Skip to main content
SpringerLink
Log in

Trans-statistical Behavior of a Multiparticle System in an Ontology of Properties

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

In the last years, the surprising bosonic behavior that a many-fermion system may acquire has raised interest because of theoretical and practical reasons. This trans-statistical behavior is usually considered to be the result of approximation modeling methods generally employed by physicists when faced with complexity. In this paper, we take a tensor product structure and an ontology of properties approach and provide two versions (standard and algebraic) of a toy model in order to argue that trans-statistical behavior allows for a realistic interpretation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Butterfield, J.: Interpretation and identity in quantum theory. Stud. Hist. Philos. Sci. 24, 443–476 (1993)

    Article  Google Scholar 

  2. Fortin, S., Lombardi, O.: Entanglement and indistinguishability in a quantum ontology of properties. Stud. Hist. Philos. Sci. 91, 234–243 (2021)

    Article  MathSciNet  Google Scholar 

  3. Law, C.K.: Quantum entanglement as an interpretation of bosonic character in composite two-particle systems. Phys. Rev. A 71, 034306 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  4. Chudzicki, C., Oke, O., Wootters, W.K.: Entanglement and composite bosons. Phys. Rev. Lett. 104, 070402 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  5. Tichy, M.C., Bouvrie, P.A., Mølmer, K.: How bosonic is a pair of fermions? Appl. Phys. B 117, 785–796 (2014)

    Article  ADS  Google Scholar 

  6. Gigena, N., Rossignoli, R.: Entanglement in fermion systems. Phys. Rev. A 92, 042326 (2015)

    Article  ADS  Google Scholar 

  7. Avancini, S., Marinelli, J.R., Krein, G.: Compositeness effects in the Bose-Einstein condensation. Phys. Rev. A 36, 9045 (2003)

    MathSciNet  MATH  Google Scholar 

  8. Rombouts, S., Van Neck, D., Peirs, K., Pollet, L.: Comment on New criteria for bosonic behavior of excitons by M. Combescot and C. Tanguy. Europhys. Lett. 63, 785 (2003)

    Article  ADS  Google Scholar 

  9. Combescot, M., Tanguy, C.: New criteria for bosonic behavior of excitons. Europhys. Lett. 55, 390 (2001)

    Article  ADS  Google Scholar 

  10. Belkhir, L., Randeria, M.: Collective excitations and the crossover from Cooper pairs to composite bosons in the attractive Hubbard model. Phys. Rev. B 45, 5087 (1992)

    Article  ADS  Google Scholar 

  11. Cuestas, E., Bouvrie, P.A., Majtey, A.P.: Fermionic versus bosonic behavior of confined Wigner molecules. Phys. Rev. A 101, 033620 (2020)

    Article  ADS  Google Scholar 

  12. Harshman, N.L., Wickramasekara, S.: Tensor product structures, entanglement, and particle scattering. Open. Syst. Inf. Dyn. 14, 341–351 (2007)

    Article  MathSciNet  Google Scholar 

  13. Zanardi, P.: Virtual quantum systems. Phys. Rev. Lett. 87, 077901 (2001)

    Article  ADS  Google Scholar 

  14. Dugić, M., Jeknić-Dugić, J.: What is «system»: The information-theoretic arguments. Int. J. Theoret. Phys. 47, 805–813 (2008)

    Article  MathSciNet  Google Scholar 

  15. Lombardi, O.: A Kantian-rooted pluralist realism for science. In: Soto, C. (ed.) Current Debates in Philosophy of Science: In Honor of Roberto Torretti. Springer, Dordrecht (2021)

    Google Scholar 

  16. da Costa, N., Lombardi, O.: Quantum mechanics: ontology without individuals. Found. Phys. 44, 1246–1257 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  17. Brooks, J.S., Donnelly, R.J.: The calculated thermodynamic properties of superfluid helium-4. J. Phys. Chem. Ref. Data 6, 51 (1977)

    Article  ADS  Google Scholar 

  18. Rombouts, S., Van Neck, D., Peirs, K., Pollet, L.: Maximum occupation number for composite boson states. Mod. Phys. Lett. A 17, 1899–1907 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  19. Combescot, M., Betbeder-Matibeta, O., Dubinb, F.: The many-body physics of composite bosons. Phys. Rep. 463, 215–320 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  20. Nagel, E.: Issues in the logic of reductive explanations. In: Bedau, M.A., Humphreys, P. (eds.) Emergence: Contemporary Readings in Philosophy and Science, book section 19. MIT Press, Cambridge (2008)

    Google Scholar 

  21. Franklin, A., y Eleanor Knox: Emergence without limits: The case of phonons. Stud. Hist. Philos. Sci. 64, 68–78 (2018)

    MATH  Google Scholar 

  22. Weyl, H.: The Theory of Groups and Quantum Mechanics, 2nd edn. Methuen and Co., London (1931)

    MATH  Google Scholar 

  23. Krause, D.: On a Quasi-set Theory. Notre Dame Journal of Formal Logic 33, 402–411 (1992)

    Article  MathSciNet  Google Scholar 

  24. van Fraassen, B.: Statistical Behaviour of Indistinguishable Particles: Problems of Interpretation. In: Mittelstaed, P., Stachow, E.W. (eds.) Recent Developments in Quantum Logic, pp. 161–187. Oxford University Press, Mannheim (1985)

    Google Scholar 

  25. French, S.: Identity and individuality in classical and quantum physics. Australas. J. Philos. 67(4), 432–446 (1989)

    Article  Google Scholar 

  26. Muller, F.A., Saunders, S.: Discerning Fermions. Br. J. Philos. Sci. 59, 499–548 (2008)

    Article  MathSciNet  Google Scholar 

  27. da Costa, N., Lombardi, O., Lastiri, M.: A modal ontology of properties for quantum mechanics. Synthese 190, 3671–3693 (2013)

    Article  MathSciNet  Google Scholar 

  28. Lombardi, O., Dieks, D.: Particles in a quantum ontology of properties. In: Bigaj, T., Wüthrich, C. (eds.) Metaphysics in Contemporary Physics, pp. 123–143. Brill-Rodopi, Leiden (2016)

    Google Scholar 

  29. Ballentine, L.: Quantum Mechanics: A Modern Development. World Scientific, Singapore (1998)

    Book  Google Scholar 

  30. Lombardi, O., Castagnino, M.: A modal-Hamiltonian interpretation of quantum mechanics. Stud. Hist. Philos. Mod. Phys. 39, 380–443 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to thank Olimpia Lombardi for her advice and invaluable help. We also appreciate the explanations and discussions of Ana Majtey and Eloisa Cuestas. This research was partially supported by grants “Fenómenos irreversibles en mecánica cuántica desde una perspectiva holista” from the Agencia de Promoción Científica y Tecnológica, “Tres problemas filosóficos en la fundamentación de la física: Interpretación de la mecánica cuántica, irreversibilidad y relaciones interdisciplinares” from CONICET, “The Cosmological Origin of the Arrow of Time”, from the John Templeton Foundation, “Mecánica cuántica: interpretación y relaciones interteóricas” from the Universidad de Buenos Aires, “Relaciones interteóricas entre la mecánica cuántica y otros dominios teóricos” from the Universidad Austral, and “La interpretación de la mecánica cuántica y de sus relaciones con otros dominios teóricos y disciplinares” from the Agencia de Promoción Científica y Tecnológica.

Author information

Authors and Affiliations

  1. CONICET – Instituto de Investigaciones “Dr. Adolfo Prieto”, Universidad Nacional de Rosario, Santa Fe, Argentina

    Matías Pasqualini

  2. CONICET – Universidad de Buenos Aires, Buenos Aires, Argentina

    Sebastian Fortin

Authors
  1. Matías Pasqualini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Fortin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian Fortin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pasqualini, M., Fortin, S. Trans-statistical Behavior of a Multiparticle System in an Ontology of Properties. Found Phys 52, 70 (2022). https://doi.org/10.1007/s10701-022-00590-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10701-022-00590-w

Keywords

Search

Navigation