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Continuous-time quantum walks: Models for coherent transport on complex networks

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Mülken, Oliver, Blumen, Alexander·2011·Physics Reports
DOI 10.1016/j.physrep.2011.01.002
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Abstract

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.

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Metadata

Authors
Mülken, O., & Blumen, A.
Venue
Physics Reports
Publisher
Elsevier BV
Published
2011-05
Volume
502
Issue
2-3
Pages
37-87
ISSN
0370-1573 (ISSN-L)
DOI
10.1016/j.physrep.2011.01.002
OpenAlex
W2004855787
Cited by
325
References
20
FWCI
17.44
Type
journal article
Language
en
Open access
green
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)

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Mülken, O., & Blumen, A. (2011). Continuous-time quantum walks: Models for coherent transport on complex networks. Physics Reports. https://doi.org/10.1016/j.physrep.2011.01.002

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