Linear response theory lies at the heart of studying quantum matters, because it connects the dynamical response of a quantum system to an external probe to correlation functions of the unprobed equilibrium state. Thanks to linear response theory, various experimental probes can be used for determining equilibrium properties. However, so far, both the unprobed system and the probe operator are limited to Hermitian ones. Here, we develop a non-Hermitian linear response theory that considers the dynamical response of a Hermitian system to a non-Hermitian probe, and we can also relate such a dynamical response to the properties of an unprobed Hermitian system at equilibrium. As an application of our theory, we consider the real-time dynamics of momentum distribution induced by one-body and two-body dissipations. Remarkably, for a critical state with no well-defined quasi-particles, we find that the dynamics are slower than the normal state with well-defined quasi-particles, and our theory provides a model-independent way to extract the critical exponent in the real-time correlation function. We find surprisingly good agreement between our theory and a recent cold atom experiment on the dissipative Bose–Hubbard model. We also propose to further quantitatively verify our theory by performing experiments on dissipative one-dimensional Luttinger liquid.

线性响应理论是研究量子问题的核心，因为它将量子系统的动力学响应与外部探针连接到未探测平衡态的相关函数。借助线性响应理论，可以使用各种实验探针来确定平衡特性。但是，到目前为止，未探测的系统和探测算子都限于厄米系统。在这里，我们开发了一种非埃尔米特线性响应理论，该理论考虑了埃尔米特系统对非埃尔米特探测器的动力响应，并且还可以将这种动力响应与处于平衡状态的未经探测的埃尔米特系统的特性联系起来。作为我们理论的一种应用，我们考虑由一体和两体耗散引起的动量分布的实时动力学。值得注意的是 对于没有明确定义的准粒子的临界状态，我们发现动力学比具有明确定义的准粒子的正常状态慢，并且我们的理论提供了一种与模型无关的方式来提取实数时间相关函数。我们发现我们的理论与最近关于耗散Bose-Hubbard模型的冷原子实验之间达成了令人惊讶的良好一致性。我们还建议通过在耗散的一维Luttinger液体上进行实验来进一步定量验证我们的理论。我们发现我们的理论与最近关于耗散Bose-Hubbard模型的冷原子实验之间达成了令人惊讶的良好一致性。我们还建议通过在耗散的一维Luttinger液体上进行实验来进一步定量验证我们的理论。我们发现我们的理论与最近关于耗散Bose-Hubbard模型的冷原子实验之间达成了令人惊讶的良好一致性。我们还建议通过在耗散的一维Luttinger液体上进行实验来进一步定量验证我们的理论。