Mathematical Physics Of Quantum Wires And Devices
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| Author | : N.E. Hurt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 318 |
| Release | : 2013-03-14 |
| Genre | : Science |
| ISBN | : 9401596263 |
This monograph on quantum wires and quantum devices is a companion vol ume to the author's Quantum Chaos and Mesoscopic Systems (Kluwer, Dordrecht, 1997). The goal of this work is to present to the reader the mathematical physics which has arisen in the study of these systems. The course which I have taken in this volume is to juxtapose the current work on the mathematical physics of quantum devices and the details behind the work so that the reader can gain an understanding of the physics, and where possible the open problems which re main in the development of a complete mathematical description of the devices. I have attempted to include sufficient background and references so that the reader can understand the limitations of the current methods and have direction to the original material for the research on the physics of these devices. As in the earlier volume, the monograph is a panoramic survey of the mathe matical physics of quantum wires and devices. Detailed proofs are kept to a min imum, with outlines of the principal steps and references to the primary sources as required. The survey is very broad to give a general development to a variety of problems in quantum devices, not a specialty volume.
| Author | : N. E. Hurt |
| Publisher | : |
| Total Pages | : 320 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9789401596275 |
| Author | : Pavel Exner |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829009 |
This work contains contributions presented at the conference, QMath-8: Mathematical Results in Quantum Mechanics'', held at Universidad Nacional Autonoma de Mexico in December 2001. The articles cover a wide range of mathematical problems and focus on various aspects of quantum mechanics, quantum field theory and nuclear physics. Topics vary from spectral properties of the Schrodinger equation of various quantum systems to the analysis of quantum computation algorithms. The book should be suitable for graduate students and research mathematicians interested in the mathematical aspects of quantum mechanics.
| Author | : Hamed Kalhori |
| Publisher | : MDPI |
| Total Pages | : 218 |
| Release | : 2021-06-15 |
| Genre | : Technology & Engineering |
| ISBN | : 3036510664 |
The inverse dynamics problem was developed in order to provide researchers with the state of the art in inverse problems for dynamic and vibrational systems. Contrasted with a forward problem, which solves for the system output in a straightforward manner, an inverse problem searches for the system input through a procedure contaminated with errors and uncertainties. An inverse problem, with a focus on structural dynamics, determines the changes made to the system and estimates the inputs, including forces and moments, to the system, utilizing measurements of structural vibration responses only. With its complex mathematical structure and need for more reliable input estimations, the inverse problem is still a fundamental subject of research among mathematicians and engineering scientists. This book contains 11 articles that touch upon various aspects of inverse dynamic problems.
| Author | : Floyd Williams |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200091 |
This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.
| Author | : Pavel Exner |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 721 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821844717 |
This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.
| Author | : Aref Jeribi |
| Publisher | : Birkhäuser |
| Total Pages | : 406 |
| Release | : 2015-10-05 |
| Genre | : Mathematics |
| ISBN | : 331918041X |
This contributed volume presents some recent theoretical advances in mathematics and its applications in various areas of science and technology. Written by internationally recognized scientists and researchers, the chapters in this book are based on talks given at the International Conference on Advances in Applied Mathematics (ICAAM), which took place December 16-19, 2013, in Hammamet, Tunisia. Topics discussed at the conference included spectral theory, operator theory, optimization, numerical analysis, ordinary and partial differential equations, dynamical systems, control theory, probability, and statistics. These proceedings aim to foster and develop further growth in all areas of applied mathematics.
| Author | : Gregory Berkolaiko |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 291 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 0821892118 |
A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
| Author | : Rolando Rebolledo |
| Publisher | : World Scientific |
| Total Pages | : 339 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9814338737 |
This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
| Author | : Rolando Rebolledo |
| Publisher | : World Scientific |
| Total Pages | : 339 |
| Release | : 2011-01-19 |
| Genre | : Mathematics |
| ISBN | : 9814462179 |
This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
