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Low-frequency analogue Hawking radiation: the Korteweg–de Vries model

Coutant, Antonin; Weinfurtner, Silke


Antonin Coutant


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 ow profiles. Our analytical expressions provide estimates to guide ongoing experimental efforts.


Coutant, A., & Weinfurtner, S. (2018). Low-frequency analogue Hawking radiation: the Korteweg–de Vries model. Physical Review D, 97(2),

Journal Article Type Article
Acceptance Date Dec 8, 2017
Online Publication Date Jan 8, 2018
Publication Date Jan 15, 2018
Deposit Date Jan 29, 2018
Publicly Available Date Jan 29, 2018
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 97
Issue 2
Public URL
Publisher URL


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