2006/10/25 by Antonio Volta, A. Volta, Oliver Muelken +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Combinatorics #Computer science #Function (biology) #Geometry #Mathematical analysis #Mathematics #Measure (data warehouse) #Periodic boundary conditions #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum graph #Quantum mechanics #Quantum-Dot Cellular Automata #Statistical physics #Torus #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/48/011
published as J. Phys. A 39, 14997 (2006) · 22 pages, 11 figure, acceted for publication in J.Phys.A
arxiv created 2006/10/25 · openalex publication_date 2006/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.