Asymptotic Statistics of Nodal Domains of Quantum Chaotic Billiards in the Semiclassical Limit
Asymptotic Statistics of Nodal Domains of Quantum Chaotic Billiards in the Semiclassical Limit
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半经典极限下量子混沌台球节点域的渐近统计
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发表时间：
2012
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通讯作者：
K. Konrad
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作者：
K. Konrad
量子混沌涉及拉普拉斯算子在台球混沌弹跳域中的本征函数。人们推测这种混沌本征函数与简单的渗流模型共享其节点域的统计特性，从中可以分析计算许多有趣的量。我们在非常高的能量下对量子混沌本征函数的节点域的数量和大小进行了数值测试，接近半经典极限。我们使用高效的缩放方法来快速计算低分辨率的特征函数并插值到更高分辨率。我们计算了 10 个特征函数并计算了 10 个节点域。我们的结果与推测的节点域大小一致，但与推测的节点域数量平均值和方差不同。章
Quantum chaos concerns eigenfunctions of the Laplace operator in a domain where a billiard ball would bounce chaotically. Such chaotic eigenfunctions have been conjectured to share statistical properties of their nodal domains with a simple percolation model, from which many interesting quantities can be computed analytically. We numerically test conjectures on the number and size of nodal domains of quantum chaotic eigenfunctions at very high energies, approaching the semiclassical limit. We use a highly efficient scaling method to quickly compute eigenfunctions at low resolution and interpolate to higher resolution. We computed 10 eigenfunctions and counted 10 nodal domains. Our results agree with the conjectured size nodal domains but disagree with the conjectured mean and variance of the number of nodal domains. Chapter