Title: QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION
Author(s): A.E.Kobryn (Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan; Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan) , T.Hayashi, T.Arimitsu (Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan)

Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.

Key words: stochastic processes, boson Brownian motion, fermion Brownian motion
PACS: 02.50.Ey, 05.30.-d