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Schrodinger Diffusion Processes
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Book Synopsis Schrödinger Diffusion Processes by : Robert Aebi
Download or read book Schrödinger Diffusion Processes written by Robert Aebi and published by Birkhäuser. This book was released on 2012-12-06 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.
Book Synopsis Schrödinger Equations and Diffusion Theory by : M. Nagasawa
Download or read book Schrödinger Equations and Diffusion Theory written by M. Nagasawa and published by Birkhäuser. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.
Book Synopsis Schrödinger Equations and Diffusion Theory by : Masao Nagasawa
Download or read book Schrödinger Equations and Diffusion Theory written by Masao Nagasawa and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schrödinger Equations and Diffusion Theory addresses the question “What is the Schrödinger equation?” in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews)
Book Synopsis Stochastic Processes in Quantum Physics by : Masao Nagasawa
Download or read book Stochastic Processes in Quantum Physics written by Masao Nagasawa and published by Birkhäuser. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. The book under review is recommended to mathematicians, physicists and graduate students interested in mathematical physics and stochastic processes. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry." ZAA
Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis
Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Book Synopsis Stochastic Processes, Physics And Geometry Ii - Proceedings Of The Iii International Conference by : Sergio Albeverio
Download or read book Stochastic Processes, Physics And Geometry Ii - Proceedings Of The Iii International Conference written by Sergio Albeverio and published by World Scientific. This book was released on 1995-02-17 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: As was already evident from the previous two meetings, the theory of stochastic processes, the study of geometrical structures, and the investigation of certain physical problems are inter-related. In fact the trend in recent years has been towards stronger interactions between these areas. As a result, a large component of the contributions is concerned with the theory of stochastic processes, quantum theory, and their relations.
Book Synopsis Seminar on Stochastic Analysis, Random Fields and Applications by : Erwin Bolthausen
Download or read book Seminar on Stochastic Analysis, Random Fields and Applications written by Erwin Bolthausen and published by Birkhäuser. This book was released on 2012-12-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied stochastic analysis and random fields form the subject of this book. The collection of articles on these topics represent the state of the art of the research in the field, with particular attention being devoted to stochastic models in finance. Some are review articles, others are original papers; taken together, they will apprise the reader of much of the current activity in the area.
Book Synopsis Handbooks in Operations Research and Management Science: Financial Engineering by : John R. Birge
Download or read book Handbooks in Operations Research and Management Science: Financial Engineering written by John R. Birge and published by Elsevier. This book was released on 2007-11-16 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.
Book Synopsis Itô’s Stochastic Calculus and Probability Theory by : Nobuyuki Ikeda
Download or read book Itô’s Stochastic Calculus and Probability Theory written by Nobuyuki Ikeda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.
Download or read book Schrodinger written by Walter Moore and published by Cambridge University Press. This book was released on 2015-10-06 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a biography of the great scientist, Erwin Schrödinger (author of What is Life?), which draws upon recollections of his family and friends, as well as on contemporary records, diaries and letters. It aims to reveal the fundamental motives that drove him.
Download or read book Schrödinger written by Walter J. Moore and published by Cambridge University Press. This book was released on 1992-05-29 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Erwin Schrödinger was a brilliant and charming Austrian, a great scientist, and a man with a passionate interest in people and ideas. In this, the first comprehensive biography of Schrödinger, Walter Moore draws upon recollections of Schrödinger's friends, family and colleagues, and on contemporary records, letters and diaries. Schrödinger's life is portrayed against the backdrop of Europe at a time of change and unrest. His best-known scientific work was the discovery of wave mechanics, for which he was awarded the Nobel prize in 1933. However, Erwin was also an enthusiastic explorer of the ideas of Hindu mysticism, and in the mountains of his beloved Tyrol he sought a philosophic unity of Mind and Nature. Although not Jewish, he left his prestigious position at Berlin University as soon as the Nazis seized power. After a short time in Oxford he moved to Graz, but barely escaped from Austria after the Anschluss. He then helped Eamon de Valera establish an Institute for Advanced Studies in Dublin. It was here that he spent the happiest years of his life, and also where he wrote his most famous and influential book What is Life?, which attracted some of the brightest minds of his generation into molecular biology. Schrodinger enjoyed a close friendship with Einstein, and the two maintained a prolific correspondence all their lives. Schrödinger led a very intense life, both in his scientific research and in his personal life. Walter Moore has written a highly readable biography of this fascinating and complex man which will appeal not only to scientists but to anyone interested in the history of our times, and in the life and thought of one of the great men of twentieth-century science.
Book Synopsis From Brownian Motion to Schrödinger’s Equation by : Kai L. Chung
Download or read book From Brownian Motion to Schrödinger’s Equation written by Kai L. Chung and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics. A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.
Book Synopsis Classes of Linear Operators by : Israel Gohberg
Download or read book Classes of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2013-03-09 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.
Book Synopsis New Perspectives In The Physics Of Mesoscopic Systems: Quantum-like Descriptions And Macroscopic Cohe by : Renato Fedele
Download or read book New Perspectives In The Physics Of Mesoscopic Systems: Quantum-like Descriptions And Macroscopic Cohe written by Renato Fedele and published by World Scientific. This book was released on 1997-10-22 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The very fast progress registered during the last few decades in physics has clearly shown the great necessity to give an interdisciplinary character to the scientific programs. This has made the intersection between different branches of physics more and more important. This volume contains theoretical and experimental results concerning the relationships among quantum-like models, macroscopic coherence and stochastic mechanics. The wide range of topics, covering particle accelerator physics, plasma physics, quantum optics, superconductivities and mesoscopic gravitation, is presented from a cross-disciplinary point of view.
Book Synopsis Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters by : Nitta, Tohru
Download or read book Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters written by Nitta, Tohru and published by IGI Global. This book was released on 2009-02-28 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book covers the current state-of-the-art theories and applications of neural networks with high-dimensional parameters"--Provided by publisher.
Book Synopsis Invariant Measures for Stochastic Nonlinear Schrödinger Equations by : Jialin Hong
Download or read book Invariant Measures for Stochastic Nonlinear Schrödinger Equations written by Jialin Hong and published by Springer Nature. This book was released on 2019-08-22 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Book Synopsis Numerical Methods for Optimal Control Problems by : Maurizio Falcone
Download or read book Numerical Methods for Optimal Control Problems written by Maurizio Falcone and published by Springer. This book was released on 2019-01-26 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.
