Quantum Quadratic Operators and Processes, 1st ed. 2015 Lecture Notes in Mathematics Series, Vol. 2133

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.

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.

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