论文标题
高度连接无序系统的振动光谱的普遍集体行为
Universal Collective Behavior of the Vibration Spectrum of Highly Connected Disordered Systems
论文作者
论文摘要
我们研究高度连接系统的小振荡，这是与更熟悉的晶体案例相反的极限。作为一个具体的例子，我们分析了复合摆的振动光谱。值得注意的是，这些光谱表现出普遍的行为，具有声子态密度的零频率极限。这种通用性由此类系统的自然随机矩阵模型捕获。我们使用自由概率理论的S-转换分析了该模型，并在大型系统大小的极限下明确地获得模式的密度。
We study small oscillations of highly connected systems, which represent a limit opposite to the more familiar case of disordered crystals. As a concrete example we analyze the vibrational spectra of composite pendula. Remarkably, these spectra exhibit universal behavior with non-vanishing zero-frequency limit of the density of phonon states. This universality is captured by a natural random matrix model for such systems. We analyze this model using S-transforms of free probability theory and obtain the density of modes explicitly, in the limit of large system size.
