### Abstract

An exact analytic solution to the non-Markoffian spin one-half exciton linear chain system is found by diagonalising and Laplace transforming the coupled space and spin equations. As a particular example, numerical calculations of the time evolution of the two-site exciton system are presented for several realistic values of space and spin memory times. The unimportance of the cross-channel non-Markoffian behaviour for the cases where the space and spin memory times differ by at least a factor of ten is illustrated by comparison with the traditional Pauli master equation solutions. The memory can lead to oscillating populations which, on time scales shorter than or comparable with the relevant memory time, look like coherent transfer. Coherent motion can be observed, for certain values of the parameters, in the slower channel long after the more normal channel has become Markoffian. Interference regimes are possible, but require similar values of space and spin transfer integrals; this is improbable for organics.

Original language | English |
---|---|

Article number | 014 |

Pages (from-to) | 707-718 |

Number of pages | 12 |

Journal | Journal of Physics C: Solid State Physics |

Volume | 11 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1978 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Journal of Physics C: Solid State Physics*,

*11*(4), 707-718. [014]. https://doi.org/10.1088/0022-3719/11/4/014

**An exact dynamical solution to a linear chain doublet exciton with exponential memory.** / Ratner, Mark A; Swenberg, C. E.

Research output: Contribution to journal › Article

*Journal of Physics C: Solid State Physics*, vol. 11, no. 4, 014, pp. 707-718. https://doi.org/10.1088/0022-3719/11/4/014

}

TY - JOUR

T1 - An exact dynamical solution to a linear chain doublet exciton with exponential memory

AU - Ratner, Mark A

AU - Swenberg, C. E.

PY - 1978

Y1 - 1978

N2 - An exact analytic solution to the non-Markoffian spin one-half exciton linear chain system is found by diagonalising and Laplace transforming the coupled space and spin equations. As a particular example, numerical calculations of the time evolution of the two-site exciton system are presented for several realistic values of space and spin memory times. The unimportance of the cross-channel non-Markoffian behaviour for the cases where the space and spin memory times differ by at least a factor of ten is illustrated by comparison with the traditional Pauli master equation solutions. The memory can lead to oscillating populations which, on time scales shorter than or comparable with the relevant memory time, look like coherent transfer. Coherent motion can be observed, for certain values of the parameters, in the slower channel long after the more normal channel has become Markoffian. Interference regimes are possible, but require similar values of space and spin transfer integrals; this is improbable for organics.

AB - An exact analytic solution to the non-Markoffian spin one-half exciton linear chain system is found by diagonalising and Laplace transforming the coupled space and spin equations. As a particular example, numerical calculations of the time evolution of the two-site exciton system are presented for several realistic values of space and spin memory times. The unimportance of the cross-channel non-Markoffian behaviour for the cases where the space and spin memory times differ by at least a factor of ten is illustrated by comparison with the traditional Pauli master equation solutions. The memory can lead to oscillating populations which, on time scales shorter than or comparable with the relevant memory time, look like coherent transfer. Coherent motion can be observed, for certain values of the parameters, in the slower channel long after the more normal channel has become Markoffian. Interference regimes are possible, but require similar values of space and spin transfer integrals; this is improbable for organics.

UR - http://www.scopus.com/inward/record.url?scp=36149039120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149039120&partnerID=8YFLogxK

U2 - 10.1088/0022-3719/11/4/014

DO - 10.1088/0022-3719/11/4/014

M3 - Article

AN - SCOPUS:36149039120

VL - 11

SP - 707

EP - 718

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 4

M1 - 014

ER -