Low-frequency analogue Hawking radiation: the Korteweg–de Vries model
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 me...
| Main Authors: | , |
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| Format: | Article |
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American Physical Society
2018
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| Online Access: | https://eprints.nottingham.ac.uk/49381/ |
| _version_ | 1848797984538492928 |
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| author | Coutant, Antonin Weinfurtner, Silke |
| author_facet | Coutant, Antonin Weinfurtner, Silke |
| author_sort | Coutant, Antonin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:12:34Z |
| format | Article |
| id | nottingham-49381 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:12:34Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-493812020-05-04T19:26:46Z https://eprints.nottingham.ac.uk/49381/ Low-frequency analogue Hawking radiation: the Korteweg–de Vries model Coutant, Antonin Weinfurtner, Silke 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. American Physical Society 2018-01-15 Article PeerReviewed Coutant, Antonin and Weinfurtner, Silke (2018) Low-frequency analogue Hawking radiation: the Korteweg–de Vries model. Physical Review D, 97 (2). 025005. ISSN 2470-0029 https://doi.org/10.1103/PhysRevD.97.025005 doi:10.1103/PhysRevD.97.025005 doi:10.1103/PhysRevD.97.025005 |
| spellingShingle | Coutant, Antonin Weinfurtner, Silke Low-frequency analogue Hawking radiation: the Korteweg–de Vries model |
| title | Low-frequency analogue Hawking radiation: the Korteweg–de Vries model |
| title_full | Low-frequency analogue Hawking radiation: the Korteweg–de Vries model |
| title_fullStr | Low-frequency analogue Hawking radiation: the Korteweg–de Vries model |
| title_full_unstemmed | Low-frequency analogue Hawking radiation: the Korteweg–de Vries model |
| title_short | Low-frequency analogue Hawking radiation: the Korteweg–de Vries model |
| title_sort | low-frequency analogue hawking radiation: the korteweg–de vries model |
| url | https://eprints.nottingham.ac.uk/49381/ https://eprints.nottingham.ac.uk/49381/ https://eprints.nottingham.ac.uk/49381/ |