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The Independence on Boundary Conditions for the Thermodynamic Limit of Charged Systems

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Abstract

We study systems containing electrons and nuclei. Based on the fact that the Thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such as Neumann, periodic, or elastic boundary conditions. The result is proven for all limiting sequences of domains which are obtained by scaling a bounded open set, with smooth boundary, except for isolated edges and corners.

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References

  1. Lieb, E.H., Lebowitz, J.L.: The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei. Adv. in Math. 9, 316–398 (1972)

    Google Scholar 

  2. Conlon, J.G., Lieb, E.H., Yau, H.-T.: The N7/5 Law for Charged Bosons. Commun. Math. Phys. 116, 417–448 (1988)

    Google Scholar 

  3. Graf, G.M., Schenker, D.: On the Molecular Limit of Coulomb Gases. Commun. Math. Phys. 174, 215–227 (1995)

    Google Scholar 

  4. Robinson, D.W.: Statistical mechanics of quantum mechanical particles with hard cores. I. The thermodynamic pressure. Commun. Math. Phys. 16, 290–309 (1970)

    Google Scholar 

  5. Robinson, D.W.: The thermodynamic pressure in quantum statistical mechanics. Lecture Notes in Physics. Vol. 9, Berlin–New York: Springer–Verlag, 1971, iv+115 pp

  6. Reed, M., Simon, B.: Methods of modern mathematical physics IV: Analysis of operators, New York-London: Academic Press, 1978

  7. Lieb, E.H.: The stability of matter. Rev. Mod. Phys. 48, 553–569 (1976)

    Google Scholar 

  8. Lieb, E.H., Yau, H.-T.: The stability and instability of relativistic matter. Commun. Math. Phys. 118, 177–213 (1988)

    Google Scholar 

  9. Fisher, M.E.: The free energy of a macroscopic system. Arch. Rat. Mech. Anal. 17, 337–410 (1964)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vanocuver, BC, Canada

    David Hasler

  2. Department of Mathematics, University of Copenhagen, 2100, Copenhagen, Denmark

    Jan Philip Solovej

Authors
  1. David Hasler
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  2. Jan Philip Solovej
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Communicated by H. Spohn

Work partially supported by EU grant HPRN-CT-2002-00277.

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Hasler, D., Solovej, J. The Independence on Boundary Conditions for the Thermodynamic Limit of Charged Systems. Commun. Math. Phys. 261, 549–568 (2006). https://doi.org/10.1007/s00220-005-1449-8

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  • DOI: https://doi.org/10.1007/s00220-005-1449-8

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