Skip to main content
SpringerLink
Log in

Fluctuation spectrum in an exactly solvable model with dissipation: A new model of the Flicker noise

  • Elementary Particle Physics and Field Theory
  • Published:
Soviet Physics Journal Aims and scope

Abstract

A system is considered consisting of a harmonic oscillator and a field interacting with it. A quadratic Lagrangian is used, so that the model is exactly solvable. Under some conditions, the model exhibits a dissipative behavior of a selected oscillator. A canonical transformation is found which brings the Hamiltonian to a diagonal form, which is used to compute the quantum correlation and spectral functions of the oscillator fluctuations. It is found that the model allows for a low-frequency spectrum of the form\(\left| \omega \right|^{ - 1 + \varepsilon } \) for the driving force, and\(\left| \omega \right|^{ - 1 - \varepsilon } \) for the oscillator coordinate (Flicker noise).

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

Literature cited

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

    Google Scholar 

  2. J. Messer, Acta Phys. Austriaca,50, 75 (1979).

    Google Scholar 

  3. H. Dekker, Phys. Rep.,80, 1 (1981).

    Google Scholar 

  4. V. V. Dodonov and V. I. Man'ko, Proceedings of the Physical Institute of the Academy of Sciences,167, 7 (1986).

    Google Scholar 

  5. G. Glauber and V. I. Man'ko, Proceedings of the Physical Institute of the Academy of Sciences,167, 102 (1986).

    Google Scholar 

  6. A. Lopez, Zeitschrift für Physik,192, 63 (1966).

    Google Scholar 

  7. O. Yu. Dinariev and A. B. Mosolov, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 1, 94 (1988).

    Google Scholar 

  8. O. Yu. Dinariev, Dokl. Akad. Nauk SSSR,305, 60 (1989).

    Google Scholar 

  9. K. Moren, Methods in Hubert Space [Russian translation], Mir, Moscow (1965).

    Google Scholar 

  10. N. Dunford and J. T. Schwartz, Spectral Theory, Self Adjoint Operators in Hilbert Space, Wiley-Interscience, New York.

  11. P. A. M. Dirac, Principles of Quantum Mechanics [Russian translation], Nauka, Moscow (1979).

    Google Scholar 

  12. L. D. Landau and E. M. Lifshits, Statistical Physics [in Russian], Part 1, Nauka, Moscow (1976).

    Google Scholar 

  13. Sh. M. Kogan, Usp. Fiz. Nauk,123, 131 (1977).

    Google Scholar 

  14. Sh. M. Kogan, Usp. Fiz. Nauk,145, 285 (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. All-Union Research Institute of Gas, USSR

    O. Yu. Dinariev

Authors
  1. O. Yu. Dinariev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 13–18, October, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dinariev, O.Y. Fluctuation spectrum in an exactly solvable model with dissipation: A new model of the Flicker noise. Soviet Physics Journal 33, 821–826 (1990). https://doi.org/10.1007/BF00897301

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00897301

Keywords

Search

Navigation