Skip to main content
SpringerLink
Log in

Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of N n “nuclei” and N e “electrons.” We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenheimer Ansatz, whose validity and breakdown can be understood from a quantum information point of view.

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. M.C. Tichy, F. Mintert, A. Buchleitner, J. Phys. B 44, 192001 (2011)

    Article  ADS  Google Scholar 

  2. P. Tommasini, E. Timmermans, A.F.R. de Toledo Piza, Am. J. Phys. 66, 881 (1998)

    Article  ADS  Google Scholar 

  3. H. Venzl, A.J. Daley, F. Mintert, A. Buchleitner, Phys. Rev. E 79, 056223 (2009)

    Article  ADS  Google Scholar 

  4. J. Eisert, M. Cramer, M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. D. Perez-Garcia, F. Verstraete, M. Wolf, J. Cirac, Quantum Inf. Comput. 7, 401 (2007)

    MATH  MathSciNet  Google Scholar 

  6. G. Tanner, K. Richter, J.-M. Rost, Rev. Mod. Phys. 72, 497 (2000)

    Article  ADS  Google Scholar 

  7. R.J. Yáñez, A.R. Plastino, J.S. Dehesa, Eur. Phys. J. D 56, 141 (2010)

    Article  ADS  Google Scholar 

  8. D. Manzano, A.R. Plastino, J.S. Dehesa, T. Koga, J. Phys. A 43, 275301 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  9. J.S. Dehesa, T. Koga, R.J. Yáñez, A.R. Plastino, R.O. Esquivel, J. Phys. B 45, 015504 (2012), Corrigendum, J. Phys. B 45, 239501 (2012)

    Article  ADS  Google Scholar 

  10. G. Benenti, S. Siccardi, G. Strini, Eur. Phys. J. D 67, 83 (2013)

    Article  ADS  Google Scholar 

  11. P.A. Bouvrie, A.P. Majtey, A.R. Plastino, P. Sánchez-Moreno, J.S. Dehesa, Eur. Phys. J. D 66, 1 (2012)

    Article  Google Scholar 

  12. A.P. Majtey, A.R. Plastino, J.S. Dehesa, J. Phys. A 45, 115309 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  13. M. Moshinsky, Am. J. Phys. 36, 52 (1968), Erratum: Am. J. Phys. 36, 763 (1968)

    Article  ADS  Google Scholar 

  14. M. Moshinsky, N. Méndez, E. Murow, Ann. Phys. 163, 1 (1985)

    Article  ADS  Google Scholar 

  15. C.L. Benavides-Riveros, J.M. Gracia-Bondía, J.C. Várilly, Phys. Rev. A 86, 022525 (2012)

    Article  ADS  Google Scholar 

  16. W. Heisenberg, Z. Phys. 38, 411 (1926)

    Article  ADS  MATH  Google Scholar 

  17. C. Benavides-Riveros, J. Várilly, Eur. Phys. J. D 66, 274 (2012)

    Article  ADS  Google Scholar 

  18. C. Amovilli, N.H. March, Phys. Rev. A 67, 022509 (2003)

    Article  ADS  Google Scholar 

  19. C. Amovilli, N.H. March, Phys. Rev. A 69, 054302 (2004)

    Article  ADS  Google Scholar 

  20. J. Pipek, I. Nagy, Phys. Rev. A 79, 052501 (2009)

    Article  ADS  Google Scholar 

  21. H.G. Laguna, R.P. Sagar, Phys. Rev. A 84, 012502 (2011)

    Article  ADS  Google Scholar 

  22. P. Kościk, A. Okopińska, Few-Body Syst. 54, 1637 (2013)

    Article  ADS  Google Scholar 

  23. M. Srednicki, Phys. Rev. Lett. 71, 666 (1993)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. L.S. Cederbaum, J. Chem. Phys. 138, 224110 (2013)

    Article  ADS  Google Scholar 

  25. S. Takahashi, K. Takatsuka, J. Chem. Phys. 124, 144101 (2006)

    Article  ADS  Google Scholar 

  26. P. Schmelcher, L.S. Cederbaum, H.D. Meyer, J. Phys. B 21, L445 (1988)

    Article  ADS  Google Scholar 

  27. M.H. Alexander, G. Capecchi, H.-J. Werner, Science 296, 715 (2002)

    Article  ADS  Google Scholar 

  28. T. Yonehara, K. Hanasaki, K. Takatsuka, Chem. Rev. 112, 499 (2012)

    Article  Google Scholar 

  29. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. G. Vidal, J. Mod. Opt. 47, 355 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  31. F. Buscemi, P. Bordone, A. Bertoni, Phys. Rev. A 75, 032301 (2007)

    Article  ADS  Google Scholar 

  32. A.R. Plastino, D. Manzano, J.S. Dehesa, Europhys. Lett. 86, 20005 (2009)

    Article  ADS  Google Scholar 

  33. M.C. Tichy, P.A. Bouvrie, K. Mølmer, Phys. Rev. A 86, 042317 (2012)

    Article  ADS  Google Scholar 

  34. M.C. Tichy, P.A. Bouvrie, K. Mølmer, Phys. Rev. Lett. 109, 260403 (2012)

    Article  ADS  Google Scholar 

  35. S. Pruski, J. Maćkowiak, O. Missuno, Rep. Math. Phys. 3, 241 (1972)

    Article  ADS  Google Scholar 

  36. M. Born, J.R. Oppenheimer, Ann. Phys. 84, 457 (1927)

    Article  MATH  Google Scholar 

  37. D.A. McQuarrie, Quantum Chemistry, 2nd edn. (University Science Books, 2007)

  38. W. Demtröder, Molecular Physics: Theoretical Principles and Experimental Methods (Wiley-VCH, Weinheim, 2007)

  39. M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, Oxford, 1954)

  40. C. Chudzicki, O. Oke, W.K. Wootters, Phys. Rev. Lett. 104, 070402 (2010)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto Carlos I de Física Teórica y Computacional and Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071, Granada, Spain

    Peter A. Bouvrie, Ana P. Majtey, Jesus S. Dehesa & Angel R. Plastino

  2. Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, Brazil

    Ana P. Majtey

  3. Department of Physics and Astronomy, University of Aarhus, 8000, Aarhus C, Denmark

    Malte C. Tichy

  4. CeBio y Secretaría de Investigaciones, Universidad Nacional del Noroeste de la Prov. de Buenos Aires, UNNOBA-Conicet, Roque Saenz-Pea 456, Junin, Argentina

    Angel R. Plastino

Authors
  1. Peter A. Bouvrie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ana P. Majtey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Malte C. Tichy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jesus S. Dehesa
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Angel R. Plastino
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Angel R. Plastino.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bouvrie, P.A., Majtey, A.P., Tichy, M.C. et al. Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system. Eur. Phys. J. D 68, 346 (2014). https://doi.org/10.1140/epjd/e2014-50349-2

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2014-50349-2

Keywords

Search

Navigation