Skip to main content
SpringerLink
Log in

Information-theoretic aspects of friction in the quantum mechanics of an interacting two-electron harmonic atom

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

In the standard prescriptions (Albrecht in Phys Lett 56B:127, 1975; Hasse in J Math Phys 16:2005, 1975), nonlinear potentials were proposed to introduce a Hermitian potential operator into a Hamiltonian in order to consider quantized friction at the Schrödinger wave-function level. However, this route to understanding quantized friction is not unique. Thus, motivated by important sub-questions put forward by Albrecht and Hasse in the works cited above on the proper choice of parameters introduced in the proposed potentials, we investigate here the information-theoretic aspect of friction using an exact stationary solution for a two-particle interacting one-dimensional oscillator model atom. Specifically, we calculate the change in the diagonal entropy with respect to the well-documented frictionless case, and analyze its parameter-dependence.

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. D. Schuch, Phys. Rev. A 55, 935 (1997)

    Article  CAS  Google Scholar 

  2. I.V. Tokatly, Phys. Rev. Lett. 110, 233001 (2013)

    Article  CAS  Google Scholar 

  3. A. Bulgac, M.M. Forbes, K.J. Roche, G. Wlazlowski, arXiv:1305.6891v1 (nucl-th)

  4. K. Albrecht, Phys. Lett. 56B, 127 (1975)

    Article  Google Scholar 

  5. R.W. Hasse, J. Math. Phys. 16, 2005 (1975)

    Article  Google Scholar 

  6. P. Caldirola, Nuovo Cimento 18, 393 (1941)

    Article  Google Scholar 

  7. E. Kanai, Prog. Theor. Phys. 3, 440 (1948)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. M. Moshinsky, Am. J. Phys. 36, 52 (1968)

    Article  Google Scholar 

  10. M.L. Glasser, I. Nagy, Phys. Lett. A 377, 2317 (2013)

    Article  CAS  Google Scholar 

  11. Ch. Schilling, Phys. Rev. A 88, 042105 (2013)

    Article  Google Scholar 

  12. A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, New York, 1953)

    Google Scholar 

  13. A. Polkovnikov, Ann. Phys. (N.Y.) 326, 486 (2011)

    Article  CAS  Google Scholar 

  14. I. Nagy, I. Aldazabal, A. Rubio, Phys. Rev. A 86, 022512 (2012)

    Article  Google Scholar 

  15. C.R. Galley, Phys. Rev. Lett. 110, 174301 (2013)

    Article  Google Scholar 

  16. S. Sauer, C. Gneiting, A. Buchleitner, Phys. Rev. A 89, 022327 (2014)

    Article  Google Scholar 

  17. C.R. McDonald, G. Orlando, J.W. Abraham, D. Hochstuhl, M. Bonitz, T. Brabec, Phys. Rev. Lett. 111, 256801 (2013)

    Article  CAS  Google Scholar 

  18. R. Crandall, R. Whitnell, R. Bettega, Am. J. Phys. 52, 438 (1984)

    Article  CAS  Google Scholar 

  19. P. Koscik, Phys. Lett. A 379, 293 (2015)

    Article  CAS  Google Scholar 

  20. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1965)

    Google Scholar 

Download references

Acknowledgments

The authors thank Professor P. M. Echenique for warm hospitality at the DIPC. One of us (I.N.) acknowledges useful conversations with Professor I. V. Tokatly. This work has been supported in part by the Basque Departamento de Educación, Universidades e Investigación, the University of the Basque Country UPV/EHU (Grant No. IT-366-07).

Author information

Authors and Affiliations

  1. Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    I. Nagy

  2. Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018, San Sebastián, Spain

    I. Nagy & M. L. Glasser

  3. Department of Physics, Clarkson University, Potsdam, NY, 13699-5820, USA

    M. L. Glasser

Authors
  1. I. Nagy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. L. Glasser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. L. Glasser.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nagy, I., Glasser, M.L. Information-theoretic aspects of friction in the quantum mechanics of an interacting two-electron harmonic atom. J Math Chem 53, 1274–1279 (2015). https://doi.org/10.1007/s10910-015-0487-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-015-0487-5

Keywords

Search

Navigation