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Book
Probability and randomness : quantum versus classical
Author:
ISBN: 9781783267965 1783267968 Year: 2016 Publisher: Covent Garden, London : Imperial College Press,

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Abstract

"Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Interrelation of Classical and Quantum Randomness rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level"--


Book
Social laser : application of quantum information and field theories to modeling of social processes
Author:
ISBN: 100073045X 0367817209 1000730212 Year: 2020 Publisher: Singapore : Jenny Stanford Publishing,

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The recent years have been characterized by stormy social protests throughout the world. These protests have some commonalities, but at the same time, their sociopolitical, psychological, and economic contexts differ essentially. An important class of such protests is known as color revolutions. The analysis of these events in social and political literature is characterized by huge diversity of opinions. We remark that the sociopolitical perturbations under consideration are characterized by the cascade dynamics leading to the exponential amplification of coherent social actions. In quantum physics, such exponential and coherent amplification is the basic feature of laser's functioning. (Laser is acronym for light amplification by stimulated emission of radiation). In this book we explore the theory of laser to model aforementioned waves of social protests, from color revolutions to Brexit and Trump's election. We call such social processes Stimulated Amplification of Social Actions (SASA), but to keep closer to the analogy with physics we merely operate with the term social laser.


Book
Contextual reinterpretation of quantum nonlocality
Author:
ISBN: 9781009313490 1009313495 9781009313469 1009313460 9781009313476 Year: 2024 Publisher: Cambridge Cambridge University Press

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The quantum information revolution has had a huge impact not only on quantum technologies, including quantum computing and cryptography, but also on the foundations of quantum mechanics. This book presents the information viewpoint on the foundations of quantum physics by highlighting the role of complementarity and contextuality and coupling the ideas of the fathers of quantum mechanics, Bohr and Einstein, with the modern quantum information framework. The classical-quantum dilemma is resolved through an appeal to the Bild conception of scientific theories established in the 19th century by Hertz and Boltzmann. Bell inequalities are treated from the complementarity-contextuality viewpoint, supporting the attempts to discard nonlocality from quantum physics. Philosophical aspects of the topic are explored from a physicist's perspective, balancing accessibility with scientific rigour. This unique approach to quantum foundations will be of interest to graduates, Ph.D. students and researchers in fields ranging from quantum information to philosophy.


Book
Quantum social science
Authors: ---
ISBN: 9781107012820 9781139003261 9781139840033 1139840037 1139003267 9781139842419 1139842412 9781139844772 1139844776 1107012821 9781283942935 1283942933 1139853856 1107234832 113984122X 1139845756 Year: 2013 Publisher: Cambridge Cambridge University Press

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Written by world experts in the foundations of quantum mechanics and its applications to social science, this book shows how elementary quantum mechanical principles can be applied to decision-making paradoxes in psychology and used in modelling information in finance and economics. The book starts with a thorough overview of some of the salient differences between classical, statistical and quantum mechanics. It presents arguments on why quantum mechanics can be applied outside of physics and defines quantum social science. The issue of the existence of quantum probabilistic effects in psychology, economics and finance is addressed and basic questions and answers are provided. Aimed at researchers in economics and psychology, as well as physics, basic mathematical preliminaries and elementary concepts from quantum mechanics are defined in a self-contained way.


Book
Theory of p-adic distributions
Authors: --- ---
ISBN: 9781139127776 1139127772 9781139107167 113910716X 9781139117111 1139117114 9780521148566 0521148561 113910716X 9781139114943 1139114948 1107203732 9781107203730 1283295997 9781283295994 1139122851 9781139122856 9786613295996 661329599X 1139112759 9781139112758 Year: 2010 Publisher: Cambridge Cambridge University Press

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This 2010 book was the first devoted to the theory of p-adic wavelets and pseudo-differential equations in the framework of distribution theory. This relatively recent theory has become increasingly important in the last decade with exciting applications in a variety of fields, including biology, image analysis, psychology, and information science. p-Adic mathematical physics also plays an important role in quantum mechanics and quantum field theory, the theory of strings, quantum gravity and cosmology, and solid state physics. The authors include many new results, some of which constitute new areas in p-adic analysis related to the theory of distributions, such as wavelet theory, the theory of pseudo-differential operators and equations, asymptotic methods, and harmonic analysis. Any researcher working with applications of p-adic analysis will find much of interest in this book. Its extended introduction and self-contained presentation also make it accessible to graduate students approaching the theory for the first time.


Book
Ultrametric pseudodifferential equations and applications
Authors: --- ---
ISBN: 1108100104 1316986705 1108102905 9781108102902 9781316986707 9781107188822 1107188822 Year: 2018 Publisher: Cambridge Cambridge University Press

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Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.

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