Exact time evolution of the pair distribution function for an entangled two-electron initial state

exact time-evolving wave function from a prescribed correlated initial state. Using this evolving wave function, the time-dependent pair probability function R(x1,x2,t) ≡ n2(x1,x2,t)/[n(x1,t) n(x2,t)] is determined via the pair density n2(x1,x2,t) and single-particle density n(x,t). It is found that R(0,0,t =∞ ) = R(0,0,t = 0) > 1, and R(x1,x2,t ∗ ) = 1 at a finite t ∗ for � � 0 interparticle interaction strength in the initial two-electron model. By expanding n(x,t) in an infinite sum of closed-shell products of time-dependent normalized single-particle states and time-dependent occupation numbers Pk(�,t ), the von Neumann entropy S(�,t ) =− ∞=0 Pk(t)lnPk(t )i s calculated as well. The such-defined information entropy is zero at t ∗ (� ) and its maximum in time is S(�,t = ∞) = S(�,t = 0).