Abstract :
Using atomic resolution microscopy, it is now possible to observe directly discrete random walks of single atoms and small atom-clusters, nucleation and dissociation of clusters and surface layers, etc. on solid surfaces. Such information is needed for understanding atomic interactions, mechanisms of growth of thin films and crystals, and the dynamic behavior of surfaces. In this type of experiment, data analysis is very direct without the need of relying on uncertain physical modeling. For analyzing data, all we need usually are some of the equations available in mathematical theory of random walks. Some of the mathematical problems we still have to solve are the finite size effect of the small surfaces, how the jump length distribution of the atomic jump is related to the mean square displacement and displacement distribution, and how the random walk of a simple cluster is related to the coupled but otherwise still random jumps of each of the atoms in the cluster, etc. In the past, one focused on equilibrium statistics of infinite systems and their universal behavior. Recent interest shifts to small and steady state systems where fiite size and quantum effects are important. They may exhibit universal behavior also.
