A solvable model for symmetry-breaking phase transitions
Abstract Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as integrable equations which produce solitons do not admit...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-08-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-40704-6 |
| _version_ | 1797577066429808640 |
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| author | Shatrughna Kumar Pengfei Li Liangwei Zeng Jingsong He Boris A. Malomed |
| author_facet | Shatrughna Kumar Pengfei Li Liangwei Zeng Jingsong He Boris A. Malomed |
| author_sort | Shatrughna Kumar |
| collection | DOAJ |
| description | Abstract Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as integrable equations which produce solitons do not admit intrinsic transitions in them. We introduce a solvable model for symmetry-breaking phase transitions of both the first and second kinds (alias sub- and supercritical bifurcations) for solitons pinned to a combined linear-nonlinear double-well potential, represented by a symmetric pair of delta-functions. Both self-focusing and defocusing signs of the nonlinearity are considered. In the former case, exact solutions are produced for symmetric and asymmetric solitons. The solutions explicitly demonstrate a switch between the symmetry-breaking transitions of the first and second kinds (i.e., sub- and supercritical bifurcations, respectively). In the self-defocusing model, the solution demonstrates the transition of the second kind which breaks antisymmetry of the first excited state. |
| first_indexed | 2024-03-10T22:02:41Z |
| format | Article |
| id | doaj.art-c447c40eeef04de9ba34f0468d91f0ea |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-10T22:02:41Z |
| publishDate | 2023-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-c447c40eeef04de9ba34f0468d91f0ea2023-11-19T12:55:05ZengNature PortfolioScientific Reports2045-23222023-08-0113112010.1038/s41598-023-40704-6A solvable model for symmetry-breaking phase transitionsShatrughna Kumar0Pengfei Li1Liangwei Zeng2Jingsong He3Boris A. Malomed4Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv UniversityDepartment of Physics, Taiyuan Normal UniversityDepartment of Basic Course, Guangzhou Maritime UniversityInstitute for Advanced Study, Shenzhen UniversityDepartment of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv UniversityAbstract Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as integrable equations which produce solitons do not admit intrinsic transitions in them. We introduce a solvable model for symmetry-breaking phase transitions of both the first and second kinds (alias sub- and supercritical bifurcations) for solitons pinned to a combined linear-nonlinear double-well potential, represented by a symmetric pair of delta-functions. Both self-focusing and defocusing signs of the nonlinearity are considered. In the former case, exact solutions are produced for symmetric and asymmetric solitons. The solutions explicitly demonstrate a switch between the symmetry-breaking transitions of the first and second kinds (i.e., sub- and supercritical bifurcations, respectively). In the self-defocusing model, the solution demonstrates the transition of the second kind which breaks antisymmetry of the first excited state.https://doi.org/10.1038/s41598-023-40704-6 |
| spellingShingle | Shatrughna Kumar Pengfei Li Liangwei Zeng Jingsong He Boris A. Malomed A solvable model for symmetry-breaking phase transitions Scientific Reports |
| title | A solvable model for symmetry-breaking phase transitions |
| title_full | A solvable model for symmetry-breaking phase transitions |
| title_fullStr | A solvable model for symmetry-breaking phase transitions |
| title_full_unstemmed | A solvable model for symmetry-breaking phase transitions |
| title_short | A solvable model for symmetry-breaking phase transitions |
| title_sort | solvable model for symmetry breaking phase transitions |
| url | https://doi.org/10.1038/s41598-023-40704-6 |
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