text: *c-number correlation functions:*By choosing some partic- 
  ular ordering for products of atomic and ﬁeld operators, one 
  could derive the c-number stochastic Langevin equations from 
  the quantum Langevin equations derived above, and all of the 
  dynamic equations for c-number stochastic variables are the 
  same as in [26]. The diﬀerences are from the correlation func- 
  tions. On the other hand, we convert the quantum noise oper- 
  ators into the c-number noise variables ˜*Fk*(*t*)(*k*=*a*,*b*,*M*,*M*†), 
  whose correlation functions are expressed as 
  
  ˙*a*(*t*) =  *a*(*t*) +*gM*(*t*) +*F*κ(*t*),  (3) 
  
  *A*0 +*A*1 − 
  (γ*a*+ γ′*a*)*Na*(*t*) 
  
  *R*(1 
  *g*[*M*†(*t*)*a*(*t*) +*a*†(*t*)*M*(*t*)] +*Fa*(*t*), 
  
  *A*2) 
  − 
  
  ˜*Fk*(*t*) ˜*Fk*(*t*′) 
  E 
  
  (4) 
  − 
  τ)  *t*′ 
  −  − 
  ˙*Nb*(*t*) =  *B*1 +*B*2) 
  *R*(*B*0 − 