论文标题
部分可观测时空混沌系统的无模型预测
Transverse quantum decoherence of a fast particle in a gas
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
The decoherence of a fast quantum particle in a gas is studied by applying the Kramers-Moyal expansion to the quantum master equation for the reduced density matrix of the particle. This expansion leads to a general form of the Caldeira-Leggett master equation accounting for the angular variation of the differential cross section. The equation describes the decoherence in both the longitudinal and transverse directions with respect to the particle motion. It is shown that, when the differential cross section is concentrated in the forward direction, transverse decoherence dominates. The coherence region off the diagonal of the density matrix is characterized by coherence lengths, which can be deduced, for Gaussian states, from the momentum covariance matrix according to a Heisenberg-type uncertainty relation. Finally, the longitudinal-to-transverse ratio of the coherence lengths is estimated for an alpha particle of a few MeVs. This ratio indicates that the coherence region looks like an ellipsoid elongated in the direction of motion.
