标题： 稳态期望值的时间关联 显示英文标题

标题： Time correlations from steady-state expectation values

摘要： 恢复相关函数的性质通常具有挑战性。 一方面，实验上需要比系统动力学更精细的时间分辨率来进行测量。 另一方面，分析或数值分析需要求解系统的演化过程。 在这里，我们利用连续测量的量子计量学最新成果，推导出弛豫时间和二阶相关时间的一般下限，这些下限易于计算和测量。 这些界限仅基于稳态期望值及其对控制参数的导数，并可直接扩展到任意可观测量的自相关函数。 我们在两个临界量子系统的例子中验证了我们的方法：一个临界驱动耗散谐振器，在该系统中，该界限与动力学的解析结果相匹配；以及无限范围的伊辛模型，在该模型中只有稳态是可解的，因此该界限提供了现有解析方法无法达到的信息。 我们的结果可以用于实验表征超快系统，并用于理论分析在解析或数值上难以处理的动力学的多体模型。 显示英文摘要

摘要： Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.