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

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.

23 pages, 5 figures. v2: typo corrected, references added

References in corpus (8)

• Measurement of stimulated Hawking emission in an analogue system
• Observation of self-amplifying Hawking radiation in an analog black hole laser
• Hawking radiation from ultrashort laser pulse filaments
• On the origin of the particles in black hole evaporation
• Probing the thermal character of analogue Hawking radiation for shallow water waves?
• Step-like discontinuities in Bose-Einstein condensates and Hawking radiation: dispersion effects
• Low frequency gray-body factors and infrared divergences: rigorous results
• Gray-body factor and infrared divergences in 1D BEC acoustic black holes

Cited by in corpus (8)

• Low frequency analogue Hawking radiation: The Bogoliubov-de Gennes model
• Analogue gravity and the Hawking effect: historical perspective and literature review
• Classical Hydrodynamics for Analogue Spacetimes: Open Channel Flows and Thin Films
• Analogue quantum simulation of the Hawking effect in a polariton superfluid
• Nonlinear dispersion relation of dust acoustic waves using the Korteweg-de Vries model
• Perturbative Approach to Analog Hawking Radiation in dielectric media in subcritical regime
• Superluminal modes in a quantum field simulator for cosmology from analog trans-Planckian physics
• On the analogy between black holes and bathtub vortices