Calculus And Mechanics On Two Point Homogenous Riemannian Spaces
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Calculus And Mechanics On Two Point Homogenous Riemannian Spaces
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Author : Alexey V. Shchepetilov
language : en
Publisher: Springer
Release Date : 2006-09-04
Calculus And Mechanics On Two Point Homogenous Riemannian Spaces written by Alexey V. Shchepetilov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-04 with Science categories.
Mathematics develops both due to demands of other sciences and due to its internal logic. The latter fact explains the attention of mathematicians to many problems, which are in close connection with basic mathematical notions, even if these problems have no direct practical applications. It is well known that the space of constant curvature is one of the basic geometry notion [208], which induced the wide ?eld for investigations. As a result there were found numerous connections of constant curvature spaces with other branches of mathematics, for example, with integrable partial dif- 1 ferential equations [36, 153, 189] and with integrable Hamiltonian systems [141]. Geodesic ?ows on compact surfaces of a constant negative curvature (with the genus 2) generate many test examples for ergodic theory (see also 3 [183] and the bibliography therein). The hyperbolic space H (R) is the space of velocities in special relativity (see Sect. 7.4.1) and also arises as space-like sections in some models of general relativity.
Calculus And Mechanics On Two Point Homogenous Riemannian Spaces
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Author : Alexey V. Shchepetilov
language : en
Publisher: Springer
Release Date : 2009-09-02
Calculus And Mechanics On Two Point Homogenous Riemannian Spaces written by Alexey V. Shchepetilov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Science categories.
This is an introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, empahsizing spaces with constant curvature. Chapters 1-4 provide basic notations for studying two-body dynamics. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 investigates the classical counterpart of the quantum system introduced in Chapter 5. Chapter 8 discusses applications in the quantum realm.
Modern Aspects Of Spin Physics
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Author : Walter Pötz
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-26
Modern Aspects Of Spin Physics written by Walter Pötz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-26 with Science categories.
The spin degree of freedom is an intrinsically quantum-mechanical phenomenon, leading to both intriguing applications and unsolved fundamental issues (such as "where does the proton spin come from"). The present volume investigates central aspects of modern spin physics in the form of extensive lectures on semiconductor spintronics, the spin-pairing mechanism in high-temperature semiconductors, spin in quantum field theory and the nucleon spin.
Relative Equilibria Of The Curved N Body Problem
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Author : Florin Diacu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-17
Relative Equilibria Of The Curved N Body Problem written by Florin Diacu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-17 with Mathematics categories.
The guiding light of this monograph is a question easy to understand but difficult to answer: {What is the shape of the universe? In other words, how do we measure the shortest distance between two points of the physical space? Should we follow a straight line, as on a flat table, fly along a circle, as between Paris and New York, or take some other path, and if so, what would that path look like? If you accept that the model proposed here, which assumes a gravitational law extended to a universe of constant curvature, is a good approximation of the physical reality (and I will later outline a few arguments in this direction), then we can answer the above question for distances comparable to those of our solar system. More precisely, this monograph provides a mathematical proof that, for distances of the order of 10 AU, space is Euclidean. This result is, of course, not surprising for such small cosmic scales. Physicists take the flatness of space for granted in regions of that size. But it is good to finally have a mathematical confirmation in this sense. Our main goals, however, are mathematical. We will shed some light on the dynamics of N point masses that move in spaces of non-zero constant curvature according to an attraction law that naturally extends classical Newtonian gravitation beyond the flat (Euclidean) space. This extension is given by the cotangent potential, proposed by the German mathematician Ernest Schering in 1870. He was the first to obtain this analytic expression of a law suggested decades earlier for a 2-body problem in hyperbolic space by Janos Bolyai and, independently, by Nikolai Lobachevsky. As Newton's idea of gravitation was to introduce a force inversely proportional to the area of a sphere the same radius as the Euclidean distance between the bodies, Bolyai and Lobachevsky thought of a similar definition using the hyperbolic distance in hyperbolic space. The recent generalization we gave to the cotangent potential to any number N ofbodies, led to the discovery of some interesting properties. This new research reveals certain connections among at least five branches of mathematics: classical dynamics, non-Euclidean geometry, geometric topology, Lie groups, and the theory of polytopes.
Mathematical Implications Of Einstein Weyl Causality
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Author : Hans Jürgen Borchers
language : en
Publisher: Springer
Release Date : 2007-02-22
Mathematical Implications Of Einstein Weyl Causality written by Hans Jürgen Borchers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-22 with Science categories.
Here is a systematic approach to such fundamental questions as: What mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The author proposes an axiomatization of the physics inspired notion of Einstein-Weyl causality and investigating the consequences in terms of possible topological spaces. One significant result is that the notion of causality can effectively be extended to discontinuum.
Controlled Nanoscale Motion
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Author : Heiner Linke
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-09
Controlled Nanoscale Motion written by Heiner Linke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-09 with Science categories.
When the size of a machine approaches the nanometer scale, thermal fluctuations become large compared to the energies that drive the motor. The control of motion at the nanoscale therefore requires physical understanding and technical approaches that are fundamentally different from those that are successful at the macroscale. This volume provides an introduction to the state-of-the-art of controlled nanoscale motion in biological and artificial systems. Topics include the control and function of protein motors, the physics of non-equilibrium Brownian motion, and the physics and fabrication of synthetic molecular motors. The chapters in this book are based on selected contributions on the 2005 Nobel Symposium to Controlled Nanoscale Motion and are written by leading experts in their fields.
Lie Algebras And Applications
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Author : Francesco Iachello
language : en
Publisher: Springer
Release Date : 2007-02-22
Lie Algebras And Applications written by Francesco Iachello and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-22 with Science categories.
In the second part of the 20th century, algebraic methods have emerged as a powerful tool to study theories of physical phenomena, especially those of quantal systems. The framework of Lie algebras, initially introduced by - phus Lie in the last part of the 19th century, has been considerably expanded to include graded Lie algebras, in?nite-dimensional Lie algebras, and other algebraic constructions. Algebras that were originally introduced to describe certainpropertiesofaphysicalsystem,inparticularbehaviorunderrotations and translations, have now taken center stage in the construction of physical theories. This book contains a set of notes from lectures given at Yale Univ- sity and other universities and laboratories in the last 20 years. The notes are intended to provide an introduction to Lie algebras at the level of a one-semester graduate course in physics. Lie algebras have been particularly useful in spectroscopy, where they were introduced by Eugene Wigner and Giulio Racah. Racah’s lectures were given at Princeton University in 1951 (Group Theory and Spectroscopy) and they provided the impetus for the initial applications in atomic and nuclear physics. In the intervening years, many other applications have been made. This book contains a brief account of some of these applications to the ?elds of molecular, atomic, nuclear, and particle physics. The application of Lie algebraic methods in Physics is so wide that often students are overwhelmed by the sheer amount of material to absorb.
Quantum Dynamical Semigroups And Applications
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Author : Robert Alicki
language : en
Publisher: Springer
Release Date : 2007-04-03
Quantum Dynamical Semigroups And Applications written by Robert Alicki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-03 with Science categories.
Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention. This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.
Very High Resolution Photoelectron Spectroscopy
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Author : Stephan Hüfner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-09
Very High Resolution Photoelectron Spectroscopy written by Stephan Hüfner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-09 with Science categories.
Photoemission spectroscopy is one of the most extensively used methods to study the electronic structure of atoms, molecules, and solids and their surfaces. This volume introduces and surveys the field at highest energy and momentum resolutions allowing for a new range of applications, in particular for studies of high temperature superconductors.
Progress In Understanding Of Polymer Crystallization
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Author : Günter Reiter
language : en
Publisher: Springer
Release Date : 2007-04-15
Progress In Understanding Of Polymer Crystallization written by Günter Reiter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-15 with Technology & Engineering categories.
In the context of polymer crystallization there are several still open and often controversially debated questions. The present volume addresses issues such as novel general views and concepts which help to advance our understanding of polymer crystallisation, nucleation phenomena, long living melt structures affecting crystallization, confinement effects on crystallization, crystallization in flowing melts, fluid mobility restrictions caused by crystallites, the role of mesophases in the crystal formation and presents new ideas in a connected and accessible way. The intention is thus not only to provide a summary of the present state of the art to all active works but to provide an entry point to newcomer and graduate students entering the field.