Using exact results from the theory of completely integrable systems of the Painlevé/Toda type, we examine the consequences for the theory of polyelectrolytes in the (nonlinear) Poisson-Boltzmann approximation.

We compute exactly the transverse time-dependent spin-spin correlation functions 〈Sx1(0)SxR+1(t)〉 and 〈Sy1(0)SyR+1(t)〉 at zero temperature for the one-dimensional XY model that is defined by the hamiltonian HN = - ΣNi=1 [(1 + γ)SxiSxi+1 + (1 − γ)SyiSyi+1 + hSzi]. We then analyze...