Semiflexible polymer on an anisotropic Bethe lattice

The mean-square end-to-end distance of an N-step polymer on a Bethe lattice is calculated. We consider semiflexible polymers placed on isotropic and a nisotropic lattices. The distance on the Cayley tree is defined by embeddin g the tree on a sufficiently high-dimensional Euclidean space, considering that every bend of the polymer defines a direction orthogonal to all the pr evious ones. In the isotropic case, the result obtained for the mean-square end-to-end distance turns out to be identical to the one obtained for idea l chains without immediate returns on an hypercubic lattice with the same c oordination number of the Bethe lattice. For the general case, we obtain as ymptotic behavior in both the semiflexible and almost rigid limits.