text: σ*j* σ*j* = 
  
  *a*(*t j*+ τ) 
  *q*
  E 
  *a*(*t j*+ 2τ +*T*) 
  
  = 
  
  *a*(*t j*+ τ +*T*) 
  D 
  = 
  *b*(*t j*+ τ) 
  σ*j*
  *b*(*t j*+ 2τ +*T*) 
  D 
  *i*σ*j*
  (*t j*+ τ +*T*) 
  D− 
  − 
  
  with*A*0  ,*A*1 
  
  *q*
  E 
  *q*
  E 
  *q*
  E 
  *q*
  E 
  *C*2 = 
  *R*is the mean pumping 
  . 
  *q*
  E 
  rate, which is deﬁned in [26]. It is very easy to check that the 
  average values of the above Langevin forces are all zero. 
  
  D 
  σ*j* σ*j* = 
  *A*2  ,  *B*0 
  
  *q*
  E 
  ,*B*2 
  
  D 
  σ*j*
  *b*(*t j*+ τ +*T*) 
  D 
  *i*σ*j*
  (*t j*+ τ) 
  D− 
  − 
  *i*σ*j*
  (*t j*+ 2τ +*T*) 
  − 
  
  D 
  =  = 
  *B*1 
  
  *q*
  E 
  ,*C*1 
  *q*
  =  = 
  *C*0 
  E 
  
  D− 