Skip to main content
SpringerLink
Log in

Equilibrium in quantum systems of particles with magnetic interaction. Fermi and bose statistics

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Quantum systems of particles interacting via an effective electromagnetic potential with zero electrostatic component are considered (magnetic interaction). It is assumed that the j th component of the effective potential for n particles equals the partial derivative with respect to the coordinate of the jth particle of “magnetic potential energy” of n particles almost everywhere. The reduced density matrices for small values of the activity are computed in the thermodynamic limit for d-dimensional systems with short-range pair magnetic potentials and for one-dimensional systems with long-range pair magnetic interaction, which is an analog of the interaction of three-dimensional Chern-Simons electrodynamics (“magnetic potential energy” coincides with the one-dimensional Coulomb (electrostatic) potential energy).

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. R. Jackiw and S-Y. Pi, “Classical and quantum non-relativistic Chern — Simons theory,” Phys. Rev. D15, 42, 35000 (1990).

    MathSciNet  Google Scholar 

  2. J. Lykken, J. Sonnenschein, and N. Wess, The Theory of Anionic Superconductivity. A Review, Preprint, TAUP-1858-91 (1991).

  3. E. Fradkin, Field Theories of Condensed Matter Systems, Addison Wesley (1988).

  4. Y. Kitazava and H. Murayama, “Topological phase transitions of anion systems,” Nucl. Phys. B333, 777 (1990).

  5. S-J. Rey and A. Zee, “Self-duality of three-dimensional Chern-Simons theory,” Nucl. Phys. B352, 857 (1991).

  6. V. I. Skrypnik, “Gibbs states for systems of charged particles with Chern-Simons interaction,” Ukr. Fiz. Zh., 40, No. 3, 133 (1995).

    Google Scholar 

  7. W. Skrypnik, On Quantum System of Particles with Singular Magnetic Interaction in One Dimension. M-B Statistic, Preprint DIAS-STR-95-21 (1995).

  8. J. Ginibre, “Reduced density matrices of quantum gases. I,” J. Math. Phys., 6, No. 3, 252 (1992).

    MathSciNet  Google Scholar 

  9. D. Ya. Petrina, Mathematical Foundations of Quantum Statistical Mechanics. Continuous Systems, Kluwer, Dordrecht (1995).

    Google Scholar 

Download references

Authors
  1. V. I. Skrypnik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 691–698, May 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skrypnik, V.I. Equilibrium in quantum systems of particles with magnetic interaction. Fermi and bose statistics. Ukr Math J 49, 770–778 (1997). https://doi.org/10.1007/BF02486458

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02486458

Keywords

Search

Navigation