Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential
Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential
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DOI：
10.4310/cms.2017.v15.n7.a10
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发表时间：
2011-04
期刊：
影响因子：
--
通讯作者：
B. Cooke;David P. Herzog;Jonathan C. Mattingly;Scott A. McKinley;S. Schmidler
中科院分区：
文献类型：
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作者：
B. Cooke;David P. Herzog;Jonathan C. Mattingly;Scott A. McKinley;S. Schmidler
在本文中，我们建立了涉及 Lennard-Jones 型势的简单双粒子系统的 Langevin 动力学的遍历性。据我们所知，这是在这种潜力下运行的系统的第一个这样的结果。此外，我们表明动力学是{\it几何上}遍历的（具有谱间隙）并以几何速率收敛。随机平均方法用于确定李雅普诺夫函数的存在性。在这种情况下，李亚普诺夫函数的存在似乎对更传统的方法有抵抗力。这是该文章的更正版本。
In this paper we establish the ergodicity of Langevin dynamics for simple two-particle system involving a Lennard-Jones type potential. To the best of our knowledge, this is the first such result for a system operating under this type of potential. Moreover we show that the dynamics are {\it geometrically} ergodic (have a spectral gap) and converge at a geometric rate. Methods from stochastic averaging are used to establish the existence of a Lyapunov function. The existence of a Lyapunov function in this setting seems resistant to more traditional approaches. This is a corrected version of the article.