Skip to main content
SpringerLink
Log in

Fourier's Law confirmed for a class of small quantum systems

  • Original Paper
  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength. For a large class of couplings we find a normal heat conduction and confirm Fourier's Law. In a fully quantum mechanical approach linear transport behavior appears to be generic even for small quantum systems.

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. P. Garrido, P. Hurtado, B. Nadrowski, Phys. Rev. Lett. 86, 5486 (2001)

    Google Scholar 

  2. J. Gemmer, G. Mahler, Europhys. Lett. 59, 159 (2002)

    Google Scholar 

  3. J. Gemmer, G. Mahler, Eur. Phys. J. B 31, 249 (2003)

    Google Scholar 

  4. J. Gemmer, A. Otte, G. Mahler, Phys. Rev. Lett. 86, 1927 (2001)

    Google Scholar 

  5. S. Lepri, R. Livi, A. Politi, Europhys. Lett. 43, 271 (1998)

    Google Scholar 

  6. G. Mahler, V.A. Weberru, Quantum Networks 2nd edn. (Springer, Berlin, 1998)

  7. H. Michel, M. Wagner, Phys. Stat. Sol. 75, 507 (1976)

    Google Scholar 

  8. A. Otte, G. Mahler, Phys. Rev. A 62, 012303 (2000)

    Google Scholar 

  9. R. Peierls, Ann. Phys. 3, 1055 (1929)

    MATH  Google Scholar 

  10. R. Peierls, Quantum Theory of Solids (Oxford University Press, London, 1955)

  11. K. Saito, Europhys. Lett. 61, 34 (2003)

    Google Scholar 

  12. K. Saito, S. Takesue, S. Miyashita, Phys. Rev. E 54, 2404 (1996)

    Google Scholar 

  13. K. Saito, S. Takesue, S. Miyashita, Phys. Rev. E 61, 2397 (2000)

    Google Scholar 

  14. A. Savin, G. Tsironis, A. Zolotaryuk, Phys. Rev. Lett. 88, 154301 (2002)

    Google Scholar 

  15. J. Ziman, Electrons and Phonons (Oxford, Clarendon Pr., Oxford, 2001)

  16. According to the Grüneisen formula, thermal expansion, an often used indicator for temperature, is taken to be proportional to the free energy, \(F(T)\), see [15], p. 64 (2001)

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics I, University of Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany

    M. Michel, J. Gemmer & G. Mahler

  2. Institute of Thechnical Physics, DLR Stuttgart, Pfaffenwaldring 38-40, 70569, Stuttgart, Germany

    M. Hartmann

Authors
  1. M. Michel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Hartmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Gemmer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Mahler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Michel.

Additional information

Received: 14 May 2003, Published online: 11 August 2003

PACS:

05.60.Gg Quantum transport - 05.30.-d Quantum statistical mechanics - 05.70.Ln Nonequilibrium and irreversible thermodynamics

Rights and permissions

Reprints and permissions

About this article

Cite this article

Michel, M., Hartmann, M., Gemmer, J. et al. Fourier's Law confirmed for a class of small quantum systems. Eur. Phys. J. B 34, 325–330 (2003). https://doi.org/10.1140/epjb/e2003-00228-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2003-00228-x

Keywords

Search

Navigation