing revival of research in quantum foundations, as well as stimulate a reconsideration of the historical development of quantum physics. A more detailed description of the book may be found in the Preface. (Copyright by Cambridge University Press (ISBN: 9780521814218).)Comment: 553 pages, 33 figures. Draft of a book (as of Sept. 2006, same as v1). Published in Oct. 2009, with corrections and an appendix, by Cambridge University Press (available at http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521814218

Two-particle level diagrammatic approaches for strongly correlated systems

This thesis presents the development of new numerical methods for the treatment of strongly correlated electron systems based on self-consistent approaches at both the one and the two-particle level such as the parquet formalism. The parquet formalism was solved for the first time on a two-dimensional cluster. When the fully irreducible vertex is approximated by the bare vertex, we obtain the parquet approximation. Its validity was investigated by comparing results that it produces to those of other conserving approximations such as the FLuctuation EXchange (FLEX) approximation or the Second Order Perturbation Theory (SOPT). We found that it provides a significant improvement of FLEX or SOPT and a satisfactory agreement with Quantum Monte Carlo results despite instabilities in the self-consistency at low temperatures and for strong Coulomb interaction. We use the parquet formalism to study the Quantum Critical Point at finite doping in the Hubbard model by decomposing the vertex into its contributions from different channels. We apply this decomposition to the pairing channel and we find that the dominant contribution to the vertex originates in the spin channel even at the quantum critical doping. Furthermore, we explore the divergence of the two parts of the pairing matrix at optimal doping and observe that the irreducible vertex decreases monotonically as the doping is increased while the bare susceptibility exhibits an algebraic divergence at the quantum critical doping supporting the Quantum Critical BCS scenario proposed by She and Zaanen. To circumvent the instabilities in the iteration of the parquet formalism, we explored the dual fermion approach introduced by Rubtsov et al. Here, we extended the formalism to the Dynamical Cluster Approximation, in the process introducing a small parameter in the dual fermions perturbation theory. We demonstrate the quality of the resulting Dual Fermion DCA through a systematic study of the cluster size dependence and of the different perturbative approximations. These efforts represent the initial steps in the development of the Multi-Scale Many Body approach that appropriately treats correlations at different length scales

Higher dimensional theories in physics, following the Kaluza model of unification

This thesis traces the origins and evolution of higher dimensional models in physics, with particular reference to the five-dimensional Kaluza-Klein unification. It includes the motivation needed, and the increasing status and significance of the multidimensional description of reality for the 1990's. The differing conceptualisations are analysed, from the mathematical, via Kasner's embedding dimensions and Schrodinger's waves, to the high status of Kaluza-Klein dimensions in physics today. This includes the use of models, and the metaphysical interpretations needed to translate the mathematics. The main area of original research is the unpublished manuscripts and letters of Theodor Kaiuza, some Einstein letters, further memoirs from his son Theodor Kaiuza Junior and from some of his original students. Unpublished material from Helsinki concerns the Finnish physicist Nordstrom, the real originator of the idea that 'forces' in 4-dimensional spacetime might arise from gravity in higher dimensions. The work of the Swedish physicist Oskar Klein and the reactions of de Broglie and Einstein initiated the Kaluza-Klein connection which is traced through fifty years of neglect to its re-entry into mainstream physics. The cosmological significance and conceptualisation through analogue models is charted by personal correspondence with key scientists across a range of theoretical physics, involving the use of aesthetic criteria where there is no direct physical verification. Qualitative models implicitly indicating multidimensions are identified in the paradoxes and enigmas of existing physics, in Quantum Mechanics and the singularities in General Relativity. The Kaluza-Klein philosophy brings this wide range of models together in the late 1980's via supergravity, superstrings and supermanifolds. This new multidimensional paradigm wave is seen to produce a coherent and consistent metaphysics, a new perspective on reality. It may also have immense potential significance for philosophy and theology. The thesis concludes with the reality question, "Are we a four-dimensional projection of a deeper reality of many, even infinite, dimensions?

Physics-based multiscale modeling of III-nitride light emitters

The application of computer simulations to scientific and engineering problems has evolved to an established phase over the last decades. In the field of semiconductor device physics, Technology CAD (TCAD) has been regarded as an indispensable tool for the interpretation and prediction of device behavior. More specifically, TCAD modeling and simulation of nanostructured III-nitride light emitters still have challenging problems and is currently a topic under active research. This thesis devotes to the theoretical and numerical investigations of III-nitride bulk and quantum structures, following a bottom-up approach aimed at modeling and understanding photoluminescence and electroluminescence in these structures. In the first part, the calculation of electronic bandstructure is addressed, where a novel k · p model derived from Non-local Empirical Pseudopotential method(NL-EPM) is presented. Optical properties are then calculated employing both Poisson-k · p and a density-matrix based approach, gain and luminescence spectra can be extracted by solving the semiconductor-Bloch equation numerically. The last part of this thesis deals with the microscopic quantum transport, within the framework of the quantum-statistical nonequilibrium Greens function formalism(NEGF). While classical drift-diffusion models assume that bound carriers hold their coherence in the confined direction and unbound carriers are completely incoherent, NEGF does not distinguish between bound and unbound states and treats them on equal footing. In addition, NEGF also provides intuitive insights into energy-resolved carrier distributions, currents and coherence loss mechanisms. The numerical computations alongside this thesis can be computationally very involved, some code developed along with this thesis is deployed on the clusters and able to scale up to more than 1000 CPU cores, thanks to the parallel implementation technique such as OpenMP and MPI, as well as HPC infrastructures available at CINECA computing center

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

Wavelet-based semiconductor device simulation.

by Pun Kong-Pang.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 94-[96]).Acknowledgement --- p.iAbstract --- p.iiiList of Tables --- p.viiList of Figures --- p.viiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Role of Device Simulation --- p.2Chapter 1.2 --- Classification of Device Models --- p.3Chapter 1.3 --- Sections of a Typical Simulator --- p.6Chapter 1.4 --- Arrangement of This Thesis --- p.7Chapter 2 --- Classical Physical Model --- p.9Chapter 2.1 --- Carrier Densities --- p.12Chapter 2.2 --- Space Charge --- p.14Chapter 2.3 --- Carrier Mobilities --- p.15Chapter 2.4 --- Generation and Recombination --- p.17Chapter 2.5 --- Modeling of Device Boundaries --- p.20Chapter 2.6 --- Limits of Classical Device Modeling --- p.22Chapter 3 --- Computational Aspects --- p.23Chapter 3.1 --- Normalization --- p.24Chapter 3.2 --- Discretization --- p.26Chapter 3.2.1 --- Finite Difference Method --- p.26Chapter 3.2.2 --- Finite Element Method --- p.27Chapter 3.3 --- Nonlinear Systems --- p.28Chapter 3.3.1 --- Newton's Method --- p.28Chapter 3.3.2 --- Gummel's Method and its modification --- p.29Chapter 3.3.3 --- Comparison and discussion --- p.30Chapter 3.4 --- Linear System and Sparse Matrix --- p.32Chapter 4 --- Cubic Spline Wavelet Collocation Method for PDEs --- p.34Chapter 4.1 --- Cubic spline scaling functions and wavelets --- p.35Chapter 4.1.1 --- Approximation for a function in H2(I) --- p.43Chapter 4.2 --- Wavelet interpolation --- p.45Chapter 4.2.1 --- Interpolant operator Ivo in Vo --- p.45Chapter 4.2.2 --- Interpolation operator IWjf in Wj --- p.47Chapter 4.3 --- Derivative Matrices --- p.51Chapter 4.3.1 --- First derivative matrix --- p.51Chapter 4.3.2 --- Second derivative matrix --- p.53Chapter 4.4 --- Wavelet Collocation Method for Solving Device Equations --- p.55Chapter 4.4.1 --- Steady state solution --- p.57Chapter 4.4.2 --- Transient solution --- p.58Chapter 4.5 --- Reducing Collocation Points --- p.59Chapter 4.5.1 --- Error evaluation --- p.59Chapter 4.5.2 --- Deleting collocation points --- p.61Chapter 5 --- Numerical Results --- p.64Chapter 5.1 --- P-N Junction Diode --- p.64Chapter 5.1.1 --- Steady state solution --- p.69Chapter 5.1.2 --- Transient solution --- p.76Chapter 5.1.3 --- Convergence --- p.79Chapter 5.2 --- Bipolar Transistor --- p.81Chapter 5.2.1 --- Boundary Model --- p.82Chapter 5.2.2 --- DC Solution --- p.83Chapter 5.2.3 --- Transient Solution --- p.89Chapter 6 --- Conclusions --- p.92Bibliography --- p.9