论文标题
Hasimoto框架和Gibbs定期非线性Schrödinger方程的测量
Hasimoto frames and the Gibbs measure of periodic nonlinear Schrödinger Equation
论文作者
论文摘要
本文将立方非线性schrödinger方程解释为具有无限尺寸相空间的哈密顿系统。有一个吉布斯度量是在与规范运动方程相关的流程下不变的。 Gibbs度量的对数Sobolev和度量不平等的浓度，此处扩展到相关经验措施的$ K $ - 点相关函数和分布。通过Hasimoto的定理，NLSE给出了一对宽松的耦合颂歌，该解决方案为其提供了移动框架的系统。论文研究了通过吉布斯度量在移动框架上引起的量度的演变。
The paper interprets the cubic nonlinear Schrödinger equation as a Hamiltonian system with infinite dimensional phase space. There is a Gibbs measure which is invariant under the flow associated with the canonical equations of motion. The logarithmic Sobolev and concentration of measure inequalities hold for the Gibbs measures, and here are extended to the $k$-point correlation function and distributions of related empirical measures. By Hasimoto's theorem, NLSE gives a Lax pair of coupled ODE for which the solutions give a system of moving frames. The paper studies the evolution of the measure induced on the moving frames by the Gibbs measure.
