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The microscopic derivation of Open Quantum Brownian Motion (OQBM) is presented [1,2]. OQBM is obtained as a special limit (scaling limit) of the recently introduced Open Quantum Walks [3,4]. The quantum master equation for OQBM is derived for a weakly driven system interacting with the decoherent environment. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented.
 M. Bauer, D. Bernard and A. Tilloy, Phys. Rev. A 88
 M. Bauer, D. Bernard and A. Tilloy, The Open Quantum
Brownian Motion, math-ph/1312.1600.
 S. Attal, F. Petruccione and I. Sinayskiy, Phys. Lett. A 376 (2012), 1545.
 S. Attal, F. Petruccione, C. Sabot and I. Sinayskiy, J. Stat. Phys. 147 (2012), 832.