Some Applications Of Local Quantum Bernoulli Noises

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 are the localization of quan-tum Bernoulli noises.In this paper,we mainly discuss application of local quantum Bernoulli noises to some problems in mathematical physics.Our main work is as followsFirstly,we give communication relations of several operators on discrete-time Bernoulli noises functionalsSecondly,we consider a class of non-linear stochastic Schrodinger equations(NLSSE)associated with local quantum Bernoulli noises(LQBN)on the space L2(Z)of square integrable functionals of Z,which might play a role in the description of random evolution of open quantum system.Using the known results on a general NLSSE,we establish the existence and uniqueness of regular strong solutions to a NLSSE associated with LQBN,discuss Markov-type property of its solutions,and acquire a sufficient condition for the existence of regular invariant probability measures for EquationsFinally,we consider quantum Master equations associated with local quantum Bernoulli noises(LQBN)on the space L2(Z)of square integrable functionals of Z Using the known results on a general quantum Master equations,we establish the existence and uniqueness of semigroup regular solution to quantum Master equations associated with LQBN,and discuss the existence of the regular stationary solution of the Equations.