Dissipative Stochastic Schr(?)dinger Equation In Terms Of Local Quantum Bernoulli Noises

Linear stochastic Schr(?)dinger equation(LSSE)is a stochastic evolution equation in complex separable Hilbert space,which is used to describe open quantum systems.Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals,which satisfy a canonical anti-commutation relation(CAR)in equal-time.Local quantum Bernoulli noises is the localization of quantum Bernoulli noises.In this paper,we use quantum Bernoulli noises to study linear stochastic Schr(?)dinger equation.The main work is as follows:Firstly,we investigate the linear stochastic Schr(?)dinger equation in terms of local quantum Bernoulli noises,it is proved that the equation is dissipative under appropriate conditions.From this,the existence and uniqueness of weak topology solution of the equations are obtained.Secondly,a class of quantum dynamical semigroups is constructed by using the weak topology solutions of the dissipative stochastic Schr(?)dinger equation in terms of local quantum Bernoulli noises.Thirdly,as a example,we consider a linear stochastic Schr(?)dinger equation in terms of local quantum Bernoulli noises,which is perturbed by a special positive operator.