Propagating wave correlations in complex systems
Propagating wave correlations in complex systems
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DOI：
10.1088/1751-8121/50/4/045101
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发表时间：
2017-01-27
影响因子：
2.1
通讯作者：
Tanner, Gregor
中科院分区：
文献类型：
--
作者：
Creagh, Stephen C.;Gradoni, Gabriele;Tanner, Gregor
我们描述了一种新的方法来计算有限空间域内的波相关函数，该方法由复杂的统计信号源驱动。通过利用半经典近似，我们提供了显式算法来计算这些关联函数在潜在经典动力学下的局部平均值。通过定义适当的系综平均值，我们证明了关于平均值的波动可以用经典关联来刻画。我们特别给出了将对角线贡献的涨落与全波相关函数的涨落联系起来的显式表达式。这些方法在量子力学和经典波动问题中都有广泛的应用，例如在振声学和电磁学中。我们将这里的方法应用于简单的量子系统，即所谓的量子映射，它模拟了庞加莱截面上一般问题的行为。虽然这些模型是低维的，但它们表现出混沌的经典极限，并与复杂结构中的波传播具有共同的特征。
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincare sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures.