经典域论中Kramers率分岔的反常行为
Anomalous behavior of the Kramers rate at bifurcations in classical field theories
摘要：
考虑了在有界区间上受弱时空噪声扰动的Ginzburg-Landau偏微分方程。随着间隔长度的增加，激活机制之间发生转变，其中经典Kramers速率发散[R.S. Maier和D.L. Stein，Phys. Rev. Lett. 87，270601（2001）]。我们确定了一个修正的Kramers公式在过渡点，产生一个有限的，但噪声相关的前因子，证实了Maier和Stein的猜想[第5114卷SPIE Proceeding（2003）]。对于周期性和Neumann边界条件，我们得到明确的表达式的前因子的贝塞尔和误差函数。
英文摘要：
We consider a Ginzburg-Landau partial differential equation in a bounded interval, perturbed by weak spatio-temporal noise. As the interval length increases, a transition between activation regimes occurs, in which the classical Kramers rate diverges [R.S. Maier and D.L. Stein, Phys. Rev. Lett. 87, 270601 (2001)]. We determine a corrected Kramers formula at the transition point, yielding a finite, though noise-dependent prefactor, confirming a conjecture by Maier and Stein [vol. 5114 of SPIE Proceeding (2003)]. For both periodic and Neumann boundary conditions, we obtain explicit expressions of the prefactor in terms of Bessel and error functions.
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