2011/01/12 by Oliver Muelken, Alexander Blumen · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physrep.2011.01.002
published as Physics Reports 502, 37-87 (2011) · review article to appear in Physics Reports, 39 pages, 44 figures
arxiv created 2011/01/12 · arxiv updated 2015/05/27
This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the theoretical ideas behind CTQW and of its relation to classical continuous-time random walks (CTRW) in Sec.~2, implications for the efficiency of the transport are presented in Sec.~3. The fourth section gives an overview of different types of networks on which CTQW have been studied so far. Extensions of CTQW to systems with long-range interactions and with static disorder are discussed in section V. Systems with traps, i.e., systems in which the walker's probability to remain inside the system is not conserved, are presented in section IV. Relations to similar approaches to the transport are studied in section VII. The paper closes with an outlook on possible future directions.