{"id":{"repo_id":"brazil-ufpe","oai_identifier":"oai:repositorio.ufpe.br:123456789/24737"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-ufpe/oai:repositorio.ufpe.br:123456789/24737","repository":{"repo_id":"brazil-ufpe","name":"Brazil UFPE","base_url":"https://repositorio.ufpe.br/oai/request"},"display":{"title":"Transition from integrable to chaotic domain in spectra of spin chains","abstract":"In this thesis we present an approach, similar to random matrix ensembles, in order to study the integrable-chaotic transition in the Heisenberg spin model. We consider three ways to break the integrability: presence on an external field on a single spin, coupling of an external random field with each spin in the chain and next nearest neighbor interaction between spins. We propose a transition described by a power law in the spectral density, i.e. S(k) ∝ 1/kα, where α = 2 for the integrable case and α = 1 for the chaotic case, with 1 < α < 2 for systems in the crossover regime. The transition is also described by the behavior of the \"burstiness\" B and the Kullback–Leibler divergence DLK(PW−D(s)|Pdata(s)), where PW−D(s) and Pdata(s) are the Wigner-Dyson and the system’s spacing distribution respectively. The B coefficient is associated to a sequence of events in the system. The Kullback–Leibler divergence provides information on how two distributions differ from each other. From analyzing the behavior of these three quantities, we obtain a universal description of integrable-chaotic transition in the spin chains.","abstract_html":"In this thesis we present an approach, similar to random matrix ensembles, in order to study the integrable-chaotic transition in the Heisenberg spin model. We consider three ways to break the integrability: presence on an external field on a single spin, coupling of an external random field with each spin in the chain and next nearest neighbor interaction between spins. We propose a transition described by a power law in the spectral density, i.e. S(k) ∝ 1/kα, where α = 2 for the integrable case and α = 1 for the chaotic case, with 1 &lt; α &lt; 2 for systems in the crossover regime. The transition is also described by the behavior of the &quot;burstiness&quot; B and the Kullback–Leibler divergence DLK(PW−D(s)|Pdata(s)), where PW−D(s) and Pdata(s) are the Wigner-Dyson and the system’s spacing distribution respectively. The B coefficient is associated to a sequence of events in the system. The Kullback–Leibler divergence provides information on how two distributions differ from each other. From analyzing the behavior of these three quantities, we obtain a universal description of integrable-chaotic transition in the spin chains.","abstract_has_math":false,"creators":["MORENO TARQUINO, Juan Nicolas"],"institution":"Universidade Federal de Pernambuco","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["MACEDO, Antonio Murilo Santos"],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-08-31","date_published":"2016-08-31","updated_at":"2026-07-24T01:18:52Z","subjects":["Matéria condensada","Transporte quântico","Caos quântico"],"languages":["eng"],"rights":["openAccess","Attribution-NonCommercial-NoDerivs 3.0 Brazil"],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/3.0/br/"],"identifier_entries":[]},"links":{"outbound_url":"https://repositorio.ufpe.br/handle/123456789/24737","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["MACEDO, Antonio Murilo Santos"]},{"key":"dc:creator","label":"Author","values":["MORENO TARQUINO, Juan Nicolas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-06-04T21:25:20Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-06-04T21:25:20Z"]},{"key":"dc:date.issued","label":"Date","values":["2016-08-31"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal de Pernambuco"]},{"key":"dc:type","label":"Dc Type","values":["masterThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Matéria condensada","Transporte quântico","Caos quântico"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["openAccess","Attribution-NonCommercial-NoDerivs 3.0 Brazil"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-nd/3.0/br/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repositorio.ufpe.br/handle/123456789/24737"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we present an approach, similar to random matrix ensembles, in order to study the integrable-chaotic transition in the Heisenberg spin model. We consider three ways to break the integrability: presence on an external field on a single spin, coupling of an external random field with each spin in the chain and next nearest neighbor interaction between spins. We propose a transition described by a power law in the spectral density, i.e. S(k) ∝ 1/kα, where α = 2 for the integrable case and α = 1 for the chaotic case, with 1 < α < 2 for systems in the crossover regime. The transition is also described by the behavior of the \"burstiness\" B and the Kullback–Leibler divergence DLK(PW−D(s)|Pdata(s)), where PW−D(s) and Pdata(s) are the Wigner-Dyson and the system’s spacing distribution respectively. The B coefficient is associated to a sequence of events in the system. The Kullback–Leibler divergence provides information on how two distributions differ from each other. From analyzing the behavior of these three quantities, we obtain a universal description of integrable-chaotic transition in the spin chains."]},{"key":"dc:title","label":"Title","values":["Transition from integrable to chaotic domain in spectra of spin chains"]}]}],"canonical_facts":{"dc:contributor.advisor":["MACEDO, Antonio Murilo Santos"],"dc:creator":["MORENO TARQUINO, Juan Nicolas"],"dc:date.accessioned":["2018-06-04T21:25:20Z"],"dc:date.available":["2018-06-04T21:25:20Z"],"dc:date.issued":["2016-08-31"],"dc:description.abstract":["In this thesis we present an approach, similar to random matrix ensembles, in order to study the integrable-chaotic transition in the Heisenberg spin model. We consider three ways to break the integrability: presence on an external field on a single spin, coupling of an external random field with each spin in the chain and next nearest neighbor interaction between spins. We propose a transition described by a power law in the spectral density, i.e. S(k) ∝ 1/kα, where α = 2 for the integrable case and α = 1 for the chaotic case, with 1 < α < 2 for systems in the crossover regime. The transition is also described by the behavior of the \"burstiness\" B and the Kullback–Leibler divergence DLK(PW−D(s)|Pdata(s)), where PW−D(s) and Pdata(s) are the Wigner-Dyson and the system’s spacing distribution respectively. The B coefficient is associated to a sequence of events in the system. The Kullback–Leibler divergence provides information on how two distributions differ from each other. From analyzing the behavior of these three quantities, we obtain a universal description of integrable-chaotic transition in the spin chains."],"dc:identifier.uri":["https://repositorio.ufpe.br/handle/123456789/24737"],"dc:language.iso":["eng"],"dc:publisher":["Universidade Federal de Pernambuco"],"dc:rights":["openAccess","Attribution-NonCommercial-NoDerivs 3.0 Brazil"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-nd/3.0/br/"],"dc:subject":["Matéria condensada","Transporte quântico","Caos quântico"],"dc:title":["Transition from integrable to chaotic domain in spectra of spin chains"],"dc:type":["masterThesis"]},"updated_at":"2026-07-24T01:18:52Z"}