有序和随机介质中相互作用线性波的推论
Inference for interacting linear waves in ordered and random media
摘要：
统计推断方法的发展和测试成对相互作用的系统，其自由度是连续的角度变量，如平面自旋磁系统或波相位在光学和声学。我们调查两个极端的拓扑结构：完整的和稀疏的图形与确定性和淬火无序耦合系统。为了配合在光学中的进一步应用，还考虑了复耦合和外场，并从复关联函数的实部和虚部导出了厄米特耦合矩阵的实部和虚部的一般推断公式。整个过程，最终，测试数值生成的关联函数和本地磁化通过蒙特卡罗模拟。
英文摘要：
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We investigate systems with both deterministic and quenched disordered couplings on two extreme topologies: complete and sparse graphs. To match further applications in optics also complex couplings and external fields are considered and general inference formulas are derived for real and imaginary parts of Hermitian coupling matrices from real and imaginary parts of complex correlation functions. The whole procedure is, eventually, tested on numerically generated correlation functions and local magnetizations by means of Monte Carlo simulations.
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