论文标题
在非线性存在下特殊点的命运
Fate of exceptional points in the presence of nonlinearities
论文作者
论文摘要
开放系统的非热动力学涉及封闭系统的复杂相干效应如何与耦合到环境的影响交织在一起。然后，系统 - 环境动力学可以导致所谓的特殊点，这些点是相变的开放系统标记，即复杂频谱中光谱间隙的截止。即使在阻尼谐波振荡器的无处不在的例子中，耗散环境也会导致一个特殊的点，在临界阻尼点之间在阻尼不足和过度阻尼的动力学之间分离。在这里，我们在存在强相关性的情况下，即非线性振荡器的情况下研究了这个特殊点的命运。通过采用功能性重归其化组方法，我们确定了该模型的非扰动制度，在该方法中，非线性使系统更加稳健，以抵制耗散的影响，并可以完全消除特殊点。特殊点的熔化发生在关键的非线性阈值之上。有趣的是，特殊点随温度升高而更快地融化，在耦合到温暖的环境时，表现出令人惊讶的连贯动态流动。
The non-Hermitian dynamics of open systems deal with how intricate coherent effects of a closed system intertwine with the impact of coupling to an environment. The system-environment dynamics can then lead to so-called exceptional points, which are the open-system marker of phase transitions, i.e., the closing of spectral gaps in the complex spectrum. Even in the ubiquitous example of the damped harmonic oscillator, the dissipative environment can lead to an exceptional point, separating between under-damped and over-damped dynamics at a point of critical damping. Here, we examine the fate of this exceptional point in the presence of strong correlations, i.e., for a nonlinear oscillator. By employing a functional renormalization group approach, we identify non-perturbative regimes of this model where the nonlinearity makes the system more robust against the influence of dissipation and can remove the exceptional point altogether. The melting of the exceptional point occurs above a critical nonlinearity threshold. Interestingly, the exceptional point melts faster with increasing temperatures, showing a surprising flow to coherent dynamics when coupled to a warm environment.
