Quantizing neutrino billiards: an expanded boundary integral method
With the pioneering fabrication of graphene the field of relativistic quantum chaos emerged. We will focus on the spectral properties of massless spin-1/2 particles confined in a bounded two-dimensional region, named neutrino billiards by Berry and Mondragon in 1987. A commonly used method for the d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ab2fde |
| _version_ | 1797750055559495680 |
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| author | Pei Yu B Dietz L Huang |
| author_facet | Pei Yu B Dietz L Huang |
| author_sort | Pei Yu |
| collection | DOAJ |
| description | With the pioneering fabrication of graphene the field of relativistic quantum chaos emerged. We will focus on the spectral properties of massless spin-1/2 particles confined in a bounded two-dimensional region, named neutrino billiards by Berry and Mondragon in 1987. A commonly used method for the determination of the eigenvalues is based on a boundary integral equation originating from Green’s theorem. Yet, in the quantization one might face problems similar to those occurring for non-relativistic quantum billiards. Especially in cases where the eigenvalue spectrum contains near degeneracies the identification of complete sequences of eigenvalues might be extremely elaborate, if not unfeasible. We propose an expanded boundary integral method, which yields complete eigenvalue sequences with a considerably lower numerical effort than the standard one. Actually, it corresponds to an extension of the method introduced in Veble et al (2007 New J. Phys. 9 15) to relativistic quantum billiards. To demonstrate its validity and its superior efficiency compared to the standard method, we apply both methods to a circular billiard of which the eigenvalues are known analytically and exhibit near degeneracies. Finally, we employ it for the quantization of a neutrino billiard with a hole, of which the spectrum contains many close lying levels and exhibits unusual fluctuation properties. |
| first_indexed | 2024-03-12T16:27:18Z |
| format | Article |
| id | doaj.art-3a1091de6986475c87c28680491e6c9f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:27:18Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
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| series | New Journal of Physics |
| spelling | doaj.art-3a1091de6986475c87c28680491e6c9f2023-08-08T15:39:35ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121707303910.1088/1367-2630/ab2fdeQuantizing neutrino billiards: an expanded boundary integral methodPei Yu0B Dietz1https://orcid.org/0000-0002-8251-6531L Huang2https://orcid.org/0000-0002-3346-339XSchool of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University , Lanzhou, Gansu 730000, People's Republic of ChinaSchool of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University , Lanzhou, Gansu 730000, People's Republic of ChinaSchool of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University , Lanzhou, Gansu 730000, People's Republic of ChinaWith the pioneering fabrication of graphene the field of relativistic quantum chaos emerged. We will focus on the spectral properties of massless spin-1/2 particles confined in a bounded two-dimensional region, named neutrino billiards by Berry and Mondragon in 1987. A commonly used method for the determination of the eigenvalues is based on a boundary integral equation originating from Green’s theorem. Yet, in the quantization one might face problems similar to those occurring for non-relativistic quantum billiards. Especially in cases where the eigenvalue spectrum contains near degeneracies the identification of complete sequences of eigenvalues might be extremely elaborate, if not unfeasible. We propose an expanded boundary integral method, which yields complete eigenvalue sequences with a considerably lower numerical effort than the standard one. Actually, it corresponds to an extension of the method introduced in Veble et al (2007 New J. Phys. 9 15) to relativistic quantum billiards. To demonstrate its validity and its superior efficiency compared to the standard method, we apply both methods to a circular billiard of which the eigenvalues are known analytically and exhibit near degeneracies. Finally, we employ it for the quantization of a neutrino billiard with a hole, of which the spectrum contains many close lying levels and exhibits unusual fluctuation properties.https://doi.org/10.1088/1367-2630/ab2fderelativistic quantum chaosbilliardsboundary integral method |
| spellingShingle | Pei Yu B Dietz L Huang Quantizing neutrino billiards: an expanded boundary integral method New Journal of Physics relativistic quantum chaos billiards boundary integral method |
| title | Quantizing neutrino billiards: an expanded boundary integral method |
| title_full | Quantizing neutrino billiards: an expanded boundary integral method |
| title_fullStr | Quantizing neutrino billiards: an expanded boundary integral method |
| title_full_unstemmed | Quantizing neutrino billiards: an expanded boundary integral method |
| title_short | Quantizing neutrino billiards: an expanded boundary integral method |
| title_sort | quantizing neutrino billiards an expanded boundary integral method |
| topic | relativistic quantum chaos billiards boundary integral method |
| url | https://doi.org/10.1088/1367-2630/ab2fde |
| work_keys_str_mv | AT peiyu quantizingneutrinobilliardsanexpandedboundaryintegralmethod AT bdietz quantizingneutrinobilliardsanexpandedboundaryintegralmethod AT lhuang quantizingneutrinobilliardsanexpandedboundaryintegralmethod |