Low frequency analogue Hawking radiation: The Korteweg-de Vries model

TL;DR

This paper derives analytical formulas for low-frequency analogue Hawking radiation in weak-dispersive media, showing a thermal spectrum persists and providing insights for experimental detection.

Contribution

It introduces a linearized Korteweg-de Vries model to describe scattering processes in near-critical flows and derives exact expressions for effective temperature.

Findings

Thermal low-frequency spectrum persists despite dispersive effects.

Effective temperature matches Hawking temperature when dispersive length is small.

Spectrum coefficients decrease at low frequencies in flows without horizons.

Abstract

We derive analytic expressions for the low-frequency properties of the analogue Hawking radiation in a general weak-dispersive medium. A thermal low-frequency part of the spectrum is expected even when dispersive effects become significant. We consider the two most common class of weak-dispersive media and investigate all possible anomalous scattering processes due inhomogeneous background flows. We first argue that under minimal assumptions, the scattering processes in near-critical flows are well described by a linearized Korteweg-de Vries equation. Within our theoretical model greybody factors are neglected, that is, the mode co-moving with the flow decouples from the other ones. We also exhibit a flow example with an exact expression for the effective temperature. We see that this temperature coincides with the Hawking one only when the dispersive length scale is much smaller than the flow gradient scale. We apply the same method in inhomogeneous flows without an analogue horizon. In this case, the spectrum coefficients decrease with decreasing frequencies. Our findings are in agreement with previous numerical works, generalizing their findings to arbitrary flow profiles. Our analytical expressions provide estimates to guide ongoing experimental efforts.