The velocity distribution function for a polymer chain

The Gibbs distribution for a polymer molecule contains implicitly the correlation functions for velocity and position of the constituent monomers. The purely spatial part, ignoring potentials, gives the random flight distribution; the velocity correlation function is calculated, exploiting the markovian structure of the problem in phase space. It is shown that the problem can be reduced to an eigenfunction problem and hence solved. The form of the correlation function is quite accurately given by ( nu n1- nu n2)2=(2kT/m)(1-exp(-c mod n1-n2 mod )) where nu n1, nu n2 are the velocities of the n1th and n2th monomers and c equivalent to 1.