Molecular Propagation Through Electron Energy Level Crossings
Author: George Allan Hagedorn
Publisher:
Published: 1994
Total Pages: 130
ISBN-13: 9781470401153
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Molecular Propagation through Electron Energy Level Crossings
Author: George Allan Hagedorn
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 142
ISBN-13: 0821826050
DOWNLOAD EBOOK →The principal results of this paper involve the extension of the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through generic, minimal multiplicity electron energy level crossings. The Born-Oppenheimer approximation breaks down at electron energy level crossings, which are prevalent in molecular systems. We classify generic, minimal multiplicity level crossings and derives a normal form for the electron Hamiltonian near each type of crossing. We then extend the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through each type of electron energy level crossing.
Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday
Author: Fritz Gesztesy
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 528
ISBN-13: 082184248X
DOWNLOAD EBOOK →This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume.
Analysis, Modeling and Simulation of Multiscale Problems
Author: Alexander Mielke
Publisher: Springer Science & Business Media
Published: 2006-10-14
Total Pages: 704
ISBN-13: 3540356576
DOWNLOAD EBOOK →This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
Mathematics of Complexity and Dynamical Systems
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
Published: 2011-10-05
Total Pages: 1885
ISBN-13: 1461418054
DOWNLOAD EBOOK →Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Recent Advances in Differential Equations and Mathematical Physics
Author: Nikolai Chernov
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 354
ISBN-13: 0821838407
DOWNLOAD EBOOK →Surveys topics in differential equations that are associated with mathematical physics. This book includes such topics as asymptotic formulas for the ground-state energy of fermionic gas, $J$-self adjoint Dirac operators, and spectral theory of Schrodinger operators. It is suitable for mathematicians and physicists.
Homogenization in Time of Singularly Perturbed Mechanical Systems
Author: Folkmar Bornemann
Publisher: Springer
Published: 2006-11-15
Total Pages: 166
ISBN-13: 3540697845
DOWNLOAD EBOOK →This book is about the explicit elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and our understanding of model hierarchies. The author presents his new direct method, homogenization in time, based on energy principles and weak convergence techniques. How to use this method is shown in several general cases taken from classical and quantum mechanics. The results are applied to special problems from plasma physics, molecular dynamics and quantum chemistry. Background material from functional analysis is provided and explained to make this book accessible for a general audience of graduate students and researchers.
Mathematical Challenges of Zero-Range Physics
Author: Alessandro Michelangeli
Publisher: Springer Nature
Published: 2021-02-04
Total Pages: 331
ISBN-13: 3030604535
DOWNLOAD EBOOK →Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field.
Hilbert Modules over Operator Algebras
Author: Paul S. Muhly
Publisher: American Mathematical Soc.
Published: 1995
Total Pages: 69
ISBN-13: 0821803468
DOWNLOAD EBOOK →Addresses the three-dimensional generalization of category, offering a full definition of tricategory; a proof of the coherence theorem for tricategories; and a modern source of material on Gray's tensor product of 2-categories. Of interest to research mathematicians; theoretical physicists, algebraic topologists; 3-D computer scientists; and theoretical computer scientists. Society members, $19.00. No index. Annotation copyright by Book News, Inc., Portland, OR
Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting
Author: I. V. Evstigneev
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 113
ISBN-13: 0821825976
DOWNLOAD EBOOK →Various notions of the Markov property relative to a partial ordering have been proposed by both physicists and mathematicians. This work develops techniques for stying Markov fields on partially ordered sets. We introduce random transformations of the index set which preserves the Markov property of the field. These transformations yield new classes of Markov fields starting from relatively simple ones. Examples include a model for crack formation and a model for the distribution of fibres in a composite material.
