Wigner-Weyl Quantum Entanglement

ilustraciones, diagramas

Autores:
Murillo Mejía, Miller Mateo
Tipo de recurso:
Fecha de publicación:
2024
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
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oai:repositorio.unal.edu.co:unal/85367
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/85367
https://repositorio.unal.edu.co/
Palabra clave:
Partículas
Fuerzas nucleares (física)
Particles
Nuclear fuel elements
quantum phase space
Quantum entanglement
Toda model
Wigner function
Quantum Poincaré surface of section
Espacio de fase cuántico
Entrelazamiento cuántico
Modelo Toda
Función de Wigner
Secciones de Poincaré cuánticas
Rights
openAccess
License
Reconocimiento 4.0 Internacional
id UNACIONAL2_07173cd05ca5c25029e0f7b75a4cc470
oai_identifier_str oai:repositorio.unal.edu.co:unal/85367
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.eng.fl_str_mv Wigner-Weyl Quantum Entanglement
dc.title.translated.spa.fl_str_mv Entrelazamiento cuántico de Wigner-Weyl
title Wigner-Weyl Quantum Entanglement
spellingShingle Wigner-Weyl Quantum Entanglement
Partículas
Fuerzas nucleares (física)
Particles
Nuclear fuel elements
quantum phase space
Quantum entanglement
Toda model
Wigner function
Quantum Poincaré surface of section
Espacio de fase cuántico
Entrelazamiento cuántico
Modelo Toda
Función de Wigner
Secciones de Poincaré cuánticas
title_short Wigner-Weyl Quantum Entanglement
title_full Wigner-Weyl Quantum Entanglement
title_fullStr Wigner-Weyl Quantum Entanglement
title_full_unstemmed Wigner-Weyl Quantum Entanglement
title_sort Wigner-Weyl Quantum Entanglement
dc.creator.fl_str_mv Murillo Mejía, Miller Mateo
dc.contributor.advisor.none.fl_str_mv Viviescas Ramírez, Carlos Leonardo
dc.contributor.author.none.fl_str_mv Murillo Mejía, Miller Mateo
dc.contributor.researchgroup.spa.fl_str_mv Grupo de Investigación: Caos y Complejidad
dc.subject.lemb.spa.fl_str_mv Partículas
Fuerzas nucleares (física)
topic Partículas
Fuerzas nucleares (física)
Particles
Nuclear fuel elements
quantum phase space
Quantum entanglement
Toda model
Wigner function
Quantum Poincaré surface of section
Espacio de fase cuántico
Entrelazamiento cuántico
Modelo Toda
Función de Wigner
Secciones de Poincaré cuánticas
dc.subject.lemb.rng.fl_str_mv Particles
dc.subject.lemb.eng.fl_str_mv Nuclear fuel elements
dc.subject.proposal.eng.fl_str_mv quantum phase space
Quantum entanglement
Toda model
Wigner function
Quantum Poincaré surface of section
dc.subject.proposal.spa.fl_str_mv Espacio de fase cuántico
Entrelazamiento cuántico
Modelo Toda
Función de Wigner
Secciones de Poincaré cuánticas
description ilustraciones, diagramas
publishDate 2024
dc.date.accessioned.none.fl_str_mv 2024-01-18T19:47:09Z
dc.date.available.none.fl_str_mv 2024-01-18T19:47:09Z
dc.date.issued.none.fl_str_mv 2024
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/85367
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/85367
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv M. Mazzanti, R. X. Schüssler, J. D. Arias Espinoza, Z. Wu, R. Gerritsma, and A. Safavi-Naini. Trapped ion quantum computing using optical tweezers and electric fields. Phys. Rev. Lett., 127(260502), 2021.
X. Pan, Y. Zhou and H. Yuan. Engineering superconducting qubits to reduce quasiparticles and charge noise. Nat Commun, 13(7196), 2021.
L.S. Madsen, F. Laudenbach, M.F. Askarani, et al. Quantum computational advantage with a programmable photonic processor. Nature, 606:75-81, 2022.
D. Bluvstein, H. Levine, G. Semeghini, et al. A quantum processor based on coherent transport of entangled atom arrays. Nature, 604:451-456, 2022.
A. Y. Khrennikov. Echoing the recent google success: Foundational roots of quantum supremacy. ArXiv, abs/1911.10337, 2019.
J.J. Sakurai. Modern Quantum Mechanics. Addison-Wesley, 1994.
A. Buchleitner, C. Viviescas and M. Tiersch. Entanglement and Decoherence: Foundations and Modern Trends. Springer, Berlin Heidelberg, 2009.
D. Gross, S. T. Flammia, and J. Eisert. Most quantum states are too entangled to be useful as computational resources. Phys. Rev. Lett., 102(190501), 2022.
V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knght. Quantifying entanglement. Phys. Rev. Lett., 78(2275), 1997.
G. Manfredi & M. R. Feix. Entropy and wigner functions. Phys. Rev. E., 62(4), 2000.
D. James, P. Kwiat, W. Munro, and A. White. Measurement of qubits. Phys. Rev. A., 64(052312), 2001.
G. Sentís, C. Eltschka, O. Gühne, M. Huber, and J. Siewert. Quantifying entanglement of maximal dimension in bipartite mixed states. Phys. Rev. Lett., 117(190502), 2016.
C. Zhang Y. Huang C. Li G. Guo S. Xie, Y. Zhao and J. H. Eberly. Experimental examination of entanglement estimates. Phys. Rev. Lett., 130(150801), 2023.
J. S. Moreno. Semiclassical propagators of wigner function: a comparative study, 2020.
T. Dittrich. Semiclassical propagator of the wigner function. Phys. Rev. Lett., 96(070403), 2006.
G. Casati, I. Guarneri, & J. Reslen. Classical dynamics of quantum entanglement. Phys. Rev. E., 85(036208), 2012.
T. Prosen. Complexity and nonseparability of classical liouvillian dynamics. Phys. Rev. E., 83(031124), 2011.
J. V. José & E. J. Saletan. Classical Dynamics a contemporary approach. Cambridge University Press, 1998.
W. P. Schleich. Quantum Optics in Phase Space. Wiley-VCH., Germany, 2001.
G. Benenti, G. G. Carlo and T. Prosen. Wigner separability entropy and complexity of quantum dynamics. Phys. Rev. E., 85(051129), 2012.
P. D. Bergamasco, G. G. Carlo and A. M. F. Rivas. Quantum and classical complexity in coupled maps. Phys. Rev. E., 96(062144), 2017.
P. D. Bergamasco, G. G. Carlo and A. M. F. Rivas. Out-of-time ordered correlators, complexity, and entropy in bipartite systems. Physical Review Research, 1(033044), 2019.
J. Gong & P. Brumer. Intrinsic decoherence dynamics in smooth hamiltonian systems: Quantum-classical correspondence. Phys. Rev. A., 68(022101), 2003.
C. Miquel, J. Paz and M. Saraceno. Quantum computers in phase space. Phys. Rev. A., 65(062309), 2002.
S. Keppeler & M. Fysik. Introduction to Wigner-Weyl calculus. 2004.
D.F. Walls & G. J. Milburn. Quantum Optics. Springer, Germany, 2008.
W. K. Wootters. A wigner function formulation of finite state quantum mechanics. Annals of Physics, 176:1-21, 1987.
W. B. Case. Wigner functions and weyl transforms for pedestrians. Am. J. Phys., 76(937), 2008.
R. L. Hudson. When is the wigner quasi-probability non-negative? Reports On Mathematical Physics, 6(2), 1974.
A. Kenfack & K. Życzkowski. Negativity of the wigner function as an indicator of nonclassicality. Nature, 6:396-404, 2004.
I. I. Arkhipov, A. Barasiński and J. Svozilík. Negativity volume of the generalized wigner function as an entanglement witness for hybrid bipartite states. Nature, 8(16955), 2018.
L. E. Ballentine. Quantum Mechanics A modern development. World Scienti c Publishing Co. Pte. Ltd., Singapore, 2000.
R. Cabrera, D. I. Bondar, K. Jacobs, and H. A. Rabitz. Efficient method to generate time evolution of the wigner function for open quantum systems. Phys. Rev. A., 92(042122), 2015.
A. Ekert & P. L. Knight. Entangled quantum systems and the schmidt decomposition. Am. J. Phys., 63(415), 1995.
R. Simon. Peres horodecki separability criterion for continuous variables systems. Phys. Rev. Lett., 84(12), 2000.
B. Bergh & M. Gärttner. Entanglement detection in quantum many-body systems using entropic uncertainty relations. Phys. Rev. A., 103(052412), 2021.
W. H. Zurek, S. Habib, and J. P. Paz. Coherent states via decoherence. Phys. Rev. Lett., 70(9), 1993.
H. P. Robertson. The uncertainty principle. Phys. Rev., 34(163), 1929.
L. Y. Chew & N. N. Chung. The quantum signature of chaos through the dynamics of entanglement in classically regular and chaotic systems. Acta Physica Polonica A, 120(6A), 2011.
M. Gutzwiller. The quantum mechanical toda lattice, ii. Annals of Physics, 133(2), 1981.
B. Doyon. Generalized hydrodynamics of the classical toda system. Journal of Mathematical Physics, 60(073302), 2019.
M. Cusveller. Soliton computing in the toda lattice: controllable delay and logic gates, 2021.
S. K. Gray, D. W. Noid and B. G. Sumpter. Symplectic integrators for large scale molecular dynamics simulations: A comparison of several explicit methods. The Journal of Chemical Physics, 101(4062), 1994.
H. Yoshida. Construction of higher order symplectic integrators. Phys. Lett. A., 150(5,6,7), 1990.
E. Ott. Chaos in Dynamical Systems. Cambridge University Press, 2002.
H. Goldstein, C. Poole and J. Safko. Classical Mechanics. Addison Wesley, 2001.
W. W. Ho and D. A. Abanin. Entanglement dynamics in quantum many-body systems. Phys. Rev. B., 95(094302), 2017.
A. Lerose & S. Pappalardi. Bridging entanglement dynamics and chaos in semiclassical systems. Phys. Rev. A., 102(032404), 2020.
J. N. Bandyopadhyay & A. Lakshminarayan. Testing statistical bounds on entanglement using quantum chaos. Phys. Rev. Lett., 89(6), 2002.
T. Nishioka. Entanglement entropy: Holography and renormalization group. Reviews of Modern Physics, 90, 2018.
F. Xu, C. C. Martens and Y. Zheng. Entanglement dynamics with a trajectory-based formulation. Phys. Rev. A., 96(022138), 2017.
Z. Zhou J. Tan, Y. Luo and W. Hai. Combined effect of classical chaos and quantum resonance on entanglement dynamics. Chin. Phys. Lett, 33(7), 2016.
M. A. Nielsen & I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, United Kingdom, 2000.
L. E. Reichl. The transition to chaos: conservative classical systems and quantum manifestations. Springer, 2004.
G. Casati and F. Haake. Encyclopedia of Condensed Matter Physics: Nonlinear Dynamics and Nonlinear Dynamical Systems. Elsevier, 2005.
F. Haake. Quantum Signatures of Chaos. Springer, 2010.
P. Leboeuf & M. Saraceno. Eigenfunctions of non-integrable systems in generalised phase spaces. J. Phys. A: Math. Gen., 23:1745-1764, 1990.
P. A. Dando & T. S. Monteiro. Quantum surfaces of section for the diamagnetic hydrogen atom: Husimi functions versus wigner functions. J. Phys. B: At. Mol. Opt. Phys, 27:2681-2692, 1994.
H. S. Qureshi, S. Ullah and F. Ghafoor. Hierarchy of quantum correlations using a linear beam splitter. Scienti c Reports, 8(16288), 2018.
N. L. Balazs & A. Voros. The quantized baker's transformation. Annals of Physics, 190:1-31, 1989.
A. Argüelles & T. Dittrich. Wigner function for discrete phase space: Exorcising ghost images. Physica A: Statistical Mechanics and its Applications, 356(1):72{77, 2005.
A. Argüelles. Construcción de la función de wigner para espacios de fases discretos, 2004.
Y. A. Kravtsov & Y. I. Orlov. Caustics, Catastrophes and Wave Fields. Springer, 1993.
J. P. Gazeau. Coherent States in Quantum Physics. Wiley-VCH, 2009.
D. J. Tannor. Introduction to Quantum Mechanics. University Science Books, United Sates of America, 2007.
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dc.rights.license.spa.fl_str_mv Reconocimiento 4.0 Internacional
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dc.format.extent.spa.fl_str_mv xii, 85 páginas
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dc.publisher.program.spa.fl_str_mv Bogotá - Ciencias - Maestría en Ciencias - Física
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
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spelling Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Viviescas Ramírez, Carlos Leonardo5b30aa603ec28676fe215dfba86e3d61Murillo Mejía, Miller Mateoc08ee6f6370ee071e329991a37bee84eGrupo de Investigación: Caos y Complejidad2024-01-18T19:47:09Z2024-01-18T19:47:09Z2024https://repositorio.unal.edu.co/handle/unal/85367Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasIn this thesis, we describe the entanglement dynamics of a system of two particles interacting via a Toda potential in the Wigner-Weyl phase space representation of quantum mechanics. Firstly, we present the principal elements of the Wigner-Weyl representation of quantum mechanics, followed by the identifi cation and quanti fication of the entanglement of the two particle Toda system in the wave representation. Next, we consider some relevant approaches to classical descriptions of the entanglement dynamics, from which we inspire to describe the chaotic and regular dynamics of the Toda system in the phase space via the quantum Poincaré surface of section employing stationary Wigner functions, getting results in good agreement with the classical equivalent. Finally, we present the analysis and interpretation of entanglement dynamics measured with two entanglement measures in phase space. The fi rst one is the Wigner Separability Entropy, which hasn't been employed in a system as relevant as the Toda model, and we show that it is able to reproduce results in agreement with another entanglement measure, the Von Neumann entropy. The second one is the linear entropy in the Wigner-Weyl representation. This entanglement measure allowed us to analyze and describe elements of the entanglement dynamics as periodic behaviors based on the interpretation of the reduced Wigner function of the Toda system. (Texto tomado de la fuente)En esta tesis, describimos la dinámica de entrelazamiento de un sistema de dos partículas interactuando bajo un potencial tipo Toda en la representación de Wigner-Weyl de la mecánica cuántica. Para comenzar, se presentan los elementos principales de la representación de Wigner-Weyl de la mecánica cuántica, seguido por la identi ficación y cuanti ficación del entrelazamiento de las dos partículas en el sistema Toda en la representación ondulatoria. Posteriormente, se consideran aproximaciones relevantes a la descripción clásica de la dinámica de entrelazamiento, de donde nos inspiramos para describir la dinámica caótica y regular del sistema Toda en el espacio de fase a partir de las superficies de Poincaré cuánticas empleando funciones de Wigner estacionarias, obteniendo resultados comparables con los equivalentes clásicos. Finalmente, se presenta el análisis e interpretación de la dinámica de entrelazamiento medida empleando dos medidas de entrelazamiento en el espacio de fase. La primera medida es la entropía de separabilidad de Wigner, la cual no ha sido empleada en un sistema tan relevante como el modelo Toda, con la cual nosotros mostramos que es capaz de reproducir resultados comparables con otra medida de entrelazamiento, la entropía de Von Neumann. La segunda medida es la entropía lineal en la representación de Wigner-Weyl. Esta medida de entrelazamiento nos permitió analizar y describir elementos de la dinámica de entrelazamiento tales como comportamientos periódicos basándonos en la interpretación de la función de Wigner reducida del sistema Toda.MaestríaTeoría del entrelazamiento cuánticoxii, 85 páginasapplication/pdfengWigner-Weyl Quantum EntanglementEntrelazamiento cuántico de Wigner-WeylTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBogotá - Ciencias - Maestría en Ciencias - FísicaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede BogotáM. Mazzanti, R. X. Schüssler, J. D. Arias Espinoza, Z. Wu, R. Gerritsma, and A. Safavi-Naini. Trapped ion quantum computing using optical tweezers and electric fields. Phys. Rev. Lett., 127(260502), 2021.X. Pan, Y. Zhou and H. Yuan. Engineering superconducting qubits to reduce quasiparticles and charge noise. Nat Commun, 13(7196), 2021.L.S. Madsen, F. Laudenbach, M.F. Askarani, et al. Quantum computational advantage with a programmable photonic processor. Nature, 606:75-81, 2022.D. Bluvstein, H. Levine, G. Semeghini, et al. A quantum processor based on coherent transport of entangled atom arrays. Nature, 604:451-456, 2022.A. Y. Khrennikov. Echoing the recent google success: Foundational roots of quantum supremacy. ArXiv, abs/1911.10337, 2019.J.J. Sakurai. Modern Quantum Mechanics. Addison-Wesley, 1994.A. Buchleitner, C. Viviescas and M. Tiersch. Entanglement and Decoherence: Foundations and Modern Trends. Springer, Berlin Heidelberg, 2009.D. Gross, S. T. Flammia, and J. Eisert. Most quantum states are too entangled to be useful as computational resources. Phys. Rev. Lett., 102(190501), 2022.V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knght. Quantifying entanglement. Phys. Rev. Lett., 78(2275), 1997.G. Manfredi & M. R. Feix. Entropy and wigner functions. Phys. Rev. E., 62(4), 2000.D. James, P. Kwiat, W. Munro, and A. White. Measurement of qubits. Phys. Rev. A., 64(052312), 2001.G. Sentís, C. Eltschka, O. Gühne, M. Huber, and J. Siewert. Quantifying entanglement of maximal dimension in bipartite mixed states. Phys. Rev. Lett., 117(190502), 2016.C. Zhang Y. Huang C. Li G. Guo S. Xie, Y. Zhao and J. H. Eberly. Experimental examination of entanglement estimates. Phys. Rev. Lett., 130(150801), 2023.J. S. Moreno. Semiclassical propagators of wigner function: a comparative study, 2020.T. Dittrich. Semiclassical propagator of the wigner function. Phys. Rev. Lett., 96(070403), 2006.G. Casati, I. Guarneri, & J. Reslen. Classical dynamics of quantum entanglement. Phys. Rev. E., 85(036208), 2012.T. Prosen. Complexity and nonseparability of classical liouvillian dynamics. Phys. Rev. E., 83(031124), 2011.J. V. José & E. J. Saletan. Classical Dynamics a contemporary approach. Cambridge University Press, 1998.W. P. Schleich. Quantum Optics in Phase Space. Wiley-VCH., Germany, 2001.G. Benenti, G. G. Carlo and T. Prosen. Wigner separability entropy and complexity of quantum dynamics. Phys. Rev. E., 85(051129), 2012.P. D. Bergamasco, G. G. Carlo and A. M. F. Rivas. Quantum and classical complexity in coupled maps. Phys. Rev. E., 96(062144), 2017.P. D. Bergamasco, G. G. Carlo and A. M. F. Rivas. Out-of-time ordered correlators, complexity, and entropy in bipartite systems. Physical Review Research, 1(033044), 2019.J. Gong & P. Brumer. Intrinsic decoherence dynamics in smooth hamiltonian systems: Quantum-classical correspondence. Phys. Rev. A., 68(022101), 2003.C. Miquel, J. Paz and M. Saraceno. Quantum computers in phase space. Phys. Rev. A., 65(062309), 2002.S. Keppeler & M. Fysik. Introduction to Wigner-Weyl calculus. 2004.D.F. Walls & G. J. Milburn. Quantum Optics. Springer, Germany, 2008.W. K. Wootters. A wigner function formulation of finite state quantum mechanics. Annals of Physics, 176:1-21, 1987.W. B. Case. Wigner functions and weyl transforms for pedestrians. Am. J. Phys., 76(937), 2008.R. L. Hudson. When is the wigner quasi-probability non-negative? Reports On Mathematical Physics, 6(2), 1974.A. Kenfack & K. Życzkowski. Negativity of the wigner function as an indicator of nonclassicality. Nature, 6:396-404, 2004.I. I. Arkhipov, A. Barasiński and J. Svozilík. Negativity volume of the generalized wigner function as an entanglement witness for hybrid bipartite states. Nature, 8(16955), 2018.L. E. Ballentine. Quantum Mechanics A modern development. World Scienti c Publishing Co. Pte. Ltd., Singapore, 2000.R. Cabrera, D. I. Bondar, K. Jacobs, and H. A. Rabitz. Efficient method to generate time evolution of the wigner function for open quantum systems. Phys. Rev. A., 92(042122), 2015.A. Ekert & P. L. Knight. Entangled quantum systems and the schmidt decomposition. Am. J. Phys., 63(415), 1995.R. Simon. Peres horodecki separability criterion for continuous variables systems. Phys. Rev. Lett., 84(12), 2000.B. Bergh & M. Gärttner. Entanglement detection in quantum many-body systems using entropic uncertainty relations. Phys. Rev. A., 103(052412), 2021.W. H. Zurek, S. Habib, and J. P. Paz. Coherent states via decoherence. Phys. Rev. Lett., 70(9), 1993.H. P. Robertson. The uncertainty principle. Phys. Rev., 34(163), 1929.L. Y. Chew & N. N. Chung. The quantum signature of chaos through the dynamics of entanglement in classically regular and chaotic systems. Acta Physica Polonica A, 120(6A), 2011.M. Gutzwiller. The quantum mechanical toda lattice, ii. Annals of Physics, 133(2), 1981.B. Doyon. Generalized hydrodynamics of the classical toda system. Journal of Mathematical Physics, 60(073302), 2019.M. Cusveller. Soliton computing in the toda lattice: controllable delay and logic gates, 2021.S. K. Gray, D. W. Noid and B. G. Sumpter. Symplectic integrators for large scale molecular dynamics simulations: A comparison of several explicit methods. The Journal of Chemical Physics, 101(4062), 1994.H. Yoshida. Construction of higher order symplectic integrators. Phys. Lett. A., 150(5,6,7), 1990.E. Ott. Chaos in Dynamical Systems. Cambridge University Press, 2002.H. Goldstein, C. Poole and J. Safko. Classical Mechanics. Addison Wesley, 2001.W. W. Ho and D. A. Abanin. Entanglement dynamics in quantum many-body systems. Phys. Rev. B., 95(094302), 2017.A. Lerose & S. Pappalardi. Bridging entanglement dynamics and chaos in semiclassical systems. Phys. Rev. A., 102(032404), 2020.J. N. Bandyopadhyay & A. Lakshminarayan. Testing statistical bounds on entanglement using quantum chaos. Phys. Rev. Lett., 89(6), 2002.T. Nishioka. Entanglement entropy: Holography and renormalization group. Reviews of Modern Physics, 90, 2018.F. Xu, C. C. Martens and Y. Zheng. Entanglement dynamics with a trajectory-based formulation. Phys. Rev. A., 96(022138), 2017.Z. Zhou J. Tan, Y. Luo and W. Hai. Combined effect of classical chaos and quantum resonance on entanglement dynamics. Chin. Phys. Lett, 33(7), 2016.M. A. Nielsen & I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, United Kingdom, 2000.L. E. Reichl. The transition to chaos: conservative classical systems and quantum manifestations. Springer, 2004.G. Casati and F. Haake. Encyclopedia of Condensed Matter Physics: Nonlinear Dynamics and Nonlinear Dynamical Systems. Elsevier, 2005.F. Haake. Quantum Signatures of Chaos. Springer, 2010.P. Leboeuf & M. Saraceno. Eigenfunctions of non-integrable systems in generalised phase spaces. J. Phys. A: Math. Gen., 23:1745-1764, 1990.P. A. Dando & T. S. Monteiro. Quantum surfaces of section for the diamagnetic hydrogen atom: Husimi functions versus wigner functions. J. Phys. B: At. Mol. Opt. Phys, 27:2681-2692, 1994.H. S. Qureshi, S. Ullah and F. Ghafoor. Hierarchy of quantum correlations using a linear beam splitter. Scienti c Reports, 8(16288), 2018.N. L. Balazs & A. Voros. The quantized baker's transformation. Annals of Physics, 190:1-31, 1989.A. Argüelles & T. Dittrich. Wigner function for discrete phase space: Exorcising ghost images. Physica A: Statistical Mechanics and its Applications, 356(1):72{77, 2005.A. Argüelles. Construcción de la función de wigner para espacios de fases discretos, 2004.Y. A. Kravtsov & Y. I. Orlov. Caustics, Catastrophes and Wave Fields. Springer, 1993.J. P. Gazeau. Coherent States in Quantum Physics. Wiley-VCH, 2009.D. J. Tannor. Introduction to Quantum Mechanics. University Science Books, United Sates of America, 2007.PartículasFuerzas nucleares (física)ParticlesNuclear fuel elementsquantum phase spaceQuantum entanglementToda modelWigner functionQuantum Poincaré surface of sectionEspacio de fase cuánticoEntrelazamiento cuánticoModelo TodaFunción de WignerSecciones de Poincaré cuánticasORIGINAL1012404530.2023.pdf1012404530.2023.pdfTesis de Maestría en Ciencias - Físicaapplication/pdf47268859https://repositorio.unal.edu.co/bitstream/unal/85367/2/1012404530.2023.pdfb355da773c5d322277918b1f8e5ac49fMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/85367/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53THUMBNAIL1012404530.2023.pdf.jpg1012404530.2023.pdf.jpgGenerated Thumbnailimage/jpeg3722https://repositorio.unal.edu.co/bitstream/unal/85367/4/1012404530.2023.pdf.jpg26997a7177617a10e4c5586861f0ccc8MD54unal/85367oai:repositorio.unal.edu.co:unal/853672024-01-18 23:03:53.32Repositorio 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