Prog. Theor. Phys. Vol. 68 No. 2 (1982) pp. 471-492
Distribution of Zeros and the Equation of State. III
— Cluster Series, the Ideal Fermi-Dirac Gas and Other Problems
Department of Applied Physics, Osaka University, Suita 565
(Received February 4, 1982)
The radius of convergence of the cluster series (expressing the equation of state) is discussed in connection with the distribution of zeros of the grand partition function on the complex z(=activity) plane, by giving various examples of circular distribution. Anomalous phase transitions and phase transitions of third order are considered by showing some examples of circular distribution of zeros. For the ideal Fermi-Dirac gas, the distribution function of zeros, lying on the part of the negative real axis from -λ-3 to -∞ [where λ=h(2 πmkT)-1/ 2], is calculated , and the function-theoretical structure of the equation of state is investigated. The distribution of zeros for this gas is compared with that for Tonks' gas (having purely repulsive interparticle forces). The two-dimensional and one-dimensional Fermi-Dirac gases are dealt with from the point of view of the distribution of zeros.
DOI : 10.1143/PTP.68.471
- K. Ikeda, Prog. Theor. Phys. 58 (1977), 496, [PTP]reffered to as I.
- K. Ikeda, Prog. Thoer. Phys. 61 (1979), 27, reffered to as II.
C. N. Yang and T. D. Lee, Phys. Rev. 87 (1952), 404[APS].
- K. Ikeda, Proceedings of the International Conference of Theoretical Physics 1953, p. 544.
- K. Ikeda, Prog. Theor. Phys. 16 (1956), 341[PTP]; Busseiron Kenkyu 57 (1952), 77.
- K. Ikeda, Modern Developments in Thermodynamics, ed. B. Gal-Or (Wiley, New York, 1974), p. 311.
- For example, E. C. Titchmarsh, The Theory of Functions (Oxford Univ. Press, 1939), p. 214.
L. Tonks, Phys. Rev. 50 (1936), 955[APS].
E. H. Hauge and P. C. Hemmer, Physica 29 (1963), 1338[Elsevier].
- K. Ikeda, Prog. Theor. Phys. 52 (1974), 54[PTP].
- K. Ikeda, Prog. Theor. Phys. 52 (1974), 415[PTP].
- K. Ikeda, Prog. Theor. Phys. 52 (1974), 840[PTP].
- K. Ikeda, Prog. Theor. Phys. 53 (1975), 66[PTP].
- K. Ikeda, Lecture Notes in Phsics 39 – International Symposium on Mathematical Problems in Theoretical Physics (Springer, Berlin, 1975), p. 520.
B. Kahn and G. E. Uhlenbeck, Physica 5 (1938), 399[CrossRef].
- K. Ikeda, “Molecular Distribution in Bose-Einstein and Fermi-Dirac Gases,” Mem. Fac. Sci. Kyusyu Univ. B 2 (1956), 51.
P. C. Hemmer and E. H. Hauge, Phys. Rev. 133 (1964), A1010[APS].
Citing Article(s) :
Progress of Theoretical Physics Vol. 68 No. 3 (1982) pp. 744-763
Distribution of Zeros and the Equation of State. IV