Approach to Equilibrium for the Stochastic NLS
Approach to Equilibrium for the Stochastic NLS
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随机 NLS 的均衡方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
W.
中科院分区：
文献类型：
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作者：
J. Lebowitz;P. Mounaix;W.
我们研究的方法来平衡，描述的吉布斯措施，为一个系统的d维环面根据随机非线性薛定谔方程（SNLS）的高频截断。我们证明指数方法截断吉布斯测量的聚焦和散焦的情况下，通过适当的边界条件约束的动力学的傅立叶空间的区域，其中的哈密顿是凸的。我们的方法是基于建立一个谱间隙的非自伴Fokker-Planck算子的时间演化的措施，这是一致的频率截断N。讨论了极限N →∞。
We study the approach to equilibrium, described by a Gibbs measure, for a system on a d-dimensional torus evolving according to a stochastic nonlinear Schrödinger equation (SNLS) with a high frequency truncation. We prove exponential approach to the truncated Gibbs measure both for the focusing and defocusing cases when the dynamics is constrained via suitable boundary conditions to regions of the Fourier space where the Hamiltonian is convex. Our method is based on establishing a spectral gap for the non self-adjoint Fokker-Planck operator governing the time evolution of the measure, which is uniform in the frequency truncation N. The limit N →∞ is discussed.