Diffusion processes, quantum dynamical semigroups, and the classical KMS condition
- 1 April 1984
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (4) , 1050-1065
- https://doi.org/10.1063/1.526274
Abstract
We study some properties of the generator of a diffusion process describing the reduced dynamics of a classical system weakly coupled to an external reservoir. We show that such processes may be equivalently obtained as classical limits of quantum dynamical semigroups derived in the weak coupling limit. We prove that the stationary state is independent of the coupling if and only if the reservoir is in a state of thermal equilibrium.Keywords
This publication has 25 references indexed in Scilit:
- A mechanical model of Brownian motionCommunications in Mathematical Physics, 1981
- A limit theorem for stochastic accelerationCommunications in Mathematical Physics, 1980
- On the distributions corresponding to bounded operators in the Weyl quantizationCommunications in Mathematical Physics, 1980
- Kinetic equations from Hamiltonian dynamics: Markovian limitsReviews of Modern Physics, 1980
- Solution of Fokker Planck equations with and without manifest detailed balanceZeitschrift für Physik B Condensed Matter, 1980
- Stationary states of quantum dynamical semigroupsCommunications in Mathematical Physics, 1978
- Properties of quantum Markovian master equationsReports on Mathematical Physics, 1978
- Quantum dynamical semigroups and the neutron diffusion equationReports on Mathematical Physics, 1977
- On the detailed balance condition for non-hamiltonian systemsReports on Mathematical Physics, 1976
- Generalized thermodynamic potential for Markoff systems in detailed balance and far from thermal equilibriumThe European Physical Journal A, 1971