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We study the quantum-mechanical transport on two-dimensional graphs by meansof continuous-time quantum walks and analyse the effect of different boundaryconditions (BCs). For periodic BCs in both directions, i.e., for tori, theproblem can be treated in a large measure analytically. Some of these resultscarry over to graphs which obey open boundary conditions (OBCs), such ascylinders or rectangles. Under OBCs the long time transition probabilities(LPs) also display asymmetries for certain graphs, as a function of theirparticular sizes. Interestingly, these effects do not show up in the marginaldistributions, obtained by summing the LPs along one direction.Comment: 22 pages, 11 figure, acceted for publication in J.Phys.

Quantum transport on two-dimensional regular graphs