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Critical Properties of Relativistic Bose Gases

  • Conference paper
Dynamics of Synergetic Systems

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 6))

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Abstract

The basic phenomenon of condensation appears in a great many different but related forms throughout the sciences. After we briefly mention some of the physical properties of the special type of phase transition known as Bose-Einstein condensation (BEC) in direct connection with some of the main themes of this symposium in synergetics, we shall proceed to describe the particular collective phenomena relating to the relativistic generalization [1,2] of this problem in d spatial dimensions.

Work supported in part by the Deutsche Forschungsgemeinschaft under contract Mi211/1

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References

  1. R. Beckmann, F. Karsch and D.E. Miller, “Bose-Einstein Condensation of a Relativistic Gas in d-Dimensions,” Phys.Rev.Lett., to be published

    Google Scholar 

  2. R. Beckmann, F. Karsch and D.E. Miller, “Analysis of the Critical Structure of Bose-Einstein Condensation for a Relativistic Gas in d-Dimensions,” to appear; see also R. Beckmann, “Thermodynamische Eigenschaften hadronischer Materie für relativistische Gasmodelle in mehreren Dimensionen,” Diplomarbeit, Universität Bielefeld, 1979

    Google Scholar 

  3. A. Einstein, Sitzber. kgl. preuss. Akad. Wiss., 261 (1924), 18 (1925); also in the book, Albert Einstein, Sein Einfluß auf Physik, Philosophie und Politik, P.C. Aichelburg and R.U. Sexl (Eds.) (Vieweg, Braunschweig, 1979)

    Google Scholar 

  4. F. London, Phys. Rev. 54, 947 (1938);

    Article  ADS  MATH  Google Scholar 

  5. F. London, J. Phys. Chem. 43, 49 (1939); for a general reference see F. London, Superfluids, Vol. I, II (Dover, New York, 1950, 1954)

    Article  Google Scholar 

  6. A.B. Migdal, Rev. Mod. Phys. 50, 107 (1978);

    Article  ADS  Google Scholar 

  7. G.E. Brown and W. Weiser, Phys. Rep. 27c, 1 (1976)

    Article  ADS  Google Scholar 

  8. H. Haken, Synergetics (Springer, Berlin, 1978), see especially Chapters 6 and 8 as well as the proceedings of this conference

    MATH  Google Scholar 

  9. H. Haken, Encyclopedia of Physics, Vol. XXV/2c, “Light and Matter 1c,” (Springer, Berlin, 1970)

    Google Scholar 

  10. H. Haken, Proc. 13th IUPAP Conf. Stat. Phys., Haifa, Aug., 1977,

    Google Scholar 

  11. H. Haken, Ann. Israel Phys. Soc. 2, 99 (1978)

    ADS  Google Scholar 

  12. R. Graham and H. Haken, Z. Phys. 213, 420 (1968)

    Article  ADS  Google Scholar 

  13. H. Haug and S.W. Koch, “Nonequilibrium Phase Transition in Highly Excited Semiconductors,” in these proceedings; Phys. Lett. 69A, 445 (1979)

    ADS  Google Scholar 

  14. E. Hanamura and H. Haug, Phys. Rep. 33C, 209 (1977)

    Article  ADS  Google Scholar 

  15. H.E. Stanley, “Critical Phenomena, Past, Present and Future,” these proceedings; general reference, H.E. Stanley, Phase Transitions and Critical Phenomena (Oxford, 1971)

    Google Scholar 

  16. B. Touschek, Nuovo Cimento 58B 295 (1968);

    Google Scholar 

  17. B. Touschek and G. Rossi, Meccanica Statistica (Boringhieri, Torino, 1970), see Ch. 3

    Google Scholar 

  18. D.E. Miller and F. Karsch, “On the Theory of Relativistic Quantum Gases I. The Covariant Formulation for Ecruilibrium Systems,” Bielefeld Preprint BI-IP 79/08, April, 1979

    Google Scholar 

  19. F. Karsch and D.E. Miller, “On the Theory of Relativistic Quantum Gases II. The Exact Equations of State for Ideal Systems,” Bielefeld Preprint BI-IP 79/09, June, 1979

    Google Scholar 

  20. P.T. Landsberg and J. Dunning-Davies, Phys. Rev. 138A, 1049 (1965)

    MathSciNet  Google Scholar 

  21. J.D. Gunton and M.J. Buckingham, Phys. Rev. 166, 152 (1968)

    Article  ADS  Google Scholar 

  22. P. Lacour-Gayet and G. Toulouse. J. Phys. (Paris) 35, 425 (1974)

    Google Scholar 

  23. C.K. Hall, J. Stat. Phys. 13, 157 (1975)

    Article  ADS  Google Scholar 

  24. H. Satz, Proc. 13th IUPAP Conf. Stat. Phys. Haifa, Aug., 1977,

    Google Scholar 

  25. H. Satz, Ann. Israel Phys. Soc. 2, 255 (1978)

    ADS  Google Scholar 

  26. A.I. Akhieser et al. “On Condensation of Bose Fields in Relativistic Fermi Systems,” Kiev Preprint ITP 78, 80E, Aug., 1978

    Google Scholar 

  27. D.E. Miller, Proc. 13th IUPAP Conf. Stat. Phys., Haifa, Aug., 1977,

    Google Scholar 

  28. D.E. Miller, Ann. Israel Phys. Soc. 2, 940 (1978);

    ADS  Google Scholar 

  29. D.E. Miller, J. Math. Phys. 20, 801 (1979)

    Article  ADS  Google Scholar 

  30. K.K. Singh, Phys. Rev. B12, 2819 (1975);

    ADS  Google Scholar 

  31. K.K. Singh, Phys. Rev. B13, 3192 (1976);

    ADS  Google Scholar 

  32. K.K. Singh, Phys. Rev. B17, 324 (1978)

    ADS  Google Scholar 

  33. G. Toulouse and P. Pfeuty, Groupe de Renormalisation (Grenoble, 1975);

    Google Scholar 

  34. D.J. Amit, Field Theory, the Renormalization Group and Critical Phenomena (McGrawHill, New York, 1978)

    Google Scholar 

  35. D.W. Robinson, Comm. Math. Phys. 50, 53 (1976)

    Article  ADS  MathSciNet  Google Scholar 

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Miller, D.E., Beckmann, R., Karsch, F. (1980). Critical Properties of Relativistic Bose Gases. In: Haken, H. (eds) Dynamics of Synergetic Systems. Springer Series in Synergetics, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67592-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-67592-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-67594-2

  • Online ISBN: 978-3-642-67592-8

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