Violation of classical inequalities by resonant Hawking radiation in a sonic black hole

Abstract

We argue that, in a sonic black hole, the two-mode classical Cauchy–Schwarz inequality can be violated at nonzero frequencies, which can be viewed as a smoking gun of spontaneous analog Hawking radiation. A double-barrier structure generates resonant peaks in the spectrum where the inequality can be largely violated. For a given frequency, we compute the maximum temperature at which this violation can be observed. We also study the scenario where a space-dependent constant coupling produces a resonant spectrum. We prove that the zero-frequency peak always shows classical behavior. When we compare our results with those obtained for non-resonant structures such as the single barrier or the waterfall configuration, we find that the absolute amount of violation is extremely weak compared to that of resonant setups.