Quantum Stochastics

This book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes.

Mou-Hsiung Chang (Author)

9781107069190, Cambridge University Press

Hardback, published 19 February 2015

424 pages
26.5 x 18.5 x 3 cm, 0.94 kg

'The book by Mou-Hsiung Chang falls in the original spirit of the field, i.e. it focuses on the mathematical aspects of open quantum dynamics. As such, the book is mathematically rigorous, at least for the topics it touches. The first two chapters formally introduce operator theory and quantum probability theory. All fundamental elements of quantum mechanics and the corresponding mathematical structures are discussed in details. … there are a large number of important topics covered in this book, including dynamical semigroups, master equations, Markov processes, recurrence and transience and ergodic theory.' Kavan Modi, Contemporary Physics

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.

Introduction 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.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], Stochastics [PBWL], Probability & statistics [PBT], Calculus & mathematical analysis [PBK], Information theory [GPF]