Communications in Mathematical Physics

, Volume 48, Issue 2, pp 119–130

On the generators of quantum dynamical semigroups


  • G. Lindblad
    • Department of Theoretical PhysicsRoyal Institute of Technology

DOI: 10.1007/BF01608499

Cite this article as:
Lindblad, G. Commun.Math. Phys. (1976) 48: 119. doi:10.1007/BF01608499


The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum analogue of the Lévy-Khinchin formula. As a result the general form of a large class of Markovian quantum-mechanical master equations is obtained.

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© Springer-Verlag 1976