Scattering neutrinos, spin models, and permutations
We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N, nontrivial eigenvalues, in...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023157 |
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| author | Duff Neill Hanqing Liu Joshua Martin Alessandro Roggero |
| author_facet | Duff Neill Hanqing Liu Joshua Martin Alessandro Roggero |
| author_sort | Duff Neill |
| collection | DOAJ |
| description | We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N, nontrivial eigenvalues, in distinction to the classic Heisenberg spin-glass models, leading to distinct behavior in both the high-temperature and low-temperature regimes. When the momenta of the neutrinos are uniform and random in directions, we can calculate the large-N partition function for the quantum Heisenberg model. In particular, the high-temperature partition function predicts a non-Gaussian density of states, providing interesting counterexamples showing the limits of general theorems on the density of states for quantum spin models. We can repeat the same argument for classical Heisenberg models, also known as rotor models, and we find the high-temperature expansion is completely controlled by the eigenvalues of the coupling matrix, and again predicts non-Gaussian behavior for the density of states as long as the number of eigenvalues does not scale linearly with N. Indeed, we derive the amusing fact that these thermodynamic partition functions are essentially the generating function for counting permutations in the high-temperature regime. Finally, for the case relevant to neutrinos in a supernova, we identify the low-temperature phase as a unique state with the direction of the momenta of the neutrino dictating its coherent state in flavor-space, a state we dub the “flavor-momentum-locked” state. |
| format | Article |
| id | doaj-art-2a69fb19a62646e7afcf6eaf63a5007c |
| institution | OA Journals |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-2a69fb19a62646e7afcf6eaf63a5007c2025-08-20T01:52:21ZengAmerican Physical SocietyPhysical Review Research2643-15642025-05-017202315710.1103/PhysRevResearch.7.023157Scattering neutrinos, spin models, and permutationsDuff NeillHanqing LiuJoshua MartinAlessandro RoggeroWe consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N, nontrivial eigenvalues, in distinction to the classic Heisenberg spin-glass models, leading to distinct behavior in both the high-temperature and low-temperature regimes. When the momenta of the neutrinos are uniform and random in directions, we can calculate the large-N partition function for the quantum Heisenberg model. In particular, the high-temperature partition function predicts a non-Gaussian density of states, providing interesting counterexamples showing the limits of general theorems on the density of states for quantum spin models. We can repeat the same argument for classical Heisenberg models, also known as rotor models, and we find the high-temperature expansion is completely controlled by the eigenvalues of the coupling matrix, and again predicts non-Gaussian behavior for the density of states as long as the number of eigenvalues does not scale linearly with N. Indeed, we derive the amusing fact that these thermodynamic partition functions are essentially the generating function for counting permutations in the high-temperature regime. Finally, for the case relevant to neutrinos in a supernova, we identify the low-temperature phase as a unique state with the direction of the momenta of the neutrino dictating its coherent state in flavor-space, a state we dub the “flavor-momentum-locked” state.http://doi.org/10.1103/PhysRevResearch.7.023157 |
| spellingShingle | Duff Neill Hanqing Liu Joshua Martin Alessandro Roggero Scattering neutrinos, spin models, and permutations Physical Review Research |
| title | Scattering neutrinos, spin models, and permutations |
| title_full | Scattering neutrinos, spin models, and permutations |
| title_fullStr | Scattering neutrinos, spin models, and permutations |
| title_full_unstemmed | Scattering neutrinos, spin models, and permutations |
| title_short | Scattering neutrinos, spin models, and permutations |
| title_sort | scattering neutrinos spin models and permutations |
| url | http://doi.org/10.1103/PhysRevResearch.7.023157 |
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