Skip to main content
SpringerLink
Log in

Quantum system driven by periodic external field

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

Abstract

A quantum Floquet Theory for a periodically driven system is studied. For this purpose the periodic external fields are changed to have an increasing amplitude with exp(ηt), where η is an infinitestimal positive number to be taken to be zero at the end. By using the expansions in terms of inverse powers of the driving frequency, periodic factors of the time evolution operator are factorized successively. Each step corresponds to a periodically driven system with different strength of external field. This approach produces a time-independent effective Hamiltonian. The effectiveness of the method is examined by applying it to simple models; 1) a forced harmonic oscillator, 2) a particle in the double-well potential, and 3) a hydrogen atom in an electric potential.

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. Bloch, F., Siegert, A.: Phys. Rev.57, 522 (1940)

    Google Scholar 

  2. Magnus, W.: Commun. Pure Appl. Math.7, 649 (1954); Wilcox, R.M.: J. Math. Phys.8, 962 (1967)

    Google Scholar 

  3. Shirley, J.H.: Phys. Rev.138, B979 (1965); Barone, S.R., Narcowich, M.A., Narcowich, F.J.: Phys. Rev. A15, 1109 (1977); Gesztesy, F., Mitter, H.: J. Phys. A14, L79 (1981); Maricq, M.M.: Phys. Rev. B25, 6622 (1982)

    Google Scholar 

  4. Haeberken, U., Waugh, J.S.: Phys. Rev.175, 453 (1968)

    Google Scholar 

  5. Sauermann, G., Zhang, Y.: Physica A164, 469 (1990)

    Google Scholar 

  6. Zhang, Y., Sauermann, G.: Physica A171, 605 (1991); ibid.A176, 345 (1991)

    Google Scholar 

  7. Maricq, M.M.: Phys. Rev.31, 127 (1985)

    Google Scholar 

  8. Pegg, D.T., Series, G.W.: J. Phys. B3, L33 (1970); Pegg, D.T.: J. Phys. B6, L246 (1973)

    Google Scholar 

  9. See, for instance: Grozdanov, T.P., Pakovic, M.J.: Phys. Rev. A38, 1739 (1988)

    Google Scholar 

  10. Salzmann, W.R.: Phys. Rev. A10, 461 (1974);A16, 1552 (1977)

    Google Scholar 

  11. Lippmann, B.A., Schwinger, J.: Phys. Rev.79, 352 (1949)

    Google Scholar 

  12. Roman, P.: Advanced quantum theory, Chap. 4. Reading, Mass: Addison-Wesley 1965

    Google Scholar 

Download references

Author information

Author notes

  1. M. Ichiyanagi

    Present address: Nagasaki Institute of Applied Science, Nagasaki

Authors and Affiliations

  1. Theoretische Festkörperphysik, Technische Hochschule Darmstadt, W-6100, Darmstadt, Germany

    M. Ichiyanagi

Authors
  1. M. Ichiyanagi
    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

Ichiyanagi, M. Quantum system driven by periodic external field. Z. Physik B - Condensed Matter 91, 235–244 (1993). https://doi.org/10.1007/BF01315241

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01315241

Keywords

Search

Navigation