随机受迫无穷维耦合振子系统的反常耗散
Anomalous Dissipation in a Stochastically Forced Infinite-Dimensional System of Coupled Oscillators
摘要：
本文研究了随机受迫的无限维耦合谐振子系统。虽然这个系统形式上保持能量，并没有明确耗散，我们表明，它有一个非平凡不变的概率措施。这种现象，没有有限维等效，是由于出现了一些反常的耗散机制，传输能量到无穷大。这可以防止能量在局部积累，并允许系统收敛到不变测度。明确地构造了不变测度，并分析了它的一些性质。
英文摘要：
We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure. This phenomenon, which has no finite dimensional equivalent, is due to the appearance of some anomalous dissipation mechanism which transports energy to infinity. This prevents the energy from building up locally and allows the system to converge to the invariant measure. The invariant measure is constructed explicitly and some of its properties are analyzed.
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