We extend previous work on the numerical diagonalization of quantum stress tensor operators in the Minkowski vacuum state, which considered operators averaged in a finite time interval, to operators averaged in a finite spacetime region. Since real experiments occur over finite volumes and durations, physically meaningful fluctuations may be obtained from stress tensor operators averaged by compactly supported sampling functions in space and time. The direct diagonalization, via a Bogoliubov transformation, gives the eigenvalues and the probabilities of measuring those eigenvalues in the vacuum state, from which the underlying probability distribution can be constructed. For the normal-ordered square of the time derivative of a massless scalar field in a spherical cavity with finite degrees of freedom, analysis of the tails of these distributions confirms previous results based on the analytical treatment of the high moments. We find that the probability of large vacuum fluctuations is reduced when spatial averaging is included, but the tail still decreases more slowly than exponentially as the magnitude of the measured eigenvalues increases, suggesting vacuum fluctuations may not always be subdominant to thermal fluctuations and opening up the possibility of experimental observation under the right conditions.

中文翻译：

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时空平均量子应力张量涨落

我们将之前关于 Minkowski 真空状态下量子应力张量算符的数值对角化的工作扩展到有限时空区域中的平均算符，该算符考虑了有限时间间隔内的平均算符。由于真实的实验发生在有限的体积和持续时间，物理意义的波动可以从应力张量算子中获得，由空间和时间上的紧凑支持的采样函数平均。直接对角化通过 Bogoliubov 变换给出特征值和在真空状态下测量这些特征值的概率，从中可以构建潜在的概率分布。对于有限自由度球腔中无质量标量场的时间导数的正序平方，对这些分布尾部的分析证实了之前基于高矩分析处理的结果。我们发现，当包含空间平均时，大真空波动的概率会降低，但随着测量特征值的大小增加，尾部仍然比指数下降的速度更慢，这表明真空波动可能并不总是次于热波动，并打开了在合适的条件下进行实验观察的可能性。