Semiclassical density of degeneracies in quantum regular systems
The spectrum of eigenenergies of a quantum integrable system whose Hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the plane energy-parameter, that is the number of crossings per...
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todo:paper_03054470_v33_n12_p2345_Fendrik2023-10-03T15:21:47Z Semiclassical density of degeneracies in quantum regular systems Fendrik, A.J. Sánchez, M.J. The spectrum of eigenenergies of a quantum integrable system whose Hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the plane energy-parameter, that is the number of crossings per unit of energy and unit of parameter, in terms of classical periodic orbits. We compare the results of the semiclassical formula with exact quantum calculations for two specific quantum integrable billiards. Fil:Fendrik, A.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sánchez, M.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03054470_v33_n12_p2345_Fendrik |
| institution |
Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
The spectrum of eigenenergies of a quantum integrable system whose Hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the plane energy-parameter, that is the number of crossings per unit of energy and unit of parameter, in terms of classical periodic orbits. We compare the results of the semiclassical formula with exact quantum calculations for two specific quantum integrable billiards. |
| format |
JOUR |
| author |
Fendrik, A.J. Sánchez, M.J. |
| spellingShingle |
Fendrik, A.J. Sánchez, M.J. Semiclassical density of degeneracies in quantum regular systems |
| author_facet |
Fendrik, A.J. Sánchez, M.J. |
| author_sort |
Fendrik, A.J. |
| title |
Semiclassical density of degeneracies in quantum regular systems |
| title_short |
Semiclassical density of degeneracies in quantum regular systems |
| title_full |
Semiclassical density of degeneracies in quantum regular systems |
| title_fullStr |
Semiclassical density of degeneracies in quantum regular systems |
| title_full_unstemmed |
Semiclassical density of degeneracies in quantum regular systems |
| title_sort |
semiclassical density of degeneracies in quantum regular systems |
| url |
http://hdl.handle.net/20.500.12110/paper_03054470_v33_n12_p2345_Fendrik |
| work_keys_str_mv |
AT fendrikaj semiclassicaldensityofdegeneraciesinquantumregularsystems AT sanchezmj semiclassicaldensityofdegeneraciesinquantumregularsystems |
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