Download or read book Multi scale Analysis for Random Quantum Systems with Interaction written by Victor Chulaevsky and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: an introduction to the state-of-the-art single-particle localization theory an extensive discussion of relevant technical aspects of the localization theory a thorough comparison of the multi-particle model with its single-particle counterpart a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.
Download or read book Random Operators written by Michael Aizenman and published by American Mathematical Soc.. This book was released on 2015-12-11 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.
Download or read book Multiscale Methods in Quantum Mechanics written by Philippe Blanchard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.
Download or read book Interacting Stochastic Systems written by Jean-Dominique Deuschel and published by Springer Science & Business Media. This book was released on 2005-01-12 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work. This yields a reference work on results and methods that will be useful to all who work between applied probability and the physical, economic, and life sciences.
Download or read book Adventures in Mathematical Physics written by Jean-Michel Combes and published by American Mathematical Soc.. This book was released on 2007 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of refereed research articles written by some of the speakers at this international conference in honor of the sixty-fifth birthday of Jean-Michel Combes. The topics span modern mathematical physics with contributions on state-of-the-art results in the theory of random operators, including localization for random Schrodinger operators with general probability measures, random magnetic Schrodinger operators, and interacting multiparticle operators with random potentials; transport properties of Schrodinger operators and classical Hamiltonian systems; equilibrium and nonequilibrium properties of open quantum systems; semiclassical methods for multiparticle systems and long-time evolution of wave packets; modeling of nanostructures; properties of eigenfunctions for first-order systems and solutions to the Ginzburg-Landau system; effective Hamiltonians for quantum resonances; quantum graphs, including scattering theory and trace formulas; random matrix theory; and quantum information theory. Graduate students and researchers will benefit from the accessibility of these articles and their current bibliographies.
Download or read book Multi Scale Phenomena in Complex Fluids written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles of Multiscale Modeling written by Weinan E and published by Cambridge University Press. This book was released on 2011-07-07 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic discussion of the fundamental principles, written by a leading contributor to the field.
Download or read book Lattice Gas Cellular Automata and Lattice Boltzmann Models written by Dieter A. Wolf-Gladrow and published by Springer. This book was released on 2004-10-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Download or read book Multiscale Methods in Quantum Mechanics written by P. Blanchard and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Innovations in Biomolecular Modeling and Simulations written by Tamar Schlick and published by Royal Society of Chemistry. This book was released on 2012 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set describes innovations in biomolecular modeling and simulation, in both the algorithmic and application fronts.
Download or read book Multi Scale Phenomena in Complex Fluids written by Thomas Y. Hou and published by World Scientific. This book was released on 2009 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Scale Phenomena in Complex Fluids is a collection of lecture notes delivered during the first two series of mini-courses from OC Shanghai Summer School on Analysis and Numerics in Modern SciencesOCO, which was held in 2004 and 2006 at Fudan University, Shanghai, China. This review volume of 5 chapters, covering various fields in complex fluids, places emphasis on multi-scale modeling, analyses and simulations. It will be of special interest to researchers and graduate students who want to work in the field of complex fluids."
Download or read book Waves in Periodic and Random Media written by Peter Kuchment and published by American Mathematical Soc.. This book was released on 2003 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure. This book contains the proceedings of the research conference, ``Waves in Periodic and Random Media''. Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1994-03 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ERDA Energy Research Abstracts written by and published by . This book was released on 1989 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multi scale Phenomena in Complex Fluids written by Thomas Y. Hou and published by World Scientific. This book was released on 2009 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Scale Phenomena in Complex Fluids is a collection of lecture notes delivered during the ªrst two series of mini-courses from "Shanghai Summer School on Analysis and Numerics in Modern Sciences," which was held in 2004 and 2006 at Fudan University, Shanghai, China. This review volume of 5 chapters, covering various fields in complex fluids, places emphasis on multi-scale modeling, analyses and simulations. It will be of special interest to researchers and graduate students who want to work in the field of complex fluids.
Download or read book Dynamics of Systems on the Nanoscale written by Ilia A. Solov'yov and published by Springer Nature. This book was released on 2022-06-03 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the structure formation and dynamics of animate and inanimate matter on the nanometre scale. This is a new interdisciplinary field known as Meso-Bio-Nano (MBN) science that lies at the intersection of physics, chemistry, biology and material science. Special attention in the book is devoted to investigations of the structure, properties and dynamics of complex MBN systems by means of photonic, electronic, heavy particle and atomic collisions. This includes problems of fusion and fission, fragmentation, surfaces and interfaces, reactivity, nanoscale phase and morphological transitions, irradiation-driven transformations of complex molecular systems, collective electron excitations, radiation damage and biodamage, channeling phenomena and many more. Emphasis in the book is placed on the theoretical and computational physics research advances in these areas and related state-of-the-art experiments. Particular attention in the book is devoted to the utilization of advanced computational techniques and high-performance computing in studies of the dynamics of systems.
Download or read book Design and Applications of Nanomaterials for Sensors written by Jorge M. Seminario and published by Springer. This book was released on 2014-07-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design and Applications of Nano materials for Sensors begins with an introductory contribution by the editors that: gives an overview of the present state of computational and theoretical methods for nanotechnology; outlines hot topics in this field and points to expected developments in the near future. This general introduction is followed by 15-30 review chapters by invited experts who have substantially contributed to the recent developments of nano materials for sensors. Guided by molecular and quantum theories, this contributed volume gives a broad picture of the current and past advances that were necessary to develop nano sensors using nano materials. To illustrate the important and relevant applications of nano materials, Design and Applications of Nano materials for Sensors focuses on recent advances that extend the scope of possible applications of the theory, improve the accuracy with respect to experimentation and reduce the cost of these calculations. This volume also features new applications of theoretical chemistry methods to problems of recent general interest in nanotechnology whereby large computational experiments are now necessary.
