We apply the Leggett-Garg inequalities (LGIs) to the cases of classical and quantum unstable systems. For classical systems the two assumptions of macroscopic realism and noninvasive measurements imply that the three-measurement string $K_3$ is identically equal to 1. Also, for quantum-mechanical systems, for which the two assumptions are, in general, not valid, we find that $K_3=1$ for purely exponential decays ($K_3\le 1$ is the general LGI). On the other hand, the necessary deviations from the exponential decay law at short and long times predicted by quantum mechanics lead to values of $K_3\ne 1$. Moreover, a strict violation $K_3>1$ typically occurs at short times. Thus, we conclude that experiments in which such deviations from the exponential decay law have been observed should also have in their data violations of the LGIs.

中文翻译：

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Leggett-Garg 不等式和不稳定系统的衰变

我们将 Leggett-Garg 不等式 (LGIs) 应用于经典和量子不稳定系统的情况。对于经典系统，宏观现实主义和无创测量的两个假设意味着三测量字符串${钾}_3$ 完全等于 1。此外，对于量子力学系统，这两个假设通常都无效，我们发现 ${钾}_3=1$ 对于纯指数衰减（${钾}_3\le 1$是一般的LGI）。另一方面，量子力学预测的短期和长期指数衰减定律的必要偏差导致${钾}_3\ne 1$. 此外，严格的违反${钾}_3>1$通常在短时间内发生。因此，我们得出结论，观察到这种与指数衰减定律的偏差的实验也应该在其数据中违反 LGI。