  In reconstituting k-mer models, extended objects which occupy several sites
on a one dimensional lattice, undergo directed or undirected diffusion, and
reconstitute -when in contact- by transferring a single monomer unit from one
k-mer to the other; the rates depend on the size of participating k-mers. This
polydispersed system has two conserved quantities, the number of k-mers and the
packing fraction. We provide a matrix product method to write the steady state
of this model and to calculate the spatial correlation functions analytically.
We show that for a constant reconstitution rate, the spatial correlation
exhibits damped oscillations in some density regions separated, from other
regions with exponential decay, by a disorder surface. In a specific limit,
this constant-rate reconstitution model is equivalent to a single dimer model
and exhibits a phase coexistence similar to the one observed earlier in totally
asymmetric simple exclusion process on a ring with a defect.
