The boson and fermion Brownian motion as quantum central limits of the quantum Bernoulli processes. (English) Zbl 0858.60026

L. Accardi and A. Bach [in: Quantum probability and applications IV. Lect. Notes Math. 1396, 7-19 (1989; Zbl 0717.60034) and “The harmonic oscillators as quantum central limit of Bernoulli processes” (to appear)] have proved that the harmonic oscillator can be obtained as a quantum central limit of the Bernoulli processes and that the known boson Brownian motion arises from an invariance principle. In order to take over this shortcoming we now give a different proof of the results (loc.cit.) based on a technique which allows to obtain the analogous results in the Fermion case.


60F05 Central limit and other weak theorems
60K40 Other physical applications of random processes
46N50 Applications of functional analysis in quantum physics


Zbl 0717.60034