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On dilating quantum dynamical semigroups with classical brownian motion

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We show that any quantum dynamical semigroup can be written with the help of the solution of an operator-valued classical stochastic differential equation. Moreover, this equation leads to a canonical construction of a unitary dilation in terms of Wiener spaces. We also briefly discuss an equivalent description on a Fock-like space.

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Institute of Theoretical Physics and Astrophysics, Gdansk, Poland

Bevoegdverklaard navorser NFWO, Belgium

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Alicki, R., Fannes, M. On dilating quantum dynamical semigroups with classical brownian motion. Lett Math Phys 11, 259–262 (1986). https://doi.org/10.1007/BF00400224

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  • Differential Equation
  • Statistical Physic
  • Brownian Motion
  • Group Theory
  • Stochastic Differential Equation