Skip to main content
SpringerLink
Log in

Kirkwood–Salsburg equation for a quantum lattice system of oscillators with many-particle interaction potentials

  • Published:
Ukrainian Mathematical Journal Aims and scope

For a Gibbs system of one-dimensional quantum oscillators on a d-dimensional hypercubic lattice interacting via superstable pair and many-particle potentials of finite range, we prove the existence of a solution of the (lattice) Kirkwood–Salsburg equation for correlation functions depending on the Wiener paths. Some many-particle potentials may be nonpositive.

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. W. I. Skrypnyk, “On the polymeric decompositions for equilibrium systems of oscillators with ternary interaction,” Ukr. Mat. Zh., 53, No. 11, 1532–1544 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Albeverio, Yu. G. Kondratiev, R. A. Minlos, and O. L. Rebenko, Small Mass Behaviour of Quantum Gibbs States for Lattice Models with Unbounded Spins, Preprint UMa-CCM 22/97, Uni. da Madeira (1997).

  3. R. A. Minlos, A. Verbeure, and V. A. Zagrebnov, A Quantum Crystal Model in the Light-Mass Limit: Gibbs States, Preprint KULTP-97/16 (1997).

  4. Y. M. Park and H. J. Yoo, “Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems,” J. Stat. Phys., 80, No. 1/2, 223–271 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Ruelle, Statistical Mechanics. Rigorous Results, W. A. Benjamin, New York (1969).

    MATH  Google Scholar 

  6. G. E. Shilov and B. A. Gurevich, Integral, Measure, and Derivative [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  7. M. Reed and B. Simon, Methods of Modern Mathematical Physics. II: Fourier Analysis, Self-Adjointness, Academic Press, New York (1975).

    MATH  Google Scholar 

  8. H-H. Kuo, Gaussian Measures in Banach Spaces, Springer, Berlin (1975).

    MATH  Google Scholar 

  9. W. I. Skrypnik, “Long-range order in Gibbs lattice classical linear oscillator systems,” Ukr. Mat. Zh., 58, No. 3, 388–405 (2006).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    W. I. Skrypnyk

Authors
  1. W. I. Skrypnyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 5, pp. 689–700, May, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skrypnyk, W.I. Kirkwood–Salsburg equation for a quantum lattice system of oscillators with many-particle interaction potentials. Ukr Math J 61, 821–833 (2009). https://doi.org/10.1007/s11253-009-0239-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-009-0239-4

Keywords

Search

Navigation