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dc.contributor.authorSalazar, Robert P.-
dc.contributor.authorTéllez, Gabriel-
dc.contributor.authorJaramillo, Diego F.-
dc.contributor.authorGonzález, Diego L.-
dc.date.accessioned2021-10-15T19:32:28Z-
dc.date.available2021-10-15T19:32:28Z-
dc.date.issued2015-06-24-
dc.identifier.urihttps://repositorio.accefyn.org.co/handle/001/851-
dc.description.abstractWe analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $\xi$ which gradually change the shape of the billiard from a regular equilateral triangle ($\xi=1$) to a diamond ($\xi=0$) was used to control the transition between the regular and chaotic regimes. The classical behaviour is regular when the control parameter $\xi$ is one; in contrast, the system is chaotic when $\xi \neq 1$ even for values of $\xi$ close to one. The entropy grows fast as $\xi$ is decreased from 1 and the Lyapunov exponent remains positive for $\xi<1$. The Finite Difference Method was implemented in order to solve the quantum problem. The energy spectrum and eigenstates were numerically computed for different values of the control parameter. The nearest-neighbour spacing distribution is analysed as a function of $\xi$, finding a Poisson and a Gaussian Orthogonal Ensemble (GOE) distribution for regular and chaotic regimes respectively. Several scars and bouncing ball states are shown with their corresponding classical periodic orbits. Along the document the classical chaos identifiers are computed to show that system is chaotic. On the other hand, the quantum counterpart is in agreement with the Bohigas-Giannoni-Schmit conjecture and exhibits the standard features for chaotic billiard such as the scarring of the wavefunction.eng
dc.description.abstractSe estudia el comportamiento de una partícula en el interior de un billar triangular donde uno de sus lados toma de medio estadio que se llamó billar diamante con corona redondeada o DSRC por su siglas en inglés. Se definió un parámetro ξ que cambia suavemente la forma la frontera partiendo de un billar triangular ξ = 1 a un billar DSRC ξ = 1. Dicho parámetro controla la transicipon entre el régimen regular y caótico. Clásicamente, el sistema es regular cuando ξ = 1. Por otro lado, el istema se torna caótico para ξ = 1 incluyendo valores próximos a 1. Se calcula el coeficiente de Lyapunov y la entropía media de la distribucipon de los ángulos de incidencia para caracterizar el comportamiento caótico del sistema. Se observó un rápido crecimiento de la información de las trayectorias hasta saturar la entropía al cambiar levemente la frontera del billar triangular original. A su vez el coeficiente de Lyapunov se mantuvo positivo durante este proceso una vez que ξ se alejaba de 1. Se implementó el método de diferencias finitas FDM para obtener el espectro y los estados propios de la contraparte cuántica del sistema. La distribución de espaciamiento entre primeros vecinos para varios valores de ξ fue construida numéricamente para diferentes valores de ξ ncontrando una distribución de Poisson y otra correspondiente al ensamble ortogonal gaussiano GOE dentro de las regiones clásica y caótica respectivamente. Se identificaron cicatrices en algunos de sus estados asíı como estados de “bola rebotadora” con sus correspondientes órbitas periódicas. El sistema exhibe un comportamiento que está de acuerdo a la conjetura BGS y presenta las características típicas de un billar caótico como la cicatrización de la función de onda.spa
dc.format.extent19 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.language.isoengspa
dc.publisherAcademia Colombiana de Ciencias Exactas, Físicas y Naturalesspa
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 Internationalspa
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/spa
dc.titleChaos in the Diamond-Shaped Billiard with Rounded Crowspa
dc.typeArtículo de revistaspa
dcterms.audienceEstudiantes, Profesores, Comunidad científicaspa
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.type.driverinfo:eu-repo/semantics/articlespa
dc.type.versioninfo:eu-repo/semantics/publishedVersionspa
dc.rights.creativecommonsAtribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)spa
dc.identifier.doihttps://doi.org/10.18257/raccefyn.99-
dc.subject.proposalCaos cuánticospa
dc.subject.proposalQuantum chaoseng
dc.subject.proposalBillares cuánticosspa
dc.subject.proposalQuantum billiardseng
dc.subject.proposalMatrices aleatoriasspa
dc.subject.proposalRandom matricesspa
dc.subject.proposalMétodo de diferencias finitasspa
dc.subject.proposalFinite difference methodeng
dc.type.coarhttp://purl.org/coar/resource_type/c_6501spa
dc.relation.ispartofjournalRevista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturalesspa
dc.relation.citationvolume39spa
dc.relation.citationstartpage152spa
dc.relation.citationendpage170spa
dc.publisher.placeBogotá, Colombiaspa
dc.contributor.corporatenameAcademia Colombiana de Ciencias Exactas, Físicas y Naturalesspa
dc.relation.citationissue151spa
dc.type.contentDataPaperspa
dc.type.redcolhttp://purl.org/redcol/resource_type/ARTspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85spa
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