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Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets 4th Edition
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Book Synopsis Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (4th Edition) by : Hagen Kleinert
Download or read book Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (4th Edition) written by Hagen Kleinert and published by World Scientific Publishing Company. This book was released on 2006-07-19 with total page 1593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions.The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals.Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders.Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect.The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.The author's other book on ‘Critical Properties of φ4 Theories’ gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
Book Synopsis Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by : Hagen Kleinert
Download or read book Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets written by Hagen Kleinert and published by World Scientific. This book was released on 2009 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.
Book Synopsis Fractional Quantum Mechanics by : Nick Laskin
Download or read book Fractional Quantum Mechanics written by Nick Laskin and published by World Scientific. This book was released on 2018-05-28 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics.This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder.The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework.Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process.The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.
Download or read book Path Integrals written by Wolfhard Janke and published by World Scientific. This book was released on 2008 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals ? New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23?28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as Bose?Einstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics.
Book Synopsis Quantum Dissipative Systems (Fourth Edition) by : Ulrich Weiss
Download or read book Quantum Dissipative Systems (Fourth Edition) written by Ulrich Weiss and published by World Scientific. This book was released on 2012-03-05 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book — originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions — delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems.This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source.
Book Synopsis Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by : Hagen Kleinert
Download or read book Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets written by Hagen Kleinert and published by World Scientific. This book was released on 2004 with total page 1512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman -- Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbationexpansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chem-Simons theory of particles with fractional statistics (anyohs) is introduced and applied to explain the fractional quantum Hall effect. The relevance of path integrals to financial markets is discussed, and improvements of the famous Black -- Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.
Book Synopsis Harmonic Analysis for Engineers and Applied Scientists by : Gregory S. Chirikjian
Download or read book Harmonic Analysis for Engineers and Applied Scientists written by Gregory S. Chirikjian and published by Courier Dover Publications. This book was released on 2016-07-20 with total page 881 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.
Book Synopsis Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (5th Edition) by : Hagen Kleinert
Download or read book Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (5th Edition) written by Hagen Kleinert and published by World Scientific. This book was released on 2009-05-18 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.In addition to the time-sliced definition, the author gives a perturbative, coordinate-independent definition of path integrals, which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely products of distributions.The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strong-coupling regime where they describe critical phenomena.Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the large-order perturbation theory now also applies to small orders.Special attention is devoted to path integrals with topological restrictions needed to understand the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect.The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.
Book Synopsis Mathematics for Natural Scientists by : Lev Kantorovich
Download or read book Mathematics for Natural Scientists written by Lev Kantorovich and published by Springer Nature. This book was released on 2023 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, the second in a series (the first covered fundamentals and basics), seeks to make its material accessible to physics students. Physics/engineering can be greatly enhanced by knowledge of advanced mathematical techniques, but the math-specific jargon and laborious proofs can be off-putting to students not well versed in abstract math. This book uses examples and proofs designed to be clear and convincing from the context of physics, as well as providing a large number of both solved and unsolved problems in each chapter. This is the second edition, and it has been significantly revised and enlarged, with Chapters 1 (on linear algebra) and 2 (on the calculus of complex numbers and functions) having been particularly expanded. The enhanced topics throughout the book include: vector spaces, general (non-Hermitian, including normal and defective) matrices and their right/left eigenvectors/values, Jordan form, pseudoinverse, linear systems of differential equations, Gaussian elimination, fundamental theorem of algebra, convergence of a Fourie series and Gibbs-Wilbraham phenomenon, careful derivation of the Fourier integral and of the inverse Laplace transform. New material has been added on many physics topics meant to illustrate the maths, such as 3D rotation, properties of the free electron gas, van Hove singularities, and methods for both solving PDEs with a Fourier transform and calculating the width of a domain wall in a ferromagnet, to mention just a few. This textbook should prove invaluable to all of those with an interest in physics/engineering who have previously experienced difficulty processing the math involved. .
Book Synopsis Advanced Quantum Mechanics by : Rainer Dick
Download or read book Advanced Quantum Mechanics written by Rainer Dick and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces quantum mechanics from the discovery of photons to field quantization, relativistic quantum fields and photon-matter interactions. It emphasizes the role of quantum theory for an understanding of materials and electromagnetic radiation.
Book Synopsis Applied Stochastic Analysis by : Weinan E
Download or read book Applied Stochastic Analysis written by Weinan E and published by American Mathematical Soc.. This book was released on 2021-09-22 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.
Book Synopsis Multivalued Fields: In Condensed Matter, Electromagnetism, And Gravitation by : Kleinert Hagen
Download or read book Multivalued Fields: In Condensed Matter, Electromagnetism, And Gravitation written by Kleinert Hagen and published by World Scientific Publishing Company. This book was released on 2008-02-04 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundations of the theory of fluctuating multivalued fields with numerous applications. Most prominent among these are phenomena dominated by the statistical mechanics of line-like objects, such as the phase transitions in superfluids and superconductors as well as the melting process of crystals, and the electromagnetic potential as a multivalued field that can produce a condensate of magnetic monopoles. In addition, multivalued mappings play a crucial role in deriving the physical laws of matter coupled to gauge fields and gravity with torsion from the laws of free matter. Through careful analysis of each of these applications, the book thus provides students and researchers with supplementary reading material for graduate courses on phase transitions, quantum field theory, gravitational physics, and differential geometry.
Book Synopsis Quantum Engineering by : A. M. Zagoskin
Download or read book Quantum Engineering written by A. M. Zagoskin and published by Cambridge University Press. This book was released on 2011-07-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum engineering – the design and fabrication of quantum coherent structures – has emerged as a field in physics with important potential applications. This book provides a self-contained presentation of the theoretical methods and experimental results in quantum engineering. The book covers topics such as the quantum theory of electric circuits, theoretical methods of quantum optics in application to solid state circuits, the quantum theory of noise, decoherence and measurements, Landauer formalism for quantum transport, the physics of weak superconductivity and the physics of two-dimensional electron gas in semiconductor heterostructures. The theory is complemented by up-to-date experimental data to help put it into context. Aimed at graduate students in physics, the book will enable readers to start their own research and apply the theoretical methods and results to their current experimental situation.
Book Synopsis Geometry and Light by : Ulf Leonhardt
Download or read book Geometry and Light written by Ulf Leonhardt and published by Courier Corporation. This book was released on 2010-10-18 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. It introduces the mathematical foundations of differential geometry and demonstrates practical applications from general relativity to electrical and optical engineering. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.
Book Synopsis Fractional Dynamics by : Joseph Klafter
Download or read book Fractional Dynamics written by Joseph Klafter and published by World Scientific. This book was released on 2012 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.
Book Synopsis Non-homogeneous Random Walks by : Mikhail Menshikov
Download or read book Non-homogeneous Random Walks written by Mikhail Menshikov and published by Cambridge University Press. This book was released on 2016-12-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.
Book Synopsis Extended Lagrange And Hamilton Formalism For Point Mechanics And Covariant Hamilton Field Theory by : Jurgen Struckmeier
Download or read book Extended Lagrange And Hamilton Formalism For Point Mechanics And Covariant Hamilton Field Theory written by Jurgen Struckmeier and published by World Scientific. This book was released on 2024-08-27 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the extended Lagrange and Hamilton formalisms of point mechanics and field theory in the usual tensor language of standard textbooks on classical dynamics. The notion 'extended' signifies that the physical time of point dynamics as well as the space-time in field theories are treated as dynamical variables. It thus elaborates on some important questions including: How do we convert the canonical formalisms of Lagrange and Hamilton that are built upon Newton's concept of an absolute time into the appropriate form of the post-Einstein era? How do we devise a Hamiltonian field theory with space-time as a dynamical variable in order to also cover General Relativity?In this book, the authors demonstrate how the canonical transformation formalism enables us to systematically devise gauge theories. With the extended canonical transformation formalism that allows to map the space-time geometry, it is possible to formulate a generalized theory of gauge transformations. For a system that is form-invariant under both a local gauge transformation of the fields and under local variations of the space-time geometry, we will find a formulation of General Relativity to emerge naturally from basic principles rather than being postulated.
