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18 - Thermal Rates in a Bosonic Environment

Published online by Cambridge University Press:  11 May 2023

Uri Peskin
Affiliation:
Technion - Israel Institute of Technology, Haifa
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Summary

Formulas are derived for the rates of elementary processes in nanoscale systems. Particularly we derive thermal rate constants for charge transfer in a condensed phase environment (Marcus formula), electronic energy transfer between chromophores (Forester resonant energy transfer), and radiation emission/absorption by electronic and vibronic transitions in molecules. All these processes are characterized by changes in the electronic state, strongly coupled to nuclear motions in the nano-system or in its surroundings. The relevant systems are mapped on a generic spin-boson model Hamiltonian, where different meanings are assigned to the model parameters in the different scenarios. In each case, rate constants are derived under appropriate approximations and are identified as different realizations of Fermi’s golden rule. A semiclassical (low-frequency) approximation applied for the nuclear degrees of freedom yields transparent, well-known formulas for the thermal transition rates. The underlying physics as well as practical consequence of the results are analyzed.

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Publisher: Cambridge University Press
Print publication year: 2023

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References

Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, A., and Zwerger, W., “Dynamics of the dissipative two-state system,” Reviews of Modern Physics 59, 1 (1987).CrossRefGoogle Scholar
May, V. and Kühn, O., “Charge and Energy Transfer Dynamics in Molecular Systems,” 3rd ed. (Wiley, 2011).CrossRefGoogle Scholar
Marcus, R. A. and Sutin, N., “Electron transfers in chemistry and biology,” Biochimica et Biophysica Acta (BBA)-Reviews on Bioenergetics 811, 265 (1985).CrossRefGoogle Scholar
Condon, E. U., “Nuclear motions associated with electron transitions in diatomic molecules,” Physical Review 32, 858 (1928).Google Scholar
Peskin, U., “Quantum mechanical averaging over fluctuating rates,” Molecular Physics 110, 729 (2012).CrossRefGoogle Scholar
Förster, T., “Intermolecular energy migration and fluorescence,” Annals of Physics 437, 55 (1948).CrossRefGoogle Scholar

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  • Thermal Rates in a Bosonic Environment
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.019
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  • Thermal Rates in a Bosonic Environment
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.019
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Thermal Rates in a Bosonic Environment
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.019
Available formats
×