Quantum transport on two-dimensional regular graphs

Abstract

We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem can be treated in a large measure analytically. Some of these results carry over to graphs which obey open boundary conditions (OBCs), such as cylinders or rectangles. Under OBCs the long time transition probabilities (LPs) also display asymmetries for certain graphs, as a function of their particular sizes. Interestingly, these effects do not show up in the marginal distributions, obtained by summing the LPs along one direction.

22 pages, 11 figure, acceted for publication in J.Phys.A

References in corpus (3)

• Spatial search by quantum walk
• Coherent exciton transport in dendrimers and continuous-time quantum walks
• Coherent dynamics on hierarchical systems

Cited by in corpus (6)

• Quantum Networks on Cubelike Graphs
• Exact analytical results for quantum walks on star graph
• Dynamics of continuous-time quantum walks in restricted geometries
• Continuous-time quantum walks on one-dimension regular networks
• Coherent exciton transport and trapping on long-range interacting cycles
• Phase space patterns of quantum transport on ordered and disordered networks