以质量和动量为条件的不变Gibbs测度
On invariant Gibbs measures conditioned on mass and momentum
摘要：
我们在圆上为非线性薛定谔方程（NLS）构造一个吉布斯测度，条件是指定的质量和动量：d μ_{a，b} = Z^{-1} 1_{ \int_T |u| ^2 = a} 1_{i \int_T u \bar{u}_x = b} exp（\pm 1/p \int_T |u| ^p - 1/2 \int_{\T} |u| ^2）d P对于a \in R^+和b \in R，其中P是圆上的复值维纳测度。我们还证明了μ_{a，b}在NLS流下是不变的.我们注意到i \int_\ T u \bar{u}_x是Levy随机区域，特别是在NLS流下这是不变的。
英文摘要：
We construct a Gibbs measure for the nonlinear Schrodinger equation (NLS) on the circle, conditioned on prescribed mass and momentum: d μ_{a,b} = Z^{-1} 1_{\int_T |u|^2 = a} 1_{i \int_T u \bar{u}_x = b} exp (\pm1/p \int_T |u|^p - 1/2 \int_{\T} |u|^2) d P for a \in R^+ and b \in R, where P is the complex-valued Wiener measure on the circle. We also show that μ_{a,b} is invariant under the flow of NLS. We note that i \int_\T u \bar{u}_x is the Levy stochastic area, and in particular that this is invariant under the flow of NLS.
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