Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
arXiv:1101.2572 · doi:10.1016/j.physrep.2011.01.002
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.
review article to appear in Physics Reports, 39 pages, 44 figures
References in corpus (27)
- Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
- Dephasing assisted transport: Quantum networks and biomolecules
- Spatial search by quantum walk
- Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Quantum Communication through Spin Chain Dynamics: an Introductory Overview
- Efficiency of energy transfer in a light-harvesting system under quantum coherence
- Connecting the discrete and continuous-time quantum walks
- Quantum Walks on a Random Environment
- Survival Probabilities in Coherent Exciton Transfer with Trapping
- Relaxation and Zeno effect in qubit measurements
- Coherent exciton transport in dendrimers and continuous-time quantum walks
- Quantum transport on small-world networks: A continuous-time quantum walk approach
- Continuous-time Quantum Walks on a Cycle Graph
- Efficiency of quantum and classical transport on graphs
- Exact analytical results for quantum walks on star graph
- Dynamics of continuous-time quantum walks in restricted geometries
- Coherent transport on Apollonian networks and continuous-time quantum walks
- Trapping time statistics and efficiency of transport of optical excitations in dendrimers
- Continuous-time quantum walks on one-dimension regular networks
- Coherent dynamics on hierarchical systems
- Non-Unitary Quantum Walks on Hyper-Cycles
- Quantum transport on two-dimensional regular graphs
- Coherent exciton transport and trapping on long-range interacting cycles
- Universal Behavior of Quantum Walks with Long-Range Steps
- Slow Excitation Trapping in Quantum Transport with Long-Range Interactions
- Phase space patterns of quantum transport on ordered and disordered networks
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