open quantum system in nLab
Consider a pair of quantum systems, QQ and EE, where QQ is some system of interest and EE is some system that is external to QQ and that is in some fixed pure state |e⟩\vert e \rangle. Now let us suppose that the two systems interact and evolve via some unitary operator on the tensor product Hilbert space of each, 𝒬⊗ℰ\mathscr{Q} \otimes \mathscr{E}. If one is interested in the ℰ\mathscr{E}-trace of density operators on this system, then QQ is known as an open system and EE is the environment.
Stéphane Attal, Alain Joye, Claude-Alain Pillet (eds.), Open Quantum Systems I – The Hamiltonian Approach, Lecture Notes in Mathematics 1880, Springer (2006) [doi:10.1007/b128449]
Stéphane Attal, Alain Joye, Claude-Alain Pillet (eds.), Open Quantum Systems II – The Markovian approach, Lecture Notes in Mathematics 1881, Springer (2006) [doi:10.1007/b128451]
Stéphane Attal, Alain Joye, Claude-Alain Pillet (eds.), Open Quantum Systems III – Recent Developments, Lecture Notes in Mathematics 1882, Springer (2006) [doi:10.1007/b128453]
Heinz-Peter Breuer, Francesco Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2007) [doi:10.1093/acprof:oso/9780199213900.001.0001]
Benjamin Schumacher, Michael Westmoreland, Quantum Processes, Systems, and Information, Cambridge University Press (2010) [doi:10.1017/CBO9780511814006]
Fabrizio Minganti, Alberto Biella: Open quantum systems – A brief introduction [arXiv:2407.16855]