Analogous Hawking Radiation in Dispersive Media
In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improveme...
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MDPI AG
2024-11-01
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| author | Francesco Belgiorno Sergio L. Cacciatori Simone Trevisan |
| author_facet | Francesco Belgiorno Sergio L. Cacciatori Simone Trevisan |
| author_sort | Francesco Belgiorno |
| collection | DOAJ |
| description | In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided. |
| format | Article |
| id | doaj-art-7eef9b3a17a040669f46fcc05215e915 |
| institution | OA Journals |
| issn | 2218-1997 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj-art-7eef9b3a17a040669f46fcc05215e9152025-08-20T01:54:04ZengMDPI AGUniverse2218-19972024-11-01101141210.3390/universe10110412Analogous Hawking Radiation in Dispersive MediaFrancesco Belgiorno0Sergio L. Cacciatori1Simone Trevisan2Dipartimento di Matematica, Politecnico di Milano, 20133 Milano, ItalyDipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, 22100 Como, ItalyDipartimento di Ingegneria dell’Informazione, Università di Padova, 35131 Padova, ItalyIn the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided.https://www.mdpi.com/2218-1997/10/11/412analogous Hawking effectconnection formulasS-matrix |
| spellingShingle | Francesco Belgiorno Sergio L. Cacciatori Simone Trevisan Analogous Hawking Radiation in Dispersive Media Universe analogous Hawking effect connection formulas S-matrix |
| title | Analogous Hawking Radiation in Dispersive Media |
| title_full | Analogous Hawking Radiation in Dispersive Media |
| title_fullStr | Analogous Hawking Radiation in Dispersive Media |
| title_full_unstemmed | Analogous Hawking Radiation in Dispersive Media |
| title_short | Analogous Hawking Radiation in Dispersive Media |
| title_sort | analogous hawking radiation in dispersive media |
| topic | analogous Hawking effect connection formulas S-matrix |
| url | https://www.mdpi.com/2218-1997/10/11/412 |
| work_keys_str_mv | AT francescobelgiorno analogoushawkingradiationindispersivemedia AT sergiolcacciatori analogoushawkingradiationindispersivemedia AT simonetrevisan analogoushawkingradiationindispersivemedia |