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On a nonideal Bose gas model. (English. Russian original) Zbl 0941.82003

Theor. Math. Phys. 120, No. 1, 921-932 (1999); translation from Teor. Mat. Fiz. 120, No. 1, 130-143 (1999).
Summary: The authors consider a polynomial generalization of the Huang-Davie model in the nonideal Bose gas theory. They prove that the Gaussian dominance condition is fulfilled for all values of the chemical potential. They show that the lower bound for the critical temperature in the Huang-Davies model obtained by the infrared bound method coincides with the exact value of this quantity in the Davies theory. Using the large deviation principle, the authors prove a possibility of a generalized Bose condensation in the polynomial model.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
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References:

[1] K. Huang,Statistical Mechanics, Wiley, New York (1963).
[2] E. B. Davies,Commun. Math. Phys.,28, 69 (1972). · doi:10.1007/BF02099372
[3] A. S. Shvarts,Trudy Moskov. Mat. Obshch.,22, 165 (1970).
[4] J. L. Lebowitz and O. Penrose,J. Math. Phys.,7, 98 (1966). · Zbl 0938.82520 · doi:10.1063/1.1704821
[5] L. J. Landau and I. E. Wilde,Commun. Math. Phys.,70, 43 (1970). · doi:10.1007/BF01220501
[6] M. van den Berg, J. T. Lewis, and J. V. Pulé,Helv. Phys. Acta,59, 1271 (1986).
[7] S. R. S. Varadhan,Commun. Pure Appl. Math.,19, 261 (1966). · Zbl 0147.15503 · doi:10.1002/cpa.3160190303
[8] M. van den Berg, J. T. Lewis, and J. V. Pulé,Commun. Math. Phys.,116, 1 (1988). · Zbl 0688.53045 · doi:10.1007/BF01239022
[9] M. van den Berg and J. T. Lewis, ”Limit theorems for stochastic processes associated with a boson gas,” in:Stochastic Mechanics and Stochastic Processes (Proc. Conf. Swansea/UK, 1986) (A. Truman and I. M. Davies, eds.) (Lect. Notes Math., Vol. 1325) Springer, Berlin (1986), p. 16. · Zbl 0648.60106
[10] M. van den Berg, J. T. Lewis, and P. J. Smedt,J. Stat. Phys.,37, 697 (1984). · doi:10.1007/BF01010502
[11] M. van den Berg, J. T. Lewis, and J. V. Pulé, ”Large deviations and the boson gas,” in:Stochastic Mechanics and Stochastic Processes (Proc. Conf. Swansea/UK, 1986) (A. Truman and I. M. Davies, eds.) (Lect. Notes Math. Vol. 1325), Springer, Berlin (1986), p. 24. · Zbl 0648.60107
[12] M. Corgini and D. P. Sankovich,Theor. Math. Phys.,108, 1187 (1996). · Zbl 0936.82501 · doi:10.1007/BF02070245
[13] M. Corgini and D. P. Sankovich,Int. J. Mod. Phys. B,11, 3329 (1997). · doi:10.1142/S0217979297001635
[14] F. A. Berezin,Methods of Second Quantization [in Russian], Nauka, Moscow (1986); English transl., Acad. Press, New York (1986). · Zbl 0678.58044
[15] N. N. Bogolyubov Jr., I. G. Brankov, V. A. Zagrebnov, A. M. Kurbatov, and N. S. Tonchev,Approximating Hamiltonian Methods in Statistical Physics [in Russian], BAS Press, Sophia (1981). · Zbl 0469.70021
[16] M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. 2,Fourier Analysis. Self-Adjointness, Acad. Press, New York (1975). · Zbl 0308.47002
[17] G. H. Hardy, J. E. Littlewood, G. Polya,Inequalities, Cambridge Univ. Press, Cambridge (1934).
[18] G. Roepstorff,Commun. Math. Phys.,53, 143 (1977). · doi:10.1007/BF01609128
[19] R. Ellis,Entropy, Large Deviations, and Statistical Mechanics, Springer, Berlin (1985). · Zbl 0566.60097
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