Quantum Probability


Book Description

Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism. Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles. The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.







Quantum Probability for Probabilists


Book Description

These notes contain all the material accumulated over six years in Strasbourg to teach "Quantum Probability" to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true "Lecture Notes" material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "for probabilists" in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "Quantum Probability" , the main topic is "Quantum Stochastic Calculus" , a field which has recently got official recognition as 81825 in the Math.




Quantum Probability and Spectral Analysis of Graphs


Book Description

This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.




Quantum Mechanics


Book Description

The classic textbook on quantum mechanics from Nobel Prize–winning physicist P. J. E. Peebles This book explains the often counterintuitive physics of quantum mechanics, unlocking this key area of physics for students by enabling them to work through detailed applications of general concepts and ideas. P. J. E. Peebles states general principles first in terms of wave mechanics and then in the standard abstract linear space formalism. He offers a detailed discussion of measurement theory—an essential feature of quantum mechanics—and emphasizes the art of numerical estimates. Along the way, Peebles provides a wealth of physical examples together with numerous problems, some easy, some challenging, but all of them selected because they are physically interesting. Quantum Mechanics is an essential resource for advanced undergraduates and beginning graduate students in physics.




Helgoland


Book Description

Named a Best Book of 2021 by the Financial Times and a Best Science Book of 2021 by The Guardian “Rovelli is a genius and an amazing communicator… This is the place where science comes to life.” ―Neil Gaiman “One of the warmest, most elegant and most lucid interpreters to the laity of the dazzling enigmas of his discipline...[a] momentous book” ―John Banville, The Wall Street Journal A startling new look at quantum theory, from the New York Times bestselling author of Seven Brief Lessons on Physics, The Order of Time, and Anaximander. One of the world's most renowned theoretical physicists, Carlo Rovelli has entranced millions of readers with his singular perspective on the cosmos. In Helgoland, he examines the enduring enigma of quantum theory. The quantum world Rovelli describes is as beautiful as it is unnerving. Helgoland is a treeless island in the North Sea where the twenty-three-year-old Werner Heisenberg made the crucial breakthrough for the creation of quantum mechanics, setting off a century of scientific revolution. Full of alarming ideas (ghost waves, distant objects that seem to be magically connected, cats that appear both dead and alive), quantum physics has led to countless discoveries and technological advancements. Today our understanding of the world is based on this theory, yet it is still profoundly mysterious. As scientists and philosophers continue to fiercely debate the meaning of the theory, Rovelli argues that its most unsettling contradictions can be explained by seeing the world as fundamentally made of relationships rather than substances. We and everything around us exist only in our interactions with one another. This bold idea suggests new directions for thinking about the structure of reality and even the nature of consciousness. Rovelli makes learning about quantum mechanics an almost psychedelic experience. Shifting our perspective once again, he takes us on a riveting journey through the universe so we can better comprehend our place in it.




Quantum Mechanics


Book Description

From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum physics First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.




Quantum Probability and Infinite Dimensional Analysis


Book Description

On the central extensions of the Heisenberg algebra / L. Accardi & A. Boukas -- Representations of the Lévy-Meixner oscillator algebra and the overcompleteness of the associated sequences of coherent states / A. Barhoumi, H. Ouerdiane & A. Riahi -- Some systems of dualities in white noise analysis / T. Hida -- Quantum white noise derivatives and associated differential equations for white noise operators / U.C. Ji & N. Obata -- The Gibbs conditioning principle for white noise distributions : interacting and non-interacting cases / F. Cipriano, S. Gheryani & H. Ouerdiane -- Markov triplets on CAR algebras / J. Pitrik -- Quantum Fokker-Planck models : limiting case in the Lindblad condition / F. Fagnola & L. Neumann -- Generalized Euler heat equation / A. Barhoumi, H. Ouerdiane & H. Rguigui -- On quantum De Finetti's theorems / V. Crismale & Y.G. Lu -- Kolmogorovian model for EPR-experiment / D. Avis [und weitere] -- Free white noise stochastic equation / L. Accardi, W. Ayed & H. Ouerdiane -- Lévy models robustness and sensitivity / F.E. Benth, G. Di Nunno & A. Khedher -- Quantum heat equation with quantum K-Gross Laplacian : solutions and integral representation / S. Horrigue & H. Ouerdiane -- On Marginal Markov processes of quantum quadratic stochastic processes / F. Mukhamedov -- On the applicability of multiplicative renormalization method for certain power functions / I. Kubo, H.-H. Kuo & S. Namli -- Convolution equation : solution and probabilistic representation / J.L. Da Silva, M. Erraoui & H. Ouerdiane -- From classical to quantum entropy production / F. Fagnola & R. Rebolledo -- Extending the set of quadratic exponential vectors / L. Accardi, A. Dhahri & M. Skeide -- On operator-parameter transforms based on nuclear algebra of entire functions and applications / A. Barhoumi [und weitere] -- Dissipative quantum annealing / D. de Falco, E. Pertoso & D. Tamascelli







Understanding Quantum Mechanics


Book Description

Here Roland Omnès offers a clear, up-to-date guide to the conceptual framework of quantum mechanics. In an area that has provoked much philosophical debate, Omnès has achieved high recognition for his Interpretation of Quantum Mechanics (Princeton 1994), a book for specialists. Now the author has transformed his own theory into a short and readable text that enables beginning students and experienced physicists, mathematicians, and philosophers to form a comprehensive picture of the field while learning about the most recent advances. This new book presents a more streamlined version of the Copenhagen interpretation, showing its logical consistency and completeness. The problem of measurement is a major area of inquiry, with the author surveying its history from Planck to Heisenberg before describing the consistent-histories interpretation. He draws upon the most recent research on the decoherence effect (related to the modern resolution of the famous Schrödinger's cat problem) and an exact formulation of the correspondence between quantum and particle physics (implying a derivation of classical determinism from quantum probabilism). Interpretation is organized with the help of a universal and sound language using so-called consistent histories. As a language and a method, it can now be shown to be free of ambiguity and it makes interpretation much clearer and closer to common sense.