Skip to main content
SpringerLink
Log in

The effect of dissipation on coherent quantum tunnelling in a double-well system: Two-level model using an adjoint equation approach

  • Original Contributions
  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

We examine the effect of dissipation on coherent quantum tunnelling between the two lowest levels of a double-well system using an adjoint equation approach developed previously in the treatment of quantum-optical problems. Dissipation is modelled by a linear coupling to a bath of harmonic oscillators. The high frequency portion of the bath is adiabatically eliminated using a cumulant expansion technique, which generates frequency renormalisation terms. Making a low temperature assumption, an approximate two-level model is developed in the form of three coupled stochastic differential equations. With a decorrelation approximation, the two-level equations can be solved to yield familiar results. However, the adjoint equation also permits the use of direct stochastic simulation as a means of solution, and simulations are carried out for a range of parameters. A comparison with the decorrelation approximation is made.

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. Leggett, A.J., Chakravarty, S., Dorsey, A.T., Fisher, M.P.A., Garg, A., Zwerger, W.: Rev. Mod. Phys.59, 1 (1987)

    Google Scholar 

  2. Weiss, U., Grabert, H., Linkwitz, S.: Low Temp. Phys.68, 213 (1987)

    Google Scholar 

  3. Gardiner, C.W.: IBM J. Res. Dev.32, 127 (1988)

    Google Scholar 

  4. Gardiner, C.W., Parkins, A.S., Collett, M.J.: J. Opt. Soc. Am.B4, 1683 (1987)

    Google Scholar 

  5. Parkins, A.S., Gardiner, C.W.: Phys. Rev. A37, 3867 (1988)

    Google Scholar 

  6. Chakravarty, S., Leggett, A.J.: Phys. Rev. Lett.52, 5 (1984)

    Google Scholar 

  7. Dorsey, A.T., Fisher, M.P.A., Wartak, M.S.: Phys. Rev. A33, 1117 (1986)

    Google Scholar 

  8. Chakravarty, S., Kivelson, S.: Phys. Rev. B32, 76 (1985)

    Google Scholar 

  9. Kampen, N.G. van: Stochastic processes in physics and chemistry. Amsterdam: North-Holland 1981

    Google Scholar 

  10. Weiss, U., Grabert, H., Hänggi, P., Riseborough, P.: Phys. Rev. B35, 9535 (1987)

    Google Scholar 

  11. Aslangul, C., Pottier, N., Saint-James, D.: Phys. Lett. A110, 249 (1985)

    Google Scholar 

  12. Aslangul, C., Pottier, N., Saint-James, D.: J. Phys. (Paris)47, 1657 (1986)

    Google Scholar 

  13. Dekker, H.: Phys. Rev. A35, 1436 (1987)

    Google Scholar 

  14. Smith, A.M., Gardiner, C.W.: Phys. Rev. A39, 3511 (1989)

    Google Scholar 

  15. Weiss, U., Wollensak, M.: Phys. Rev. Lett.62, 1663 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Waikato, Hamilton, New Zealand

    A. S. Parkins, C. W. Gardiner & M. L. Stéyn-Ross

Authors
  1. A. S. Parkins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. W. Gardiner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. L. Stéyn-Ross
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parkins, A.S., Gardiner, C.W. & Stéyn-Ross, M.L. The effect of dissipation on coherent quantum tunnelling in a double-well system: Two-level model using an adjoint equation approach. Z. Physik B - Condensed Matter 83, 413–424 (1991). https://doi.org/10.1007/BF01313412

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01313412

Keywords

Search

Navigation