Universal law for piecewise dimer diffusion

We present a theoretical study of the dissociation-reassociation (DR) mechanism for one-dimensional dimer diffusion. Through a random-walk calculation we find an exact analytical expression for the jump-length (\l\) probability distribution P(\l\), and we show that such a distribution is very well approximated, already for small \l\ (\l\ greater than or similar to 3), by its simple asymptotic form P(\l\) = 1/(pi\l\(2)). We derive the exact expression of the time-dependent probability distribution Phi(l, t ), a quantity which is usually measured in scanning tunneling microscopy and field-ion microscopy experiments, both in the case in which the dimer diffuses only by the DR mechanism and in the case in which other mechanisms (such as the concerted jump and the leapfrog) are possible. This expression is useful in fitting the experimental data. Theoretical and experimental consequences are discussed.