Universal law for piecewise dimer diffusion

We present a theoretical study of the dissociation-reassociation (DR) mecha nism for one-dimensional dimer diffusion. Through a random-walk calculation we find an exact analytical expression for the jump-length (\l\) probabili ty distribution P(\l\), and we show that such a distribution is very well a pproximated, already for small \l\ (\l\ greater than or similar to 3), by i ts simple asymptotic form P(\l\) = 1/(pi\l\(2)). We derive the exact expres sion of the time-dependent probability distribution Phi(l, t ), a quantity which is usually measured in scanning tunneling microscopy and field-ion mi croscopy 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 con certed jump and the leapfrog) are possible. This expression is useful in fi tting the experimental data. Theoretical and experimental consequences are discussed. [S0163-1829(99)03239-7].