量子-热逃逸率的半经典阿伦尼乌斯定律
Semiclassical Arrhenius law for quantum-thermal escape rates
- Università di Padova（帕多瓦大学）
- INFN Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究解决了无耗散量子-热逃逸率连续谱处理在低温下发散的问题，通过保留准束缚谱离散性获得闭式半经典阿伦尼乌斯定律，并在十一个数量级内与精确率误差小于9%。
AI中文摘要：
在无耗散情况下，从亚稳态势阱的量子-热逃逸率通常被写为希尔-惠勒通量在连续能量谱上的玻尔兹曼平均。然而，这种连续谱处理在低温下会指数发散。该发散源于量子配分函数与经典通量积分之间的不匹配；保留准束缚谱的离散性质可精确消除此发散，所得半经典阿伦尼乌斯定律在交叉温度两侧均以闭式形式给出。在玻尔-索末菲能级上评估均匀的肯布尔透射概率，可进一步在零温下恢复最低共振的标准WKB衰变率。以三次和五次势的共振（通过复标度获得）为基准，该均匀半经典结果在十一个数量级范围内与精确率的误差保持在9%以内。
英文摘要：
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.
