AI 中文总结
研究物理振荡器网络中伊辛相动力学，通过推导物理相位相互作用发现未补偿谐波相位失配会致非伊辛动力学，证明延迟耦合是相位补偿机制并给出条件，还表明周期性调制延迟可消除偶数分量，建立了实现规定动力学的设计原则。
AI 中文摘要
基于振荡器的伊辛机中，耦合自持振荡器的相位朝着降低伊辛哈密顿量的方向演化，通常被解释为伊辛模型的物理实现。但这种对应通常无法保证。对于弱耦合下的任意自持振荡器，我们从注入波形与扰动投影向量（也称为脉冲灵敏度函数）之间的谐波重叠中推导物理相位相互作用。发现这两个量之间未补偿的谐波相位失配会在物理耦合函数中产生偶数分量，导致具有正确耦合拓扑的网络实现非伊辛动力学。我们进一步表明延迟耦合提供了一种通用的相位补偿机制。对于固定延迟，我们推导了一个条件使得偶数分量在L2范数意义下最小化，振荡器示例证实预测的延迟显著抑制了偶数分量并使实现的耦合函数更接近规定的奇数相互作用。然后表明周期性调制延迟在合适的时刻条件下可以消除相位动力学中的偶数分量。这些结果为在物理振荡器网络中实现规定的基于能量的动力学建立了一般设计原则。
英文摘要
Oscillator-based Ising machines, in which the phases of coupled self-sustaining oscillators evolve toward decreasing an Ising Hamiltonian, are commonly interpreted as physical realizations of the Ising model. This interpretation, however, requires the phase dynamics generated by the physical oscillator network to match a prescribed Ising dynamics. Here we show that this correspondence is generally not guaranteed. For arbitrary self-sustaining oscillators under weak coupling, we derive the physical phase interaction from the harmonic overlap between the injected waveform and the perturbation projection vector (also referred to as impulse sensitivity function). We find that uncompensated harmonic phase mismatches between these two quantities generate even components in the physical coupling function, causing a network with the correct coupling topology to implement a non-Ising dynamics. We further show that delayed coupling provides a universal phase-compensation mechanism. For a fixed delay, we derive a condition on the delay under which the even components is minimized in the sense of L2-norm, and oscillator examples confirm that the predicted delay substantially suppresses the even components and brings the realized coupling function closer to the prescribed odd interaction. We then show that a periodically modulated delay can, under suitable moment conditions, eliminate the even components in the phase dynamics. These results establish a general design principle for implementing prescribed energy-based dynamics in physical oscillator networks.
