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arXiv · 2610.29404

Bounds on Attainable Rate Modulation in Fermi's Golden Rule

Kaisei Ohata·Jun-Yu Dong·Yasutaka Kitahama·Akihito Ishizaki·Keisuke Goda
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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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Kaisei Ohata, Jun-Yu Dong, Yasutaka Kitahama, Akihito Ishizaki, Keisuke Goda. 2026-10-21. Bounds on Attainable Rate Modulation in Fermi's Golden Rule. https://arxiv.org/abs/2610.29404

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