Prog. Theor. Phys. Vol. 48 No. 2 (1972) pp. 407-432

[ Full Text PDF : FREE ACCESS (1724K) ]

A Thermodynamic Perturbation Theory of the Anharmonic Oscillator. I

— Partition Function and Free Energy —

Shigeo Naya

Department of Physics, Boston University, Boston, Massachusetts 02215, U.S.A.

(Received March 1, 1972)

Abstract:

A new formalism of the thermodynamic perturbation theory for the quantum-anharmonic oscillator is proposed. By this method, for each order of the perturbation series, the partition function and the free energy of the system can be obtained in a compact form which is expressed by the temperature Green's function of the harmonic quanta. Based upon a unified method, the various expressions of the perturbation series for the partition function and the free energy are also given. It is shown that the perturbation series for the free energy can be naturally formulated in terms of a cluster expansion.

URL : http://ptp.ipap.jp/link?PTP/48/407/
DOI : 10.1143/PTP.48.407

References:

P. Choquard, The Anharmonic Crystal (Benjamin, New York, 1967), Chap. 5, p. 174.
G. Leibfried and W. Ludwig, Theory of Anharmonic Effects in Crystals, Solid State Physics, ed. F. Zeitz and D. Turnbull (Academic, New York, 1961), Vol. 12, p. 276.
G. Leibfried et al., Anharmonic Effects, Lattice Dynamics, ed. R. F. Wallis (Pergamon, London, 1965), p. 237.
D. J. Thouless, The Quantum Mechanics of Many-Body Systems (Academic, New York, 1961), Chap. 4, p. 33.
A. Messiah, Quantum Mechanics (John Wiley and Sons, New York, 1965), Vols. I and II.
A. Siegel, Rarefied Gas Dynamics, ed. L. Talbot (Academic, New York, 1961), p. 261.
I. Kohlberg and A. Siegel, Physica 36 (1967), 557[CrossRef].
J. E. Mayer and M. G. Mayer, Statistical Mechanics (John Wiley and Sons, New York, 1940), Chap. 13, p. 277.
L. Van Hove, Interactions of Elastic Waves in Solids, Quantum Theory of Many-Particle Systems, ed. D. Pines (Benjamin, New York, 1961), p. 1.
S. Naya and A. Siegel, A Thermodynamic Perturbation Theory of the Anharmonic Oscillator, II. Density Matrix (to be published).
S. Naya and A. Siegel, Kwansei Gakuin University Annual Studies XX (1971).

Citing Article(s) :

Progress of Theoretical Physics Vol. 48 No. 3 (1972) pp. 783-807 :
A Thermodynamic Perturbation Theory of the Anharmonic Oscillator. II

Shigeo Naya and Armand Siegel