Dinámica de dos partículas en un potencial del tipo Calogero-Moser
Mecánica cuántica de Bohm y no localidad
Palabras clave:
entrelazamiento; no localidad; Broglie-Bohm; mecánica cuántica.Resumen
Este artículo explora la interpretación de De Broglie-Bohm, centrándose en la dinámica de dos partículas bajo un potencial de Calogero-Moser con el objetivo de comprender la interpretación y la no localidad del sistema, respondiendo a la pregunta: ¿cómo es la dinámica de ese sistema desde la perspectiva propuesta? Se utiliza la ecuación de Schrödinger con el potencial mencionado, en conjunto con el entrelazamiento y los sistemas de múltiples partículas, para crear un modelo matemático con el fin de realizar el análisis de las trayectorias con un simulador de código abierto. Como resultado, se tiene una visión geométrica y matemática del entrelazamiento y el enfoque de Bohm en la mecánica cuántica.
Descargas
Citas
ABRAMOWITZ, M.; STEGUN, I. A. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. New York: Dover Publications, 1965. Disponível em: https://personal.math.ubc.ca/~cbm/aands/abramowitz_and_stegun.pdf. Acesso em: 24 out. 2024.
ASPECT, A.; DALIBARD, J.; ROGER, G. Experimental test of Bell's inequalities using time-varying analyzers. Physical Review Letters, New York, v. 49, n. 25, p. 1804-1807, 1982. DOI: https://doi.org/10.1103/PhysRevLett.49.1804. Disponível em: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.49.1804. Acesso em: 23 out. 2024.
BELL, J. S. On the Einstein Podolsky Rosen paradox. Physics Physique Fizika, New York, n. 3, p. 195-200, 1964. DOI: https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195. Disponível em: https://journals.aps.org/ppf/pdf/10.1103/PhysicsPhysiqueFizika.1.195. Acesso em: 23 ago. 2023.
BETZ, M. E. M. Elementos de mecânica quântica da partícula na interpretação da onda piloto. Revista Brasileira de Ensino de Física, São Paulo, SP, v. 36, n. 4, p. 1-14, 2014. DOI: https://doi.org/10.1590/S1806-11172014000400011. Disponível em: https://www.scielo.br/j/rbef/a/ZwJFPncfzjWscDv4yQySd4R/abstract/?lang=pt. Acesso em: 23 out. 2024.
BLOH, K. V. Nonlocality in the De Broglie-Bohm interpretation of quantum mechanics. Wolfram Demonstrations Project, Champaign, IL, 21 Mar. 2016. Disponível em: https://demonstrations.wolfram.com/NonlocalityInTheDeBroglieBohmInterpretationOfQuantumMechanic/. Acesso em: 20 out. 2024.
BOHM, D. A suggested interpretation of the quantum theory in terms of hidden variables. I. Physical Review, New York, v. 85, n. 2, p. 166-179, 1952a. DOI: https://doi.org/10.1103/PhysRev.85.166. Disponível em: https://journals.aps.org/pr/abstract/10.1103/PhysRev.85.166. Acesso em: 23 out. 2024.
BOHM, D. A suggested interpretation of the quantum theory in terms of hidden variables. II. Physical Review, New York, v. 85, n. 2, p. 180-193, 1952b. DOI: https://doi.org/10.1103/PhysRev.85.166. Disponível em: https://journals.aps.org/pr/abstract/10.1103/PhysRev.85.166. Acesso em: 23 out. 2024.
BOHM, D. Causality and chance in modern physics. Philadelphia: Routledge & Kegan Paul and D. Van Nostrand Company, 1957. Disponível em: https://www.scirp.org/reference/referencespapers?referenceid=1362682. Acesso em: 23 out. 2024.
BORN, M. Zur Quantenmechanik der Stoßvorgänge. Zeitschrift für Physik, Berlin, v. 37, n. 12, p. 863-867, 1926. DOI: http://dx.doi.org/10.1007/bf01397477. Disponível em: https://link.springer.com/article/10.1007/BF01397477. Acesso em: 23 out. 2024.
BROGLIE, L. La nouvelle dynamique des quanta. In: BROGLIE, L. Electrons et photons: rapports et discussions du cinquième conseil de physique solvay. Paris: Gauthier-Villars, 1927.
COHEN-TANNOUDJI, C.; DIU, B.; LALOË, F. Quantum mechanics: volume 1: Basic concepts, tools, and applications. 2.ed. Weinheim: Wiley-VCH, 2019.
CONTOPOULOS, G.; EFTHYMIOPOULOS, C. Ordered and Chaotic Bohmian Trajectories. Celestial Mechanics and Dynamical Astronomy, Dordrecht, v. 102, n. 1-3, p. 219-239, 2008. DOI: https://doi.org/10.1007/s10569-008-9127-8. Disponível em: https://ui.adsabs.harvard.edu/abs/2008CeMDA.102..219C/abstract. Acesso em: 23 out. 2024.
DÜRR, D.; GOLDSTEIN, S.; ZANGHÌ, N. Quantum Physics Without Quantum Philosophy. Berlin, Heidelberg: Springer-Verlag, 2013.
DÜRR, D.; GOLDSTEIN, S.; ZANGHÌ, N. Quantum equilibrium and the origin of absolute uncertainty. Journal of Statistical Physics, New York, v. 67, n. 5-6, p. 843-907, 1992. DOI: https://doi.org/10.1007/BF01049004. Disponível em: https://link.springer.com/article/10.1007/BF01049004. Acesso em: 24 out. 2024.
EINSTEIN, A. On a heuristic point of view concerning the production and transformation of light. Annalen der Physik, Berlin, v. 17, n. 6, p. 132-148, 1905. DOI: https://doi.org/10.1002/andp.19053220607. Disponível em: https://www.scirp.org/reference/referencespapers?referenceid=2291185. Acesso em: 23 out. 2024.
EINSTEIN, A.; PODOLSKY, B.; ROSEN, N. Can quantum-mechanical description of physical reality be considered complete? Physical Review, New York, v. 47, n. 10, p. 777-780, 1935. DOI: http://dx.doi.org/10.1103/physrev.47.777. Disponível em: https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777. Acesso em: 23 out. 2024.
ELSAYED, T. A.; MØLMER, K.; MADSEN, L. B. Entangled quantum dynamics of many-body systems using Bohmian trajectories. Scientific Reports, London, v. 8, 12704, 2018. Disponível em: https://www.nature.com/articles/s41598-018-30730-0. Acesso em: 23 out. 2024.
GIUSTINA, M. Significant-loophole-free test of Bell's theorem with entangled photons. Physical Review Letters, New York, v. 115, n. 25, p. 1-7, 2015. DOI: http://dx.doi.org/10.1103/physrevlett.115.250401. Disponível em: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.250401. Acesso em: 23 out. 2024.
GUCKENHEIMER, J.; HOLMES, P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. New York: Springer-Verlag, 1983.
HENSEN, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, London, v. 526, n. 7575, p. 682-686, 2015. DOI: http://dx.doi.org/10.1038/nature15759. Disponível em: https://www.nature.com/articles/nature15759. Acesso em: 23 out. 2024.
HOLLAND, P. R. The quantum theory of motion: an account of the de Broglie-Bohm causal interpretation of quantum mechanics. Cambridge: Cambridge University Press, 2004.
IVANOV, I.; NAM, C. H.; KIM, K. T. Quantum chaos in strong field ionization of hydrogen. Journal of Physics B: Atomic Molecular and Optical Physics, Bristol, v. 52, n. 22, 2019. DOI: 10.1088/1361-6455/ab46f1. Disponível em: https://ui.adsabs.harvard.edu/abs/2019JPhB...52v5002I/abstract. Acesso em: 24 out. 2024.
LICHTENBERG, A. J.; LIEBERMAN, M. A. Regular and chaotic dynamics. New York: Springer-Verlag, 1992.
NEWTON, I. Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light. London: Sam. Smith and Benj. Walford, 1704.
OTT, E. Chaos in dynamical systems. Cambridge: Cambridge University Press, 2002.
PINTO NETO, N. Teoria da interpretação da mecânica quântica. São Paulo: Livraria da Física, 2011.
PIZA, A. F. R. T. Sistemas quânticos compostos e emaranhamento, sistemas quânticos abertos e decoerência. São Paulo: Instituto de Física da USP, 2009. Notas de aula.
POLCHINSKI, J. String theory. Cambridge: Cambridge University Press, 1998. (Cambridge Monographs on Mathematical Physics).
RAFSANJANI, A. A. et al. Non-local temporal interference. Scientific Reports, London, v. 14, p. 1-16, 2024. DOI: http://dx.doi.org/10.1038/s41598-024-54018-8. Disponível em: https://www.nature.com/articles/s41598-024-54018-8. Acesso em: 24 out. 2024.
ROWE, M. A. et al. Experimental violation of a Bell's inequality with efficient detection. Nature, London, v. 409, n. 6822, p. 791-794, 2001. DOI: http://dx.doi.org/10.1038/35057215. Disponível em: https://www.nature.com/articles/35057215. Acesso em: 23 out. 2024.
SCHLOSSHAUER, M. Decoherence and the quantum-to-classical transition. Berlin: Springer-Verlag, 2007.
SCHRÖDINGER, E. Collected papers on wave mechanics: together with his four lectures on wave mechanics. New York: Chelsea Publishing Company, 1982.
SIQUEIRA-BATISTA, R.; HELAYËL-NETO, J. A. A mecânica quântica de David Bohm. Vértices, Rio de Janeiro, v. 10, n. 3, p. 57-62, 2008. DOI: https://doi.org/10.5935/1809-2667.20080005. Disponível em: https://editoraessentia.iff.edu.br/index.php/vertices/article/view/1809-2667.20080005. Acesso em: 23 out. 2024.
SUN, Q.; ZUBAIRY, M. S. Entanglement criteria for continuous-variable systems. Classical, Semi-Classical and Quantum Noise, New York, p. 249-258, 2011. DOI: http://dx.doi.org/10.1007/978-1-4419-6624-7_17. Disponível em: https://link.springer.com/chapter/10.1007/978-1-4419-6624-7_17. Acesso em: 23 out. 2024.
TZEMOS, A. C.; CONTOPOULOS, G. Critical points and trajectories of the Bohmian quantum flow. Maple Transactions, Toronto, v. 3, n. 2, 2023. Disponível em: https://mapletransactions.org/index.php/maple/article/view/15546. Acesso em: 24 out. 2024.
TZEMOS, A. C.; CONTOPOULOS, G. Chaos and ergodicity in an entangled two-qubit Bohmian system. Physica Scripta, Bristol, v. 95, n. 6, p. 1-19, 2020. DOI: https://doi.org/10.48550/arXiv.2003.03989. Disponível em: https://arxiv.org/abs/2003.03989. Acesso em: 24 out. 2024.
TZEMOS, A. C.; CONTOPOULOS, G. The role of chaotic and ordered trajectories in establishing Born's rule. Physica Scripta, Bristol, v. 96, n. 6, 2021. Disponível em: https://arxiv.org/abs/2111.00846. Acesso em: 24 out. 2024.
TZEMOS, A. C.; CONTOPOULOS, G.; EFTHYMIOPOULOS, C. Bohmian trajectories in an entangled two-qubit system. Physica Scripta, Bristol, 2019. DOI: https://doi.org/10.48550/arXiv.1905.12619. Disponível em: https://arxiv.org/abs/1905.12619. Acesso em: 24 out. 2024.
TZEMOS, A. C.; CONTOPOULOS, G.; EFTHYMIOPOULOS, C. Origin of chaos in 3-D Bohmian trajectories. Physics Letters A, Amsterdam, 2016. DOI: https://doi.org/10.48550/arXiv.1609.07069. Disponível em: https://arxiv.org/abs/1609.07069. Acesso em: 24 out. 2024.
WISNIACKI, D. A.; PUJALS, E. R. Motion of vortices implies chaos in Bohmian mechanics. EPL (Europhysics Letters), Bristol, v. 71, n. 159, 2005. DOI: https://doi.org/10.48550/arXiv.quant-ph/0502108. Disponível em: https://arxiv.org/abs/quant-ph/0502108. Acesso em: 24 out. 2024.
WOLFRAM. Wolfram Demonstrations Project: visualizações interativas para a área de desktop, 2023. Disponível em: https://demonstrations.wolfram.com/. Acesso em: 11 set. 2023.
YOUNG, T. I. The Bakerian lecture: experiments and calculations relative to physical optics. Philosophical Transactions, London, v. 94, p. 1-16, 1804. DOI: http://dx.doi.org/10.1098/rstl.1804.0001. Disponível em: https://royalsocietypublishing.org/doi/10.1098/rstl.1804.0001. Acesso em: 23 out. 2024.
Descargas
Publicado
Cómo citar
Número
Sección
Licencia
Derechos de autor 2024 Revista Brasileira de Iniciação Científica
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.