双曲ϕ⁴模型的Eyring-Kramers定律
Eyring--Kramers law for the hyperbolic $ϕ^4$ model
AI总结：
本文研究了双曲ϕ⁴模型中亚稳态跃迁频率，通过变分方法计算了量子场论部分，并针对二维方程计算了传输系数。
摘要：
我们研究了具有双井势的随机波动方程两个亚稳态之间的预期跃迁频率。根据过渡态理论，频率因子分解为两个部分：一个仅依赖于不变测度，由ϕ⁴_d量子场论给出，另一个则考虑了动力学因素。我们通过变分方法对随机量化在d=2,3时计算了第一部分。对于无随机数据但无随机驱动的二维方程，我们还计算了传输系数。
英文摘要：
We study the expected transition frequency between the two metastable states of a stochastic wave equation with double-well potential. By transition state theory, the frequency factorizes into two components: one depends only on the invariant measure, given by the $ϕ^4_d$ quantum field theory, and the other takes the dynamics into account. We compute the first component with the variational approach to stochastic quantization when $d = 2, 3$. For the two-dimensional equation with random data but no stochastic forcing, we also compute the transmission coefficient.
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