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Mathematical Physics: Classical Mechanics
As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
Classical Nonintegrability, Quantum Chaos
Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in th...
Perspectives on Spin Glasses
Presenting and developing the theory of spin glasses for mathematical physicists and probabilists working in disordered systems.
Classical Planar Scattering by Coulombic Potentials
Astronomy as well as molecular physics describe non-relativistic motion by an interaction of the same form: By Newton's respectively by Coulomb's potential. But whereas the fundamental laws of motion thus have a simple form, the n-body problem withstood (for n > 2) all attempts of an explicit solution. Indeed, the studies of Poincare at the end of the last century lead to the conclusion that such an explicit solution should be impossible. Poincare himselfopened a new epoch for rational mechanics by asking qual itative questions like the one about the stability of the solar system. To a largeextent, his work, which was critical for the formation of differential geometry and topology, was motivated by problems arising in the analysis of the n-body problem ([38], p. 183). As it turned out, even by confining oneselfto questions ofqualitativenature, the general n-body problem could not be solved. Rather, simplified models were treated, like planar motion or the restricted 3-body problem, where the motion of a test particle did not influence the other two bodies.
The Mathematical Aspects of Quantum Maps
Quantum maps are presented with special emphasis on their physical origin. They represent a testing ground for understanding concepts in quantized chaotic systems. The book teaches the modern mathematical methods from analytic and algebraic number theory as applied to quantum maps. It gives a broad and in-depth overview of the mathematical problems arising in this area. Also treated are the numerical aspects in quantum chaos such as eigenvalue and eigenfunctions computations for chaotic quantum systems. The book addresses scientists and advanced students in mathematics and mathematical physics.
Chance in Physics
This selection of reviews and papers is intended to stimulate renewed reflection on the fundamental and practical aspects of probability in physics. While putting emphasis on conceptual aspects in the foundations of statistical and quantum mechanics, the book deals with the philosophy of probability in its interrelation with mathematics and physics in general. Addressing graduate students and researchers in physics and mathematics togehter with philosophers of science, the contributions avoid cumbersome technicalities in order to make the book worthwhile reading for nonspecialists and specialists alike.
The SIAM 100-Digit Challenge
Gives concrete examples of how to justify the validity of every single digit of a numerical answer.
Stochasticity and Quantum Chaos
These are the proceedings of the Third Max Born Symposium which took place at SobOtka Castle in September 1993. The Symposium is organized annually by the Institute of Theoretical Physics of the University of Wroclaw. Max Born was a student and later on an assistant at the University of Wroclaw (Wroclaw belonged to Germany at this time and was called Breslau). The topic of the Max Born Sympo sium varies each year reflecting the developement of theoretical physics. The subject of this Symposium "Stochasticity and quantum chaos" may well be considered as a continuation of the research interest of Max Born. Recall that Born treats his "Lectures on the mechanics of the atom" (published in 1925) ...
Building Resilience to Natural Hazards in the Context of Climate Change
Urban resilience and building resilience are “hot topics” of research and practice on sustainability in the context of climate change. The edited volume advances the “state of art” of urban resilience research through focusing on three important processes of building resilience: knowledge integration, implementation, and learning. In the volume, knowledge integration primarily refers to the combination of specialized knowledge domains (e.g., flood risk management and urban planning). Implementation refers to realized specific changes of the building stock and related green, blue and grey infrastructures at local level (e.g., for dealing with rising temperatures and heat waves at the neighborhood scale in cities). Learning requires moving beyond single projects and experiments of resilience to enhance sustainability at city and regional scale. The editors adopt an interdisciplinary approach to this volume of the Springer series on resilience. The volume includes contributions from civil engineering, physical geography, the social sciences, and urban planning.
Operator Theory And Analysis Of Infinite Networks
This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class o...
