Abstract:
In the present thesis a random walk on quasi-1d lattices as a model for transport processes on quasi-1d materials is analytically investigated. The scope of the present work is to shed light on the asymptotic behavior of basic statistical properties of the random walk on such structures including the first and the second moments of the walker location along the structure axis, the probability of return to the starting site, the probability of ever reach a given site, the conditional mean first-passage time to a given site and the expected number of distinct sites visited.
The first part of the thesis deals with developing a method for obtaining these basic properties by employing the concepts of generating functions and the Fourier-Laplace transform. Based on this developed method, in the remaining parts, the random walks on different quasi-1d lattices, i.e., a perfect-1d lattice, branched lattices, ladder lattices and cylindrical lattices, and their feasible applications are discussed.
