Discrete semiclassical theory of quantum-thermal escape
Abstract
The dissipationless quantum-thermal escape rate from a metastable well is often written as a Boltzmann average of the Hill-Wheeler flux over a continuum of energies. This continuum treatment diverges exponentially at low temperature, because it pairs the quantum partition function of the well with a classical flux integral. Retaining the discrete nature of the quasibound spectrum removes the divergence exactly, and the resulting rate is obtained in closed form on both sides of the crossover temperature T0. Evaluating a uniform Kemble transmission probability on Bohr-Sommerfeld levels further removes the parabolic-barrier error and recovers the 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 rate stays within 9% of the exact one over eleven orders of magnitude. Below T0, the rate rises above its zero-temperature plateau with the level spacing as activation energy, and the plateau ends at a temperature T1 noticeably below T0. In an isolated well, whose levels are not replenished, the thermal rate is only the initial slope of a decay which ceases to be single exponential at T1, while at T0 the initial escape moves from tunneling inside the well to the barrier top. We discuss implications for Josephson junctions, single-electron pumps, and nuclear burning in dense stellar matter.
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BibTeX
@misc{salasnich2026discrete,
title = {{Discrete semiclassical theory of quantum-thermal escape}},
author = {Luca Salasnich and Cesare Vianello},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.21625},
eprint = {2609.21625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21625},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Discrete semiclassical theory of quantum-thermal escape
AU - Luca Salasnich
AU - Cesare Vianello
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.21625
UR - https://arxiv.org/abs/2609.21625
AB - The dissipationless quantum-thermal escape rate from a metastable well is often written as a Boltzmann average of the Hill-Wheeler flux over a continuum of energies. This continuum treatment diverges exponentially at low temperature, because it pairs the quantum partition function of the well with a classical flux integral. Retaining the discrete nature of the quasibound spectrum removes the divergence exactly, and the resulting rate is obtained in closed form on both sides of the crossover temperature T_0. Evaluating a uniform Kemble transmission probability on Bohr-Sommerfeld levels further removes the parabolic-barrier error and recovers the 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 rate stays within 9% of the exact one over eleven orders of magnitude. Below T_0, the rate rises above its zero-temperature plateau with the level spacing as activation energy, and the plateau ends at a temperature T_1 noticeably below T_0. In an isolated well, whose levels are not replenished, the thermal rate is only the initial slope of a decay which ceases to be single exponential at T_1, while at T_0 the initial escape moves from tunneling inside the well to the barrier top. We discuss implications for Josephson junctions, single-electron pumps, and nuclear burning in dense stellar matter.
ER -