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Author : Ph. Blanchard,Ph. Combe,W. Zheng
Publisher : Unknown
Page : 184 pages
File Size : 41,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662136058
Author : Philippe Blanchard,Philippe Combe,W. Zheng
Publisher : Springer
Page : 188 pages
File Size : 41,8 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015038944057
Author : N. Bellomo,Riccardo Riganti
Publisher : World Scientific
Page : 268 pages
File Size : 45,9 Mb
Release : 1987
Category : Science
ISBN : 9971502496
This book presents the conceptional line which goes from the observation of physical systems to their modeling and analysis by ordinary differential nonlinear stochastic equations.First, the problems of the mathematical modeling of physical systems are developed. These mathematical models are then classified in terms of ordinary differential stochastic equations from which both qualitative and quantitative results are developed.Each one of the various subjects are methods dealt with ends with an application in mathematical physics or in nonlinear mechanics.
Author : Aubrey Truman,Ian M. Davies
Publisher : Springer
Page : 227 pages
File Size : 45,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540458876
The main theme of the meeting was to illustrate the use of stochastic processes in the study of topological problems in quantum physics and statistical mechanics. Much discussion of current problems was generated and there was a considerable amount of interaction between mathematicians and physicists. The papers presented in the proceedings are essentially of a research nature but some (Lewis, Hudson) are introductions or surveys.
Author : Folkert Kuipers
Publisher : Springer Nature
Page : 132 pages
File Size : 47,6 Mb
Release : 2023-05-31
Category : Science
ISBN : 9783031314483
Stochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and path integral formulations of quantum theories. It provides an equivalent formulation of quantum theories, but substantiates it with a mathematically rigorous stochastic interpretation by means of a stochastic quantization prescription. The book builds on recent developments in this theory, and shows that quantum mechanics can be unified with the theory of Brownian motion in a single mathematical framework. Moreover, it discusses the extension of the theory to curved spacetime using second order geometry, and the induced Itô deformations of the spacetime symmetries. The book is self-contained and provides an extensive review of stochastic mechanics of the single spinless particle. The book builds up the theory on a step by step basis. It starts, in chapter 2, with a review of the classical particle subjected to scalar and vector potentials. In chapter 3, the theory is extended to the study of a Brownian motion in any potential, by the introduction of a Gaussian noise. In chapter 4, the Gaussian noise is complexified. The result is a complex diffusion theory that contains both Brownian motion and quantum mechanics as a special limit. In chapters 5, the theory is extended to relativistic diffusion theories. In chapter 6, the theory is further generalized to the context of pseudo-Riemannian geometry. Finally, in chapter 7, some interpretational aspects of the stochastic theory are discussed in more detail. The appendices concisely review relevant notions from probability theory, stochastic processes, stochastic calculus, stochastic differential geometry and stochastic variational calculus. The book is aimed at graduate students and researchers in theoretical physics and applied mathematics with an interest in the foundations of quantum theory and Brownian motion. The book can be used as reference material for courses on and further research in stochastic mechanics, stochastic quantization, diffusion theories on curved spacetimes and quantum gravity.
Author : Stanley P. Gudder
Publisher : Courier Corporation
Page : 242 pages
File Size : 52,6 Mb
Release : 2005-12-10
Category : Science
ISBN : 9780486445328
This introductory treatment surveys useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory. 1979 edition.
Author : S Albeverio,P Blanchard,L Ferreira,T Hida,Y Kondratiev,R Vilela Mendes
Publisher : World Scientific
Page : 464 pages
File Size : 41,6 Mb
Release : 2000-11-24
Category : Science
ISBN : 9789814492270
In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality. The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains. List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Bollé, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M Röckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L Vázquez, D N Kozakevich, S Jiménez, V R Vieira, P D Sacramento, R Vilela Mendes, D Volný, P Samek. Contents:Some Themes of the Scientific Work of Ludwig Streit (S Albeverio)Nonlinear Lie Algebras in Quantum Physics and Their Interest in Quantum Field Theory (J Beckers)Rigged Hilbert Space Resonances and Time Asymmetric Quantum Mechanics (A Bohm & H Kaldass)The Relativistic Aharonov-Bohm-Coulomb Problem: A Path Integral Solution (J Bornales et al.)Time Dependent and Nonlinear Point Interactions (R Figari)Stochastic Processes and the Feynman Integral (Z Haba)Nonrenormalizability and Nontriviality (J R Klauder)On the Spectrum of Lattice Dirac Operators (C B Lang)External and Internal Geometry on Configuration Spaces (J L Silva)Spinor Description of a General Spin-J System (V R Vieira & P D Sacramento)and other papers Readership: Theoretical physicists, mathematical physicists, mathematicians, computer scientists and economists. Keywords:
Author : Edward Nelson
Publisher : Princeton University Press
Page : 158 pages
File Size : 45,6 Mb
Release : 2020-09-01
Category : Science
ISBN : 9780691218021
Stochastic mechanics is a description of quantum phenomena in classical probabilistic terms. This work contains a detailed account of the kinematics of diffusion processes, including diffusions on curved manifolds which are necessary for the treatment of spin in stochastic mechanics. The dynamical equations of the theory are derived from a variational principle, and interference, the asymptotics of free motion, bound states, statistics, and spin are described in classical terms. In addition to developing the formal mathematical aspects of the theory, the book contains discussion of possible physical causes of quantum fluctuations in terms of an interaction with a background field. The author gives a critical analysis of stochastic mechanics as a candidate for a realistic theory of physical processes, discussing measurement, local causality in the sense of Bell, and the failure of the theory in its present form to satisfy locality.
Author : M Chaichian,A Demichev
Publisher : CRC Press
Page : 336 pages
File Size : 46,5 Mb
Release : 2018-10-03
Category : Science
ISBN : 9781482289503
Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
Author : F. Strocchi
Publisher : World Scientific
Page : 193 pages
File Size : 53,6 Mb
Release : 2008
Category : Science
ISBN : 9789812835222
Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.
Author : F Strocchi
Publisher : World Scientific Publishing Company
Page : 160 pages
File Size : 48,9 Mb
Release : 2005-11-17
Category : Science
ISBN : 9789813106598
This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac–Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C–-algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems. For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem. The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich–Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra. Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman–Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.
Author : Anders Rantzer,Christopher I. Byrnes
Publisher : Springer
Page : 391 pages
File Size : 44,9 Mb
Release : 2003-07-01
Category : Computers
ISBN : 9783540361060
For more than three decades, Anders Lindquist has delivered fundamental cont- butions to the ?elds of systems, signals and control. Throughout this period, four themes can perhaps characterize his interests: Modeling, estimation and ?ltering, feedback and robust control. His contributions to modeling include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identi?cation. His contributions to ?ltering and estimation include the development of fast ?ltering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. His further research on the phase portrait of this dynamical system gave a better understanding of when the Kalman ?lter will converge, answering an open question raised by Kalman. While still a student he established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. He continued his interest in feedback control by deriving optimal and robust control feedback laws for suppressing the effects of harmonic disturbances. Moreover, his recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design.
Author : Ruben Aldrovandi
Publisher : World Scientific
Page : 344 pages
File Size : 49,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9812799834
Ch. 1. Some fundamental notions. 1.1. Definitions. 1.2. Components of a matrix. 1.3. Matrix functions. 1.4. Normal matrices -- ch. 2. Evolving systems -- ch. 3. Markov chains. 3.1. Non-negative matrices. 3.2. General properties -- ch. 4. Glass transition -- ch. 5. The Kerner model. 5.1. A simple example: Se-As glass -- ch. 6. Formal developments. 6.1. Spectral aspects. 6.2. Reducibility and regularity. 6.3. Projectors and asymptotics. 6.4. Continuum time -- ch. 7. Equilibrium, dissipation and ergodicity. 7.1. Recurrence, transience and periodicity. 7.2. Detailed balancing and reversibility. 7.3. Ergodicity -- ch. 8. Prelude -- ch. 9. Definition and main properties. 9.1. Bases. 9.2. Double Fourier transform. 9.3. Random walks -- ch. 10. Discrete quantum mechanics. 10.1. Introduction. 10.2. Weyl-Heisenberg groups. 10.3. Weyl-Wigner transformations. 10.4. Braiding and quantum groups -- ch. 11. Quantum symplectic structure. 11.1. Matrix differential geometry. 11.2. The symplectic form. 11.3. The quantum fabric -- ch. 12. An organizing tool -- ch. 13. Bell polynomials. 13.1. Definition and elementary properties. 13.2. The matrix representation. 13.3. The Lagrange inversion formula. 13.4. Developments -- ch. 14. Determinants and traces. 14.1. Introduction. 14.2. Symmetric functions. 14.3. Polynomials. 14.4. Characteristic polynomials. 14.5. Lie algebras invariants -- ch. 15. Projectors and iterates. 15.1. Projectors, revisited. 15.2. Continuous iterates -- ch. 16. Gases: real and ideal. 16.1. Microcanonical ensemble. 16.2. The canonical ensemble. 16.3. The grand canonical ensemble. 16.4. Braid statistics. 16.5. Condensation theories. 16.6. The Fredholm formalism.
Author : Eduard Prugovečki
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 49,5 Mb
Release : 1984-01-31
Category : Gardening
ISBN : 902771617X
The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.
Author : Vittorio Gorini,Alberto Frigerio
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468452211
Thi's book collects the contributions to the NATO Advanced Research WJrkshop on "FundaIrental Aspects of Quantum 'Iheory," held at the Centro di Cultura Scientifica "Alessandro Volta," Villa Olma, Carro, Italy, 2-7 September 1985. The rreeting was dedicated to the rremory of the late pro fessor Piero Caldirola, a prominent member of the Physics Departrrent of the University of r1ilan and a native of Como. The aim of the workshop has been to present several recent experi rrental results and theoretical developrrents concerning the various fa cets of quantum physics. The breadth of scope of the rreeting was in accordance with Professor Caldirola's vast scientific interests, and fostered communication among experirrental physicists, theoretical and mathematical physicists, and nEthematicians, working in different but related fields. Indeed, lectu rers endeavoured to make their contributions understandable to people acquainted with the problem but not necessarily familiar with the tech nical details; and these efforts were successful, as indicated by the frequent private discussions which took place among participants belon ging to different breeds and brands. 1ne rreeting was made up of six one-day sessions, each of them addres sing to a specific aspect of quantum theory: 1. General Problems and Crucial Experinents; with emphasis on sin gle-particle interference eh rirrents of neutrons and of photons, and on the rreasurerrent problem. 2. Quantization and Stochastic Processes; including stochastic quan tization of gauge fields, stochastic description of supersyrnmetric fields, quantum stochastic calculus and stochastic mechanics."