论文标题
探测量子网络几何形状的光谱维度
Probing the spectral dimension of quantum network geometries
论文作者
论文摘要
我们考虑了一个开放量子系统的环境，该系统由“具有风味的量子网络几何形状”（QNGF）描述，其中节点是耦合的量子振荡器。 QNGF的几何性质反映在网络的Laplacian矩阵的光谱特性中，该矩阵显示有限的光谱维度，还确定了QNGFS正常模式的频率。我们表明，可以通过将辅助开放量子系统耦合到网络并探测低频制度中的正常模式频率，从而间接估计一个先验未知的光谱维度。我们发现网络参数不会影响估计值；从这个意义上讲，它是网络几何形状的属性，而不是振荡器裸露频率或恒定耦合强度的值。数值证据表明，估计值对高频截止的小变化和噪声或缺失的正常模式频率都具有牢固的变化。我们建议将辅助系统与具有随机耦合强度的网络节点的子集进行，以揭示和解决正常模式频率的足够大子集。
We consider an environment for an open quantum system described by a "Quantum Network Geometry with Flavor" (QNGF) in which the nodes are coupled quantum oscillators. The geometrical nature of QNGF is reflected in the spectral properties of the Laplacian matrix of the network which display a finite spectral dimension, determining also the frequencies of the normal modes of QNGFs. We show that an a priori unknown spectral dimension can be indirectly estimated by coupling an auxiliary open quantum system to the network and probing the normal mode frequencies in the low frequency regime. We find that the network parameters do not affect the estimate; in this sense it is a property of the network geometry, rather than the values of, e.g., oscillator bare frequencies or the constant coupling strength. Numerical evidence suggests that the estimate is also robust both to small changes in the high frequency cutoff and noisy or missing normal mode frequencies. We propose to couple the auxiliary system to a subset of network nodes with random coupling strengths to reveal and resolve a sufficiently large subset of normal mode frequencies.
