Quantum Independent Increment Processes I From Classical Probability to Quantum Stochastic Calculus
 

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Quantum Independent Increment Processes I: From Classical Probability to Quantum Stochastic Calculus


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Quantum Independent Increment Processes II: Structure of Quantum Levy Processes, Classical Probability, and Physics



This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics....
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Quantum Probability and Applications III


These proceedings of the first Quantum Probability meeting held in Oberwolfach is the fourth in a series begun with the 1982 meeting of Mondragone and continued in Heidelberg ('84) and in Leuven ('85). The main topics discussed were: quantum stochastic calculus, mathematical models of quantum noise and their applications to quantum optics, the quantum Feynman-Kac formula, quantum probability and models of quantum statistical mechanics, the notion of conditioning in quantum probability and related problems (dilations, quantum Markov processes), quantum central limit theorems. With the exception of Kummerer's review article on Quantum Markov Processes, all contributions are original research papers.
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Quantum Stochastic Processes and Noncommutative Geometry


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Stochastic Processes in Classical and Quantum Systems by Sergio Albeverio



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Quantum Computation and Quantum Information: 10th Anniversary Edition


Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.


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Fundamentals of Probability, with Stochastic Processes, 3rd Edition


Topics include: axioms of probability; combinatorial methods; conditional probability and independence; distribution functions and discrete random variables; special discrete distributions; continuous random variables; special continuous distributions; bivariate distributions; multivariate distributions; sums of independent random variables and limit theorems; stochastic processes; and simulation. For anyone employed in the actuarial division of insurance companies and banks, electrical engineers, financial consultants, and industrial engineers.


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Modern canonical quantum general relativity


Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.
Modern canonical quantum general relativity
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Quantum Trajectories


Emphasizing a classical interpretation of quantum mechanics as developed by de Broglie and Bohm, this volume: Introduces the concept of the quantum theory of motion Explains the connection with conventional quantum mechanics Presents various numerical techniques generated from the Bohmian approach Describes the epistemological significance of quantum trajectories Provides an authoritative *** of the foundations of quantum mechanics vis-a-vis that of the Bohmian mechanics The popularity of using the quantum trajectory as a computational tool has exploded over the last decade, finally bringing this methodology to the level of practical applications. Many of the experts in the field who have either developed the methodology or have improved upon it have contributed chapters to this volume, making it a state-of-the-art expression of the field as it exists today and providing insight into the future of this technology.


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Chaos and Quantum Chaos [Repost]


Until now the important concept of quantum chaos has remained somewhat ill defined. This volume tackles the ubiquitous borderline between classical and quantum mechanics, studying in particular the semiclassical limit of chaotic systems. The effects of disorder from dynamics and their relation to stochastic systems, quantum coherence effects in mesoscopic systems, and the relevant theoretical approaches are fruitfully combined in this volume. The major paradigms of what is called quantum chaos, random matrix theory and applications to condensed matter and nuclear physics are presented. Detailed discussions of experimental work with particular emphasis on atomic physics are included. The book is highly recommended for graduate-student seminars.
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Foundations of Quantum Mechanics: From Photons to Quantum Computers


This accessible text with modern applications focuses on what is quantum about quantum mechanics; topics discussed include the EPR paradox, entanglement, teleportation, Bell s Theorem, quantum computing, and code-breaking with quantum computers.
Foundations of Quantum Mechanics: From Photons to Quantum Computers
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Quantum Probability and Applications to the Quantum Theory of Irreversible Processes


Its goal was to present a survey of the present status of the topics mentioned in the title. We would like to thank the sponsoring institutions, the lecturers, and the participants for their contributions to the success of the conference.
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Quantum Communication and Quantum Networking


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Introduction to Statistical Physics, Second Edition


The book first covers the classical ensembles of statistical mechanics and stochastic processes, including Brownian motion, probability theory, and the Fokker


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Quantum Gravity in 2+1 Dimensions


This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, and examines what they imply for a realistic theory of quantum gravity. General relativity in three spacetime dimensions has become a popular arena in which to explore the ramifications of quantum gravity. As a diffeomorphism-invariant theory of spacetime structure, this model shares many of the conceptual problems of realistic quantum gravity. But it is also simple enough that many programs of quantization can be carried out explicitly. After analysing the space of classical solutions, this book introduces some fifteen approaches to quantum gravity - from canonical quantization in York's 'extrinsic time' to Chern-Simons quantization, from the loop representation to covariant path integration to lattice methods. Relationships among quantizations are explored, as well as implications for such issues as topology change and the 'problem of time'. This book is an invaluable resource for all graduate students and researchers working in quantum gravity.
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Quantum mechanics and quantum fields theory collection



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Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons


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Dynamical Theories of Brownian Motion (Mathematical Notes) by Edward Nelson


These are the notes for the second term of a year course on stochastic processes. The audience was familiar with Markoff processes, martingales, the detailed nature of the sample paths of the Wiener process, and measure theory on the space of sample paths.
After some historical and elementary material in chapters 1-8, we discuss the Ornstein-Uhlenbeck theory of Brownian motion in chapters 9-10, showing that the Einstein-Smoluchowski theory is in a rigorous and strong sense the limiting theory for infinite friction. The results of the long chapter 11 are not used in the following, except for the concepts of mean forward velocity, mean backward velocity, and mean acceleration. The rest of the notes deal with probability theory in quantum mechanics and in the alternative stochastic theory due to Imre Fenyes and others.
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Applied Probability and Stochastic Processes, 2nd Edition (Repost)



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Introduction to Stochastic Processes (North Holland series in probability and applied mathematics) by D. Kannan


Stochastic processes play a basic role in several problems of many branches of physical, biological, and social sciences, business and economics, and engineering. Having recognized the applicatory value of the theory of stochastic processes, almost all colleges and universities offer a course on this subject at least for a semester or quarter to suit the needs of students majoring in various areas.
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Quantum Independent Increment Processes I From Classical Probability to Quantum Stochastic Calculus


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