Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels.

This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.

Provides a self-contained treatment of nonlinear Markov evolution, with a focus on (classical and quantum) quadratic operators and the asymptotic behavior of the dynamical systems they generate This is the first book to study both classical and quantum (non-commutative) nonlinear dynamics using the theory of Markov processes Covers the most recent developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes Includes material which has potential applications to quantum information theory Includes supplementary material: sn.pub/extras

Inhalt

Introduction.- Quadratic Stochastic Operators.- Quadratic Processes.- Analytic methods in the theory of quadratic stochastic processes.- Quantum quadratic operators.- Quantum quadratic operators on M2(C).- Infinite-dimensional quadratic operators.- Quantum quadratic stochastic processes.