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Why do bosons condense?

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Statistical Mechanics and Field Theory: Mathematical Aspects

Part of the book series: Lecture Notes in Physics ((LNP,volume 257))

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References

  1. Einstein, A.: Quantentheorie des einatomigen idealen Gases, Sitzunber. Preus. Akad. Wiss. 1, 3–14 (1925)

    Google Scholar 

  2. Uhlenbeck, G.E.: Thesis, Leyden 1927

    Google Scholar 

  3. Kahn, B., Uhlenbeck, G.E.:On the theory of condensation, Physica 5, 399–415 (1938)

    Google Scholar 

  4. London, F.: On the Bose-Einstein condensation, Phys. Rev. 54, 947–954 (1938)

    Google Scholar 

  5. London, F.: Superfluids, vol. 11. New York: John Wiley and Sons, Inc. 1954

    Google Scholar 

  6. Huang, K., Yang, C.N., Luttinger, J.M.: Imperfect Bose gas with hard-sphere interactions, Phys. Rev. 105, 776–784 (1957)

    Google Scholar 

  7. Hepp, K., Lieb, E.: Equilibrium statistical mechanics of matter interacting with the quantized radiation field, Phys. Rev. A8, 2517–2525 (1973)

    Google Scholar 

  8. van den.Berg, M., Lewis, J.T., Pulé, J.V.: A general theory of Bose-Einstein condensation, DIAS-STP-82-35 (1982)

    Google Scholar 

  9. van den Berg, M., Lewis, J.T., Pulé, J.V.: A general theory of Bose-Einstein condensation, Helv. Phys. Acta (in press) (1986)

    Google Scholar 

  10. Huang, K.: Statistical Mechanics. New York: John Wiley and Sons, Inc. 1967

    Google Scholar 

  11. Ruelle, D.: Statistical Mechanics: Rigorous Results. New York: Benjamin 1969

    Google Scholar 

  12. Davies, E.B.: The thermodynamic limit for an imperfect boson gas, Commun. math. Phys. 28, 69–86 (1972)

    Google Scholar 

  13. Fannes, M., Verbeure, A.: The imperfect Boson gas, J. Math. Phys. 21, 1809 (1980)

    Google Scholar 

  14. Buffet, E., Pulè, J.V.: Fluctuation properties of the imperfect Bose gas, J. Math. Phys. 24, 1608–1616 (1983)

    Google Scholar 

  15. van den Berg, M., Lewis, J.T., de Smedt, P.: Condensation in the imperfect boson gas, J. Stat. Phys., 697–707 (1984)

    Google Scholar 

  16. Thouless, D.J.: The Quantum-mechanics of Many-body Systems. New York: Academic Press 1961

    Google Scholar 

  17. Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one-dimension, J. Math. Phys. 1, 516–523 (1960)

    Google Scholar 

  18. Schultz, T.: Note on the one-dimensional gas of impenetrable point-particle bosons, J. Math. Phys. 4, 666–671 (1963)

    Google Scholar 

  19. Pulè, J.V.: Thesis, Oxford, 1972

    Google Scholar 

  20. Lewis, J.T.: The free boson gas, Proceedings of the LMS Instructional Conference, Bedford College 1971, Mathematical Problems in Mathematical Physics. New York: Academic Press 1972

    Google Scholar 

  21. Cannon, J.T.: Infinite-volume limits of the canonical free Bose gas states on the Weyl algebra, Commun. math. Phys. 29, 89–104 (1973)

    Google Scholar 

  22. Lewis, J.T., Pulè, J.V.: The equilibrium states of the free boson gas, Commun. math. Phys. 36, 1–18 (1974)

    Google Scholar 

  23. Ziff, R.M., Uhlenbeck, G.E., Kac, M.: The ideal Bose gas revisited, Phys. Rep. C32, 169–248 (1977)

    Google Scholar 

  24. van den Berg, M., Lewis, J.T., Pulè, J.V.: The large deviation principle and some models of an interacting boson gas, DIAS-86-(1986)

    Google Scholar 

  25. Varadhan, S.R.S.: Asymptotic probabilities and differential equations, Comm. Pure Appl. Math. 19, 261–286 (1966)

    Google Scholar 

  26. Varadhan, S.R.S.: Large Deviations and Applications. Philadelphia: Society for Industrial and Applied Mathematics 1984

    Google Scholar 

  27. Bahadur, R.R., Zabell, S.L.: Large deviations of the sample mean in general vector spaces, Ann. Prob., 7, 537–621 (1979)

    Google Scholar 

  28. Lanford, O.E.: Entropy and equilibrium states in classical statistical mechanics. Lecture Notes in Physics 20, 1–113. Berlin: Springer 1971

    Google Scholar 

  29. Azencott, R.: Grandes deviations et applications. Ecole d'Eté de Probabilités de Saint-Flour V111-1978, 1–176, Lecture Notes in Mathematics 774 Berlin: Springer 1980

    Google Scholar 

  30. Stroock, D.W.: An Introduction to the Theory of Large Deviations. New York: Springer 1984

    Google Scholar 

  31. Ellis, R.: Entropy, Large Deviations and Statistical Mechanics. New York: Springer 1985

    Google Scholar 

  32. Lewis, J.T., Pulè, J.V. The equivalence of ensembles in statistical mechanics, Lecture Notes in Mathematics 1095, 25–35 (1984)

    Google Scholar 

  33. van den Berg, M., Lewis, J.T., Pulè, J.V.: The large deviation principle and some models of an interacting boson gas, DIAS-86-12 (1986)

    Google Scholar 

  34. Lewis, J.T., Pulè, J.V., de Smedt, P.: The Superstability of pair-potentials of positive type. J. Stat. Phys. 35, 381–385 (1984)

    Google Scholar 

  35. Lieb, E.: Simplified approach to the ground-state energy of an imperfect Bose gas, Phys. Rev. 130, 2518–2528 (1963)

    Google Scholar 

  36. Kac, M.: On the partition function of a one-dimensional gas, Phys. Fluids 2, 8–12 (1959)

    Google Scholar 

  37. Baker, G.A.: Certain general order-disorder models in the limit of longrange interactions. Phys. Rev. 126, 2072–2078 (1962)

    Google Scholar 

  38. Lebowitz, J.L., Penrose, O.: Rigorous treatment of the van der Waals-Maxwell theory of the liquid-vapour transition J. Math. Phys. 7, 98–113 (1966)

    Google Scholar 

  39. Gates, D.J., Penrose, O.: The van der Waals' limit for classical systems, III Commun. math. Phys. 17, 194–209 (1970)

    Google Scholar 

  40. Lieb, E.: Quantum-mechanical extension of the Lebowitz-Penrose Theorem on the van der Waals' theory J. Math. Phys. 7, 1016–1024 (1966)

    Google Scholar 

  41. Lewis, J.T., Pule, J.V., de Smedt, P.: The persistence of boson condensation in the van der Waals' limit, DIAS-STP-83-48 (1983)

    Google Scholar 

  42. van den Berg, M., Lewis, J. T., Pule, J.V.: The existence of the pressure in a model of an interacting boson gas. DIAS-STP-86-43 (1986)

    Google Scholar 

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Authors and Affiliations

  1. Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Republic of Ireland

    J. T. Lewis

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  1. J. T. Lewis
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T. C. Dorlas N. M. Hugenholtz M. Winnink

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© 1986 Springer-Verlag

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Lewis, J.T. (1986). Why do bosons condense?. In: Dorlas, T.C., Hugenholtz, N.M., Winnink, M. (eds) Statistical Mechanics and Field Theory: Mathematical Aspects. Lecture Notes in Physics, vol 257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16777-3_80

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  • DOI: https://doi.org/10.1007/3-540-16777-3_80

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  • Online ISBN: 978-3-540-39858-5

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