Semiclassical Arrhenius law for quantum-thermal escape rates

Abstract:The quantum-thermal escape rate from a metastable well in the absence of dissipation is customarily written as a Boltzmann average of the Hill-Wheeler flux over a continuum of energies. However, this continuum treatment diverges exponentially at low temperature. The divergence originates in a mismatch between a quantum partition function and a classical flux integral; retaining the discrete nature of the quasibound spectrum removes it exactly, and the resulting semiclassical Arrhenius law is obtained in closed form on both sides of the crossover temperature. Evaluating a uniform Kemble transmission probability on Bohr-Sommerfeld levels further recovers the standard WKB decay rate of the lowest resonance at zero temperature. Benchmarked against the resonances of cubic and quintic potentials, obtained by complex scaling, this uniform semiclassical result stays within $9\%$ of the exact rate over eleven orders of magnitude.

Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.21625 [quant-ph]

(or arXiv:2609.21625v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.21625 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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