Understanding dissipative dynamics of open quantum systems remains
a challenge in mathematical physics. This problem is relevant in
various areas of fundamental and applied physics. From a
mathematical point of view, it involves a large body of knowledge.
Significant progress in the understanding of such systems has been
made during the last decade. These books present in a
self-contained way the mathematical theories involved in the
modeling of such phenomena. They describe physically relevant
models, develop their mathematical analysis and derive their
physical implications.
In Volume I the Hamiltonian description of quantum open systems
is discussed. This includes an introduction to quantum statistical
mechanics and its operator algebraic formulation, modular theory,
spectral analysis and their applications to quantum dynamical
systems.
Volume II is dedicated to the Markovian formalism of classical
and quantum open systems. A complete exposition of noise theory,
Markov processes and stochastic differential equations, both in the
classical and the quantum context, is provided. These mathematical
tools are put into perspective with physical motivations and
applications.
Volume III is devoted to recent developments and applications.
The topics discussed include the non-equilibrium properties of open
quantum systems, the Fermi Golden Rule and weak coupling limit,
quantum irreversibility and decoherence, qualitative behaviour of
quantum Markov semigroups and continual quantum measurements.
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