Communications in Mathematical Physics

, Volume 125, Issue 1, pp 153–180 | Cite as

The Coulomb Gas at low temperature and low density

  • Joseph G. Conlon
  • Elliott H. Lieb
  • Horng-Tzer Yau


We study the quantum Coulomb Gas ofN particles with HamiltonianH at low temperature and negative values of the chemical potentialμ. Ifμ is sufficiently negative the Coulomb gas is approximately a perfect rare gas of charged particles, as expected. The interesting fact is that for higher (but still negative) values ofμ the gas changes to a rare gas of some atom or molecule (which is most likely neutral). The type of molecule is determined by the ground state of the HamiltonianHμN with center of mass motion removed.


Neural Network Statistical Physic Complex System Charged Particle Nonlinear Dynamics 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brydges, D., Federbush, P.: The cluster expansion for potentials with exponential fall-off. Commun. Math. Phys.53, 19–30 (1977)Google Scholar
  2. 2.
    Conlon, J.G., Lieb, E.H., Yau, H.-T.: TheN 7/5 Law for charged bosons. Commun. Math. Phys.116, 417–448 (1988)Google Scholar
  3. 3.
    Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger operators. Berlin, Heidelberg, New York: Springer 1987Google Scholar
  4. 4.
    Dyson, F.J., Lenard, A.: Stability of matter. I, II, J. Math. Phys.8, 423–434 (1967); ibid9, 698–711 (1968)Google Scholar
  5. 5.
    Fefferman, C.: The atomic and molecular nature of matter. Rev. Math. Iberoamericana1, 1–44 (1985)Google Scholar
  6. 6.
    Lieb, E.H.: The stability of matter. Rev. Mod. Phys.48, 553–569 (1976)Google Scholar
  7. 7.
    Lebowitz, J.L., Pena, R.E.: Low density form of the free energy for real matter. J. Chem. Phys.59, 1362–1364 (1973)Google Scholar
  8. 8.
    Lieb, E.H., Lebowitz, J.L.: The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei. Adv. Math.9, 316–398 (1972)Google Scholar
  9. 9.
    Reed, M., Simon, B.: Methods of modern mathematical physics. IV. analysis of operators. New York: Academic Press 1978Google Scholar
  10. 10.
    Richards, P.I.: Manual of mathematical physics. New York: Pergamon Press 1959. This is a useful reference for a succinct presentation of the Saha equation in a general settingGoogle Scholar
  11. 11.
    Ruelle, D.: Statistical mechanics rigorous results. Reading, MA: Benjamin 1969Google Scholar
  12. 12.
    Saha, M.N.: Ionization in the solar chromosphere. Phil. Mag.40, 472–488 (1920)Google Scholar
  13. 13.
    Thirring, W.E.: A course in mathematical physics, Vol. 4. Quantum mechanics of large systems. Wien, New York: Springer 1983Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Joseph G. Conlon
    • 1
  • Elliott H. Lieb
    • 2
  • Horng-Tzer Yau
    • 3
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA
  3. 3.Courant InstituteNew York UniversityNew YorkUSA

Personalised recommendations