Time-Local Master Equations: Influence Functional and Cumulant Expansion

  • H.-P. Breuer
  • A. Ma
  • F. Petruccione


The non-Markovian behavior of open quantum systems interacting with a reservoir can often be described in terms of a time-local master equation involving a time-dependent generator which is not in Lindblad form. A systematic perturbation expansion of the generator is obtained either by means of van Kampen’s method of ordered cumulants or else by use of the Feynman — Vernon influence functional technique. Both expansions are demonstrated to yield equivalent expressions for the generator in all orders of the system-reservoir coupling. Explicit formulae are derived for the second- and the fourth-order generator in terms of the influence functional.


Open quantum system Non-Markovian quantum processes Influence functional Time-convolutionless projection operator technique Cumulant expansion Stochastic wavefunction method 


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • H.-P. Breuer
    • 1
    • 2
  • A. Ma
    • 2
    • 3
  • F. Petruccione
    • 2
    • 4
  1. 1.Fachbereich PhysikCarl von Ossietzky UniversitätOldenburgGermany
  2. 2.Fakultät für PhysikUniversität FreiburgFreiburgGermany
  3. 3.Blackett LaboratoryImperial CollegeLondonUK
  4. 4.Istituto Italiano per gli Studi FilosoficiNapoliItaly

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