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17 - Quantum Rate Processes

Published online by Cambridge University Press:  11 May 2023

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

The rates of charge transfer and energy transfer are essential for understanding nanoscale phenomena and processes. Here we introduce the general conditions for the emergence of rate processes in quantum mechanics. We refer to the generic scenario in which a transition is induced between eigenstates of a given Hamiltonian by a weak perturbation. Analysis reveals that when the initial and final states are pure states, the transition rate is time-dependent and fails to reach a finite constant value. If, however, the final state is a mixed ensemble that is sufficiently wide and dense in energy, a rate constant emerges, given by Fermi’s Golden Rule (FGR). When the initial state is also mixed, for example, a thermal equilibrium state, a thermal rate constant is formulated in terms of transition rates between specific eigenstates, summed over the final eigenstates, and averaging over the thermal distribution of the initial eigenstates.

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Publisher: Cambridge University Press
Print publication year: 2023

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References

Miller, W. H., Schwartz, S. D., and Tromp, J. W., “Quantum mechanical rate constants for bimolecular reactions,” The Journal of Chemical Physics 79, 4889 (1983).Google Scholar
Craig, I. R., Thoss, M., and Wang, H., “Proton transfer reactions in model condensed-phase environments: Accurate quantum dynamics using the multilayer multiconfiguration time-dependent Hartree approach,” The Journal of Chemical Physics 127, 144503 (2007).CrossRefGoogle ScholarPubMed

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  • Quantum Rate Processes
  • 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/10.1017/9781108877787.018
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  • Quantum Rate Processes
  • 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/10.1017/9781108877787.018
Available formats
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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.

  • Quantum Rate Processes
  • 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/10.1017/9781108877787.018
Available formats
×