Journal of Statistical Physics

, Volume 32, Issue 2, pp 299–312 | Cite as

Nonlinear quantum dynamical semigroups for many-body open systems

  • R. Alicki
  • J. Messer


The notion of a nonlinear quantum dynamical semigroup is introduced, and the existence and uniqueness of solutions of the corresponding nonlinear evolution equations are studied in a more abstract framework. The construction of nonlinear quantum dynamical semigroups is carried out for two different mean-field models. First a mean-field coupling between a system of noninteracting subsystems and the bath is investigated. As examples, a nonlinear frictional Schrödinger equation and a model for a quantum Boltzmann equation are discussed. Second, a many-body system with mean-field interaction coupled to a bath is considered. Here, again, the form of the generator is derived; however, it cannot be obtained rigorously, except for some particular examples. Finally, the quantum Ising-Weiss model is briefly studied.

Key words

Quantum dynamical semigroups open systems reduced description of many-body systems mean-field models nonlinear evolution equations nonlinear frictional Schrödinger equations quantum Boltzmann equation Hartree equation Ising-Weiss model 


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Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • R. Alicki
    • 1
  • J. Messer
    • 1
  1. 1.Sektion Physik, Theoretische PhysikUniversität MünchenMünchen 2Federal Republic of Germany

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