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Random Walks on Lattices. III. Calculation of First-Passage Times with Application to Exciton Trapping on Photosynthetic Units
Abstract
The following statistical problem arises in the theory of exciton trapping in photosynthetic units: Given an infinite periodic lattice of unit cells, each containing N points of which (N − 1) are chlorophyll molecules and one is a trap; if an exciton is produced with equal probability at any nontrapping point, how many steps on the average are required before the exciton reaches a trapping center for the first time? It is shown that, when steps can be taken to near-neighbor lattice points only, as N → ∞, our required number of steps is 〈n〉∼{N2/6, linear chain,π−1NlogN, square lattice,1.5164N, single cubic lattice.The correction terms for medium and relatively small N are obtained for a number of lattices.
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Spatial search by quantum walk
Childs, A. M., & Goldstone, J. (2004) · Physical Review A · doi:10.1103/physreva.70.022314 · Cited by 725
Ahrens, M. J., Sinks, L. E., Rybtchinski, B., Liu, W., Jones, B. A., Giaimo, J. M., Gusev, A. V., Goshe, A. J., Tiede, D. M., & Wasielewski, M. R. (2004) · Journal of the American Chemical Society · doi:10.1021/ja039820c · Cited by 295
Metadata
- Authors
- Montroll, E. W.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1969-04-01
- Volume
- 10
- Issue
- 4
- Pages
- 753-765
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2010264617
- Cited by
- 550
- References
- 0
- FWCI
- 4.41
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Random Walks on Lattices. III. Calculation of First-Passage Times with Application to Exciton Trapping on Photosynthetic Units. https://app.cochat.ai/papers/10.1063/1.1664902
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- Montroll, E. W. (1969). Random Walks on Lattices. III. Calculation of First-Passage Times with Application to Exciton Trapping on Photosynthetic Units. Journal of Mathematical Physics. https://doi.org/10.1063/1.1664902
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