Skip to main content
SpringerLink
Log in

Invariants and nonequilibrium density matrices

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

A new method of calculating nonequilibrium density matrices with the aid of the quantum integrals of motion is proposed. The method is shown to be very effective in the case of systems described by means of quadratic Hamiltonians. The possibility of constructing phenomenological nonstationary Hamiltonians for a wide class of dissipative systems is discussed. The exact formulas for nonequilibrium density matrices of arbitrary quadratic systems are obtained. The quantum problem of the motion of a charged particle in uniform electric and magnetic fields in the presence of a frictional force proportional to the velocity is solved exactly by means of introducing the new phenomenological Hamiltonian.

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. V. V. Dodonov, I. A. Malkin, and V. I. Man'ko,J. Phys. A 8:L19 (1975).

    Google Scholar 

  2. V. V. Dodonov, I. A. Malkin, and V. I. Man'ko,Teor. Mat. Fiz. 24:164 (1975);Int. J. Theor. Phys. 14:37 (1975).

    Google Scholar 

  3. D. ter Haar,Elements of Statistical Mechanics, Holt, Rinehart and Winston, New York (1961);Rep. Prog. Phys. 24:304 (1961).

    Google Scholar 

  4. G. J. Papadopoulos,Physica 74:529 (1974).

    Google Scholar 

  5. R. Kubo,J. Phys. Soc. Japan 12:570 (1957).

    Google Scholar 

  6. A. Isihara,Statistical Physics, Academic Press, New York (1971).

    Google Scholar 

  7. M. Pardy,Int. J. Theor. Phys. 8:31 (1973).

    Google Scholar 

  8. M. D. Kostin,J. Chem. Phys. 57:3589 (1973);J. Stat. Phys. 12:145 (1975).

    Google Scholar 

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

    Google Scholar 

  10. B. K. Skagerstam,Phys. Lett. 58B:21 (1975).

    Google Scholar 

  11. P. Caldirola,Nuovo Cimento 18:393 (1941);46B:172 (1966).

    Google Scholar 

  12. E. Kanai,Progr. Theor. Phys. 3:440 (1948).

    Google Scholar 

  13. W. E. Brittin,Phys. Rev. 77:396 (1950).

    Google Scholar 

  14. G. J. Papadopoulos,J. Phys. A 7:209 (1974).

    Google Scholar 

  15. L. H. Buch and H. H. Denman,Am. J. Phys. 42:304 (1974).

    Google Scholar 

  16. H. Dekker,Z. Physik B21:295 (1975).

    Google Scholar 

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

    Google Scholar 

  18. I. R. Svin'in,Teor. Mat. Fiz. 22:97 (1975);27:270 (1976).

    Google Scholar 

  19. P. Havas,Nuovo Cimento Suppl. 5:363 (1957).

    Google Scholar 

  20. V. V. Dodonov, I. A. Malkin, and V. I. Man'ko, P. N. Lebedev Institute of Physics, Preprint No. 42 (1976).

  21. F. R. Gantmaher,Teoriya Matritz, Nauka, Moscow (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. P. N. Lebedev Institute of Physics, Moscow, USSR

    V. V. Dodonov, I. A. Malkin & V. I. Man'ko

Authors
  1. V. V. Dodonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. A. Malkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. I. Man'ko
    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

Dodonov, V.V., Malkin, I.A. & Man'ko, V.I. Invariants and nonequilibrium density matrices. J Stat Phys 16, 357–370 (1977). https://doi.org/10.1007/BF01020428

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01020428

Key words

Search

Navigation