Derivation of the Lindblad generator structure by use of the Itô stochastic calculus

  title={Derivation of the Lindblad generator structure by use of the It{\^o} stochastic calculus},
  author={Stephen L. Adler},
  journal={Physics Letters A},
  • S. Adler
  • Published 24 September 1999
  • Physics
  • Physics Letters A
Abstract We use the Ito stochastic calculus to give a simple derivation of the Lindblad form for the generator of a completely positive density matrix evolution, by specialization from the corresponding global form for a completely positive map. As a by-product, we obtain a generalized generator for a completely positive stochastic density matrix evolution. 
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For an excellent exposition of the Itô calculus, see C. W. Gardiner, Handbook of Stochastic Methods
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