Skip to main content
SpringerLink
Log in

Vacuum subdynamics in large quantum systems

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

Abstract

We present a constructive procedure to deal with large quantum systems in the thermodynamic limit. Starting with a discrete spectrum, we perform a complete decomposition of the evolution into one-dimensional subdynamics. We then go to the limit of a continuous spectrum after collecting them into global subdynamics of given degrees of correlation. Previously obtained results for the vacuum subdynamics are justified. The procedure is applied to the problem of potential scattering.

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. I. Prigogine,From Being to Becoming (Freeman, San Francisco, 1980).

    Google Scholar 

  2. I. Prigogine, C. George, and F. Henin,Physica 45:418 (1969).

    Google Scholar 

  3. I. Prigogine, C. George, F. Henin, and L. Rosenfeld,Chem. Scripta 4:5 (1972).

    Google Scholar 

  4. A. Grecos, T. Guo, and W. Guo,Physica 80A:421 (1975).

    Google Scholar 

  5. C. George,Physica 65:273 (1973).

    Google Scholar 

  6. B. Misra and I. Prigogine, inLong-Time Prediction in Dynamics (Wiley, New York, 1983), p. 21.

    Google Scholar 

  7. C. George, F. Mayné, and I. Prigogine,Adv. Chem. Phys. 61:223 (1985).

    Google Scholar 

  8. F. Henin,Bull. Acad. R. Belg. Cl. Sci. 56:1113 (1970).

    Google Scholar 

  9. E. Whittaker and G. Watson,A Course of Modern Analysis (Cambridge University Press, 1965).

  10. C. George,Bull. Acad. R. Belg. Cl. Sci. 54:10 (1973).

    Google Scholar 

  11. C. George, F. Henin, F. Mayné, and I. Prigogine,Hadronic J. 1:520 (1978).

    Google Scholar 

  12. F. Henm and F. Mayné,Physica 108A:281 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Libre de Bruxelles, CP 231, 1050, Bruxelles, Belgium

    C. George & F. Mayné

Authors
  1. C. George
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Mayné
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

It is a privilege for the authors to dedicate this paper to Prof. I. Prigogine. They are both genuine offspring of the Brussels school. As such, most of the ideas they profess owe their inspiration to I. P., their mentor, colleague, and friend through fascinating teaching, stimulating discussions, and illuminating speculations, but they take full responsability for their obvious mistakes, pernicious misconceptions, and malignant deviations from the orthodoxy they have modestly helped to create.

Rights and permissions

Reprints and permissions

About this article

Cite this article

George, C., Mayné, F. Vacuum subdynamics in large quantum systems. J Stat Phys 48, 1343–1361 (1987). https://doi.org/10.1007/BF01009549

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01009549

Key words

Search

Navigation