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arXiv 1502.02687hep-th
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黑洞辐射的密度矩阵

Density matrix of black hole radiation

Lasma Alberte, Ram Brustein, Andrei Khmelnitsky, A. J. M. Medved

摘要:

霍金的黑洞蒸发模型不是幺正的,导致了辐射的混合密度矩阵,而佩奇模型描述了一个幺正的蒸发过程,其中密度矩阵从几乎热态演化到纯态。我们比较了最近提出的半经典黑洞蒸发模型的两个已建立的模型。特别是,我们研究了出射辐射的密度矩阵,并确定了三种框架的非对角校正的大小如何不同。对于霍金模型,我们发现幂律修正的两点函数,诱导指数抑制修正的非对角元素的完整密度矩阵。这证明了Hawking结果对微扰论中的所有阶数都是正确的,并允许用单粒子密度矩阵来表示完整的密度矩阵。然后,我们考虑半经典理论的修正,是非微扰从有效场论的角度来看,是少得多的抑制和增长单调的时间。在这种情况下,出射辐射的雷尼熵在早期呈线性增长;但这种增长会减慢,熵最终在佩奇时间开始下降。除了比较模型,我们强调的区别状态的辐射发射的黑洞,这是高度量子化的,从一个典型的经典黑体在相同的温度下发射的辐射。

英文摘要:

Hawking's model of black hole evaporation is not unitary and leads to a mixed density matrix for the emitted radiation, while the Page model describes a unitary evaporation process in which the density matrix evolves from an almost thermal state to a pure state. We compare a recently proposed model of semiclassical black hole evaporation to the two established models. In particular, we study the density matrix of the outgoing radiation and determine how the magnitude of the off-diagonal corrections differs for the three frameworks. For Hawking's model, we find power-law corrections to the two-point functions that induce exponentially suppressed corrections to the off-diagonal elements of the full density matrix. This verifies that the Hawking result is correct to all orders in perturbation theory and also allows one to express the full density matrix in terms of the single-particle density matrix. We then consider the semiclassical theory for which the corrections, being non-perturbative from an effective field-theory perspective, are much less suppressed and grow monotonically in time. In this case, the Rényi entropy for the outgoing radiation is shown to grow linearly at early times; but this growth slows down and the entropy eventually starts to decrease at the Page time. In addition to comparing models, we emphasize the distinction between the state of the radiation emitted from a black hole, which is highly quantum, and that of the radiation emitted from a typical classical black body at the same temperature.

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