The Hawking effect in dielectric media and the Hopfield model
The Hawking effect in dielectric media and the Hopfield model
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介电介质中的霍金效应和霍普菲尔德模型
DOI：
10.1103/physrevd.91.124063
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
F. Piazza
中科院分区：
文献类型：
--
作者：
F. Belgiorno;S. Cacciatori;F. Piazza
我们考虑介电色散介质中电磁场的所谓Hopfield模型，该模型允许微观参数的时空依赖，旨在对由克尔效应引起的时空变化介电扰动进行现象学描述。本文首先分析了Hopfield模型的几何光学特性，然后引入了一个简化的模型，该模型避免了完整Hopfield模型所涉及的许多困难，并保持了相同的色散关系，从而讨论了模拟霍金效应。给出了振幅计算，并在量子散射理论框架下推导了广义曼利-罗恒等式。我们的主要结果是在单分支情况下自发热发射的解析计算，这是第一次在介电黑洞的框架中提供非摄动。并指出了光学黑洞和声学黑洞之间的普遍热机制。
We consider the so-called Hopfield model for the electromagnetic field in a dielectric dispersive medium in a framework in which one allows a space-time dependence of microscopic parameters, aimed to a phenomenological description of a space-time varying dielectric perturbation induced by means of the Kerr effect. We discuss the analogue Hawking effect, by first analyzing the geometrical optics for the Hopfield model, and then by introducing a simplified model which has the bonus to avoid many difficulties which are involved in the full Hopfield model, still keeping the same dispersion relation. Amplitude calculations are indicated, and generalized Manley-Rowe identities are derived in a quantum scattering theory framework. Our main result is an analytical calculation of the spontaneous thermal emission in the single-branch case, which is provided non perturbatively for the first time in the framework of dielectric black holes. An universal mechanism for thermality between optical black holes and acoustic black holes is also pointed out.