Prog. Theor. Phys. Vol. 68 No. 3 (1982) pp. 744-763
Distribution of Zeros and the Equation of State. IV
— Ideal Bose-Einstein Gas
Department of Applied Physics, Osaka University, Suita 565
(Received March 20, 1982)
The ideal Bose-Einstein gas is investigated on the basis of the fundamental concept of the distribution of zeros of the grand partition function on the complex z(= activity) plane. For this gas there are no zeros; but poles play essentially the same role as zeros from an analytical point of view, and are distributed on the part of the positive real axis from λ-3(>0) to +∞, where λ=h(2πmkT)-1/2. The distribution function of poles is calculated, and the function-theoretical structure of the equation of state is discussed. The Bose-Einstein condensation (especially the continuity of the slope of the p-v isotherm at the condensation point and the continuity of the specific heat at the transition temperature) is examined from the point of view of the distribution of poles. From the same point of view the two-dimensional and one-dimensional ideal Bose-Einstein gases are treated. Finally, the n-dimensional (n≥4) ideal Bose-Einstein gas is discussed, and it is shown that for n≥5 the specific heat is discontinuous at the transition temperature.
DOI : 10.1143/PTP.68.744
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