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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.
Book Synopsis Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces by : Alexey V. Shchepetilov
Download or read book Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces written by Alexey V. Shchepetilov and published by Springer. This book was released on 2006-09-04 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 of bodies, 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.
Book Synopsis Relative Equilibria of the Curved N-Body Problem by : Florin Diacu
Download or read book Relative Equilibria of the Curved N-Body Problem written by Florin Diacu and published by Springer Science & Business Media. This book was released on 2012-08-17 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of bodies, 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.
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.
Book Synopsis Modern Aspects of Spin Physics by : Walter Pötz
Download or read book Modern Aspects of Spin Physics written by Walter Pötz and published by Springer Science & Business Media. This book was released on 2006-10-26 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Mathematical Implications of Einstein-Weyl Causality by : Hans Jürgen Borchers
Download or read book Mathematical Implications of Einstein-Weyl Causality written by Hans Jürgen Borchers and published by Springer. This book was released on 2007-02-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Controlled Nanoscale Motion by : Heiner Linke
Download or read book Controlled Nanoscale Motion written by Heiner Linke and published by Springer Science & Business Media. This book was released on 2007-02-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
Book Synopsis Lie Algebras and Applications by : Francesco Iachello
Download or read book Lie Algebras and Applications written by Francesco Iachello and published by Springer. This book was released on 2007-02-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
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.
Book Synopsis Quantum Dynamical Semigroups and Applications by : Robert Alicki
Download or read book Quantum Dynamical Semigroups and Applications written by Robert Alicki and published by Springer. This book was released on 2007-04-03 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Very High Resolution Photoelectron Spectroscopy by : Stephan Hüfner
Download or read book Very High Resolution Photoelectron Spectroscopy written by Stephan Hüfner and published by Springer Science & Business Media. This book was released on 2007-02-09 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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. It 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.
Book Synopsis Progress in Understanding of Polymer Crystallization by : Günter Reiter
Download or read book Progress in Understanding of Polymer Crystallization written by Günter Reiter and published by Springer. This book was released on 2007-04-15 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. It 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.
Understanding cooperative phenomena far from equilibrium is one of the fascinating challenges of present-day many-body physics. Glassy behaviour and the physical ageing process of such materials are paradigmatic examples. The present volume, primarily intended as introduction and reference, collects six extensive lectures addressing selected experimental and theoretical issues in the field of glassy systems.
Book Synopsis Ageing and the Glass Transition by : Malte Henkel
Download or read book Ageing and the Glass Transition written by Malte Henkel and published by Springer. This book was released on 2007-04-11 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding cooperative phenomena far from equilibrium is one of the fascinating challenges of present-day many-body physics. Glassy behaviour and the physical ageing process of such materials are paradigmatic examples. The present volume, primarily intended as introduction and reference, collects six extensive lectures addressing selected experimental and theoretical issues in the field of glassy systems.
