Two particle dynamics in a Calogero-Moser type potential

Bohm and non-locality

Authors

  • Jizreel Pereira da Silva UNINTER
  • Roberta Oliveira Lenzi UNINTER
  • Carlos Henrique de Oliveira Barreto UNINTER
  • Daniel Guimarães Tedesco UNINTER

Keywords:

entanglement; non-locality; Broglie-Bohm; quantum mechanics.

Abstract

This article explores the De Broglie-Bohm interpretation, focusing on the dynamics of two particles under a Calogero-Moser potential with the aim of understanding the interpretation and non-locality of the system, answering the question: What are the dynamics of this system from the proposed perspective? The Schrödinger equation with the mentioned potential is used, in conjunction with entanglement and multi-particle systems, to create a mathematical model to perform trajectory analysis with an open-source simulator. The results provide a geometric and mathematical view of entanglement and Bohm’s approach to quantum mechanics.

Downloads

Download data is not yet available.

Author Biographies

Jizreel Pereira da Silva , UNINTER

Undergraduate in Physics at UNINTER. Has a degree (Physics Education) from UFRJ with a professional master's degree in Physics Education from UNIRIO

Roberta Oliveira Lenzi, UNINTER

Undergraduate in Physics at UNINTER, Bachelor of Laws from PUC-RJ

Carlos Henrique de Oliveira Barreto, UNINTER

Undergraduate in Physics at UNINTER and Bachelor of Electrical Engineering from UNIVERSO

Daniel Guimarães Tedesco, UNINTER

Bachelor in Physics, Master in Physics, and Ph.D. in Physics from UERJ. Currently a teacher at the Centro Universitário Internacional UNINTER, a member of the CEP-UNINTER, and the Scientific and Technical Committee of the Wilson Picler Foundation for Research Support.

References

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.

Downloads

Published

2024-11-14

How to Cite

Pereira da Silva , J., Oliveira Lenzi, R., de Oliveira Barreto, C. H., & Guimarães Tedesco, D. (2024). Two particle dynamics in a Calogero-Moser type potential: Bohm and non-locality. Revista Brasileira De Iniciação Científica, e024047. Retrieved from https://periodicoscientificos.itp.ifsp.edu.br/index.php/rbic/article/view/1271

Issue

Volume 11, 2024 – publicação Contínua

Section

Artigos

License

Copyright (c) 2024 Revista Brasileira de Iniciação Científica

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.