Bounds on Attainable Rate Modulation in Fermi's Golden Rule
Abstract
Controlling transition rates is a central objective across quantum optics, condensed-matter physics, and chemical physics, encompassing processes such as spontaneous emission, energy and charge transfer, spin relaxation, and chemical reactions. Although Fermi's golden rule provides a powerful framework for calculating such rates of weakly coupled transitions, conventional calculations require the interaction to be specified in advance; the range of rate responses attainable over a broader interaction space remains unknown. We formulate spectral-overlap golden-rule rates as quadratic forms of the interaction and derive rigorous bounds on rate modulation over a specified interaction space. As an example, application to energy transfer from a donor to a molecular vibration coupled to an optical cavity reveals that enhancement and suppression depend jointly on the interaction and cavity detuning, including continuous reversal of the rate response for a fixed interaction. The same approach may elucidate rate control for other golden-rule processes, including excitation-energy transfer, nonadiabatic electron transfer, nonradiative electronic transitions, vibrational and spin relaxation, and spontaneous emission.
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BibTeX
@misc{ohata2026bounds,
title = {{Bounds on Attainable Rate Modulation in Fermi's Golden Rule}},
author = {Kaisei Ohata and Jun-Yu Dong and Yasutaka Kitahama and Akihito Ishizaki and Keisuke Goda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29404},
eprint = {2610.29404},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29404},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bounds on Attainable Rate Modulation in Fermi's Golden Rule
AU - Kaisei Ohata
AU - Jun-Yu Dong
AU - Yasutaka Kitahama
AU - Akihito Ishizaki
AU - Keisuke Goda
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.29404
UR - https://arxiv.org/abs/2610.29404
AB - Controlling transition rates is a central objective across quantum optics, condensed-matter physics, and chemical physics, encompassing processes such as spontaneous emission, energy and charge transfer, spin relaxation, and chemical reactions. Although Fermi's golden rule provides a powerful framework for calculating such rates of weakly coupled transitions, conventional calculations require the interaction to be specified in advance; the range of rate responses attainable over a broader interaction space remains unknown. We formulate spectral-overlap golden-rule rates as quadratic forms of the interaction and derive rigorous bounds on rate modulation over a specified interaction space. As an example, application to energy transfer from a donor to a molecular vibration coupled to an optical cavity reveals that enhancement and suppression depend jointly on the interaction and cavity detuning, including continuous reversal of the rate response for a fixed interaction. The same approach may elucidate rate control for other golden-rule processes, including excitation-energy transfer, nonadiabatic electron transfer, nonradiative electronic transitions, vibrational and spin relaxation, and spontaneous emission.
ER -