Large Deviations Applied to Classical and Quantum Field Theory
Large Deviations Applied to Classical and Quantum Field Theory

Author: Harish Parthasarathy

Publisher: Taylor & Francis

Published: 2022-12-22

Total Pages: 269

ISBN-13: 1000830551

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This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events. It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

Stochastic Processes in Classical and Quantum Physics and Engineering
Stochastic Processes in Classical and Quantum Physics and Engineering

Author: Harish Parthasarathy

Publisher: Taylor & Francis

Published: 2022-12-23

Total Pages: 275

ISBN-13: 1000815544

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This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

Advanced Classical and Quantum Probability Theory with Quantum Field Theory Applications
Advanced Classical and Quantum Probability Theory with Quantum Field Theory Applications

Author: Harish Parthasarathy

Publisher: CRC Press

Published: 2022-12-23

Total Pages: 263

ISBN-13: 1000815315

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This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years. It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

Quantum Probability & Related Topics
Quantum Probability & Related Topics

Author: Luigi Accardi

Publisher: World Scientific

Published: 1992

Total Pages: 400

ISBN-13: 9789810219796

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Quantum Probability and Related Topics is a series of volumes based on materials discussed in the various QP conferences. It aims at providing an update on the rapidly growing field of classical probability, quantum physics and functional analysis.

Entropy, Large Deviations, and Statistical Mechanics
Entropy, Large Deviations, and Statistical Mechanics

Author: Richard S. Ellis

Publisher: Springer

Published: 2007-02-03

Total Pages: 376

ISBN-13: 3540290605

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From the reviews: "... Each chapter of the book is followed by a notes section and by a problems section. There are over 100 problems, many of which have hints. The book may be recommended as a text, it provides a completly self-contained reading ..." --S. Pogosian in Zentralblatt für Mathematik

Large Deviations
Large Deviations

Author: Jean-Dominique Deuschel

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 298

ISBN-13: 082182757X

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This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).

Large Deviations
Large Deviations

Author: Jean-Dominique Deuschel and Daniel W. Stroock

Publisher: American Mathematical Soc.

Published:

Total Pages: 296

ISBN-13: 9780821869345

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This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).

Developments in Mathematical and Conceptual Physics
Developments in Mathematical and Conceptual Physics

Author: Harish Parthasarathy

Publisher: Springer Nature

Published: 2020-06-22

Total Pages: 454

ISBN-13: 9811550581

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This book presents concepts of theoretical physics with engineering applications. The topics are of an intense mathematical nature involving tools like probability and random processes, ordinary and partial differential equations, linear algebra and infinite-dimensional operator theory, perturbation theory, stochastic differential equations, and Riemannian geometry. These mathematical tools have been applied to study problems in mechanics, fluid dynamics, quantum mechanics and quantum field theory, nonlinear dynamical systems, general relativity, cosmology, and electrodynamics. A particularly interesting topic of research interest developed in this book is the design of quantum unitary gates of large size using the Feynman diagrammatic approach to quantum field theory. Through this book, the reader will be able to observe how basic physics can revolutionize technology and also how diverse branches of mathematical physics like large deviation theory, quantum field theory, general relativity, and electrodynamics have many common issues that provide the starting point for unifying the whole of physics, namely in the formulation of Grand Unified Theories (GUTS).

Select Topics in Signal Analysis
Select Topics in Signal Analysis

Author: Harish Parthasarathy

Publisher: Taylor & Francis

Published: 2022-10-20

Total Pages: 397

ISBN-13: 1000789780

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This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail. The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan’s Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory. The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.

Stochastics, Control and Robotics
Stochastics, Control and Robotics

Author: Harish Parthasarathy

Publisher: CRC Press

Published: 2021-06-23

Total Pages: 491

ISBN-13: 1000425932

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This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics. The problems are chosen to motivate the interested reader to learn more about these subjects from other standard sources. Stochastic Process theory is applied to the study of differential equations of mechanics subject to external noise. Some issues in general relativity like Geodesic motion, field theory in curved space time etc. are discussed via isolated problems. The more recent quantum stochastic process theory as formulated by R.L. Hudson and K. R. Parathasarathy is discussed. This provides a non commutative operator theoretic version of stochastic process theory. V.P. Belavkin's approach to quantum filtering based on non demolition measurements and Hudson Parathasarathy calculus has been discussed in detail. Quantum versions of the simple exclusion model in Markov process theory have been included. 3D Robots carring a current density interacting with an external Klein- Gordon or Electromagnetic field has been given some attention. The readers will after going through this book, be ready to carry out independent research in classical and quantum field theory and stochastic processes as applied to practical problems. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.