One-Dimensional Systems: Exact Solution for Nearest-Neighbor Interactions

  • Andrés Santos
Part of the Lecture Notes in Physics book series (LNP, volume 923)


One-dimensional systems with interactions restricted to nearest neighbors lend themselves to a full exact statistical-mechanical solution, what has undoubtful pedagogical and illustrative values. It is first noted in this chapter that the pair correlation function in Laplace space can be expressed in terms of the nearest-neighbor distribution function. The latter quantity is subsequently obtained in the isothermal–isobaric ensemble. As explicit examples, the square-well, square-shoulder, sticky-hard-rod, and nonadditive hard-rod fluids are worked out in detail.


Hard Sphere Radial Distribution Function Packing Fraction Statistical Ensemble Compressibility Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Z.W. Salsburg, R.W. Zwanzig, J.G. Kirkwood, J. Chem. Phys. 21, 1098 (1953)ADSCrossRefGoogle Scholar
  2. 2.
    J.L. Lebowitz, D. Zomick, J. Chem. Phys. 54, 3335 (1971)ADSCrossRefGoogle Scholar
  3. 3.
    M. Heying, D.S. Corti, Fluid Phase Equilib. 220, 85 (2004)CrossRefGoogle Scholar
  4. 4.
    A. Santos, Phys. Rev. E 76, 062201 (2007)ADSCrossRefGoogle Scholar
  5. 5.
    A. Ben-Naim, A. Santos, J. Chem. Phys. 131, 164 (2009)CrossRefGoogle Scholar
  6. 6.
    G.B. Rybicki, Astrophys. Space Sci. 14, 56 (1971)ADSCrossRefGoogle Scholar
  7. 7.
    J.G. Kirkwood, F.P. Buff, J. Chem. Phys. 19, 774 (1951)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Ben-Naim, Molecular Theory of Solutions (Oxford University Press, Oxford, 2006)zbMATHGoogle Scholar
  9. 9.
    L. van Hove, Physica 16, 137 (1950)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions (Dover, New York, 1972)zbMATHGoogle Scholar
  11. 11.
    S.B. Yuste, A. Santos, J. Stat. Phys. 72, 703 (1993)ADSCrossRefGoogle Scholar
  12. 12.
    A. Malijevský, A. Santos, J. Chem. Phys. 124, 074508 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    L. Rayleigh, Nature 45, 80 (1891)ADSCrossRefGoogle Scholar
  14. 14.
    D.T. Korteweg, Nature 45, 152 (1891)ADSCrossRefGoogle Scholar
  15. 15.
    K.F. Herzfeld, M. Goeppert-Mayer, J. Chem. Phys. 2, 38 (1934)ADSCrossRefGoogle Scholar
  16. 16.
    L. Tonks, Phys. Rev. 50, 955 (1936)ADSCrossRefGoogle Scholar
  17. 17.
    A. Santos, Radial distribution function for one-dimensional square-well and square-shoulder fluids. Wolfram Demonstrations Project (2015),
  18. 18.
    A. Santos, Radial distribution function for sticky hard rods. Wolfram Demonstrations Project (2012),
  19. 19.
    A. Santos, Radial distribution functions for nonadditive hard-rod mixtures. Wolfram Demonstrations Project (2015),

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Andrés Santos
    • 1
  1. 1.Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx)Universidad de ExtremaduraBadajozSpain

Personalised recommendations