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arXiv:2603.28373

Perspective of Fermi's golden rule and its generalizations in chemical physics

Seogjoo J. Jang, Goun Kim, Young Min Rhee

physics.chem-phquant-phSubmitted Mar 30, 2026• Announced Mar 31, 2026• Revised Apr 9, 2026 (v3)
v1 · Mar 30, 2026v2 · Mar 31, 2026v3 · Apr 9, 2026v4 · May 28, 2026
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Abstract

This perspective provides a succinct history of Fermi's golden rule (FGR), overview of its derivation, assumptions, and representative forms. Major applications of FGR, mostly in the field of chemical physics, are reviewed. These illustrate the broad applicability and success of FGR. Ambiguities and open issues encountered in practical applications of FGR are clarified. Recent advances in generalizations of FGR and computational methods for practical applications are addressed.

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24 pages, 6 figures

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This perspective provides a succinct history of Fermi's golden rule (FGR), overview of its derivation, assumptions, and representative forms. Major applications of FGR, mostly in the field of chemical physics, are reviewed. These illustrate the broad applicability and success of FGR. Ambiguities and open issues encountered in practical applications of FGR are clarified. Recent advances in generalizations of FGR and computational methods for practical applications are addressed.
We study heating dynamics in isolated quantum many-body systems driven periodically at high frequency and large amplitude. Combining the high-frequency expansion for the Floquet Hamiltonian with Fermi's golden rule (FGR), we develop a master equation termed the Floquet FGR. Unlike the conventional one, the Floquet FGR correctly describes heating dynamics, including the prethermalization regime, even for strong drives, under which the Floquet Hamiltonian is significantly dressed, and nontrivial Floquet engineering is present. The Floquet FGR depends on system size only weakly, enabling us to analyze the thermodynamic limit with small-system calculations. Our results also indicate that, during heating, the system approximately stays in the thermal state for the Floquet Hamiltonian with a gradually rising temperature.
Abstract Putting a general, physically relevant upper bound on equilibration times in closed quantum systems is a recently much pursued endeavor. In 2017 Phys. Rev. X 7 031027 García-Pintos et al suggest such a bound. We point out that the general assumptions which allow for an actual estimation of this bound are violated in cases in which Fermi’s golden rule and related open quantum system theories apply. To probe the range of applicability of Fermi’s golden rule for systems of the type addressed in the above work, we numerically solve the corresponding Schrödinger equation for some finite spin systems comprising up to 25 spins. These calculations shed light on the breakdown of standard quantum master equations in the ‘superweak’ coupling limit, which occurs for finite sized baths.