Spectral Analysis Of Quantum Bernoulli Noises

Quantum Bernoulli noises axe the family of annihilation and creation operators acting on Bernoulli functionals,whiclh satisfy a canonical anti-commutation relation(CAR)in equal-time.In this paper,we mainly discusses the spectral analysis of quantum Bernoulli noises.Let {(?)k,(?)k|k? 0} be quantum Bernoulli noises.The main work of this paper is as follows:Firstly,we verify the structural properties of the operator(?)k=(?)k*+(?)k and sum operator Sn=(?)(?)k,and we obtain the spectral decomposition of these operators.Secondly,we prove the central limit theorem in quantum form based on the above spectral decomposition results.Thirdly,we consider the application of the spectrum decomposition of quantum Bernoulli noises in the quantum random walks.