Abstract Echo protocols provide a means to investigate the arrow of time in macroscopic processes. Starting from a nonequilibrium state, the many-body quantum system under study is evolved for a certain period of time τ. Thereafter, an (effective) time reversal is performed that would – if implemented perfectly – take the system back to the initial state after another time period τ. Typical examples are nuclear magnetic resonance imaging and polarisation echo experiments. The presence of small, uncontrolled inaccuracies during the backward propagation results in deviations of the “echo signal” from the original evolution and can be exploited to quantify the instability of nonequilibrium states and the irreversibility of the dynamics. We derive an analytic prediction for the typical dependence of this echo signal for macroscopic observables on the magnitude of the inaccuracies and on the duration τ of the process, and verify it in numerical examples.

中文翻译：

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预测多体量子系统中的不完美回波动力学

摘要 Echo 协议提供了一种研究宏观过程中时间箭头的方法。所研究的多体量子系统从一个非平衡态开始，在一段时间 τ 内演化。此后，执行（有效）时间反转，如果完美实施，将在另一个时间段 τ 后将系统恢复到初始状态。典型的例子是核磁共振成像和极化回波实验。在反向传播过程中存在小的、不受控制的不准确性会导致“回波信号”与原始演化的偏差，可用于量化非平衡状态的不稳定性和动力学的不可逆性。