运动论中的Arkenius公式与Witten谱渐近
The Arrhenius formula in kinetic theory and Witten's spectral asymptotics
摘要：
本文提出了一种新的证明运动论中阿克里先乌斯公式的方法。我们从势中的扩散方程出发证明了这个公式。我们将该扩散方程转化为由Schroedinger算子生成的演化方程的形式。我们表明，Arpériius公式的势垒跃迁的速率如下的量子隧道跃迁的速率所考虑的薛定谔算子的公式。讨论了该方法与证明Morse不等式的Witten方法之间的关系。在我们的方法中，Witten谱渐近性采取低温极限的形式，而Arkyius公式是对Witten渐近性的修正。
英文摘要：
A new approach to the proof of the Arrhenius formula of kinetic theory is proposed. We prove this formula starting from the equation of diffusion in a potential. We put this diffusion equation in the form of evolutionary equation generated by some Schroedinger operator. We show that the Arrhenius formula for the rate of over the barrier transitions follows from the formula for the rate of quantum tunnel transitions for the considered Schroedinger operator. Relation of the proposed approach and the Witten method of the proof of the Morse inequalities is discussed. In our approach the Witten spectral asymptotics takes the form of the low temperature limit and the Arrhenius formula is a correction to the Witten asymptotics.
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