P. Cejnar, M. Macek, S. Heinze, J. Jolie, J. Dobeš
{"title":"可积系统中的单态和激发态量子相变:原子核的集体振动","authors":"P. Cejnar, M. Macek, S. Heinze, J. Jolie, J. Dobeš","doi":"10.1088/0305-4470/39/31/L01","DOIUrl":null,"url":null,"abstract":"Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"78","resultStr":"{\"title\":\"Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei\",\"authors\":\"P. Cejnar, M. Macek, S. Heinze, J. Jolie, J. Dobeš\",\"doi\":\"10.1088/0305-4470/39/31/L01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"78\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/31/L01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/31/L01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei
Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.