Opis: Quantum Stochastics - Mou-Hsiung Chang

The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigroups and processes, and large-time asymptotic behavior of quantum Markov semigroups. 'This excellent introductory book on quantum stochastics is most timely - the highly interdisciplinary book needed in this century. Dr Chang has organized and presented the material in a systematic and coherent manner ... [The] material is self-contained and self-readable; ideas, concepts and topics are up-to-date, well-motivated, well presented and well associated with the classical approach: starting from the idea of a quantum system, to quantum probability space, measure, processes with quantum stochastic calculus, quantum stochastic differential equations, quantum stability, quantum semigroups, and so on. I am looking forward to using this book for my graduate course on quantum stochastic dynamic systems. I will also highly recommend it to my students and colleagues.' G. S. Ladde, University of South Florida, and founder and editor of the Journal of Stochastic Analysis and Applications 'Mou-Hsiung Chang's book is a comprehensive and lucid account of quantum probability and stochastics. It is a welcome and up-to-date addition to the literature on this topic and will likely become a valuable reference for both experts and graduate students interested in specializing in this field.' Daniel Lidar, University of Southern California 'Although introduced at the same time as its standard (axiomatic) counterpart, quantum probability took almost half a century to become popular, first with physicists and then more broadly. The early books documenting this progress - by Meyer and by Accardi, Frigerio, and Lewis - targeted mostly theorists. Fortunately, this new arrival, by Mou-Hsiung Chang, speaks to a much larger readership. The book is very well written and appears to be accessible to a broad audience, including engineers, applied mathematicians, and physicists.' Boris Rozovsky, Ford Foundation Professor of Applied Mathematics, Brown UniversityIntroduction and summary; 1. Operator algebras and topologies; 2. Quantum probability; 3. Quantum stochastic calculus; 4. Quantum stochastic differential equations; 5. Quantum Markov semigroups; 6. Minimal QDS; 7. Quantum Markov processes; 8. Strong quantum Markov processes; 9. Invariant normal states; 10. Recurrence and transience; 11. Ergodic theory.

Szczegóły: Quantum Stochastics - Mou-Hsiung Chang

Tytuł: Quantum Stochastics
Autor: Mou-Hsiung Chang
Producent: Cambridge University Press
ISBN: 9781107069190
Rok produkcji: 2015
Ilość stron: 424
Oprawa: Twarda
Waga: 0.94 kg

Recenzje: Quantum Stochastics - Mou-Hsiung Chang