Space-temperature correlations in quantum-statistical mechanics

William Kunkin, Jerome Percus

Research output: Contribution to journalArticle

Abstract

The method of functional differentiation, used in classical statistical mechanics to obtain approximate integral equations for the pair distribution function, is extended to quantum systems obeying Maxwell-Boltzmann statistics. The grand partition function is written as a path integral, and space-temperature distributions are generated from it by successive functional differentiation. Distributions can be expanded in powers of an external potential via a functional Taylor series. When the series is truncated so that no distributions higher than second order enter and the external potential is specialized to one arising from a fixed particle in the system, coupled integral equations result for the two kinds of pair distributions. The first-order Ursell function calculated from these equations yields the Montroll-Ward ring summation for the grand potential. This approximate Ursell function determines also the Fourier transform of the momentum density (useful in calculating the p = 0 occupation number). Although divergences appear in the low-temperature limit, they can be removed by a simple modification of the independent functional. An extension to Fermi-Dirac and Böse-Einstein statistics is indicated at appropriate places in the text.

Original languageEnglish (US)
Pages (from-to)1029-1036
Number of pages8
JournalJournal of Mathematical Physics
Volume11
Issue number3
StatePublished - 1970

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space temperature
Quantum Statistical Mechanics
Statistical mechanics
statistical mechanics
Integral equations
integral equations
Integral Equations
Statistics
statistics
Path Space
Taylor series
Classical Mechanics
Curvilinear integral
Temperature Distribution
Ludwig Boltzmann
Statistical Mechanics
Partition Function
Summation
Quantum Systems
Coupled System

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

Space-temperature correlations in quantum-statistical mechanics. / Kunkin, William; Percus, Jerome.

In: Journal of Mathematical Physics, Vol. 11, No. 3, 1970, p. 1029-1036.

Research output: Contribution to journalArticle

Kunkin, W & Percus, J 1970, 'Space-temperature correlations in quantum-statistical mechanics', Journal of Mathematical Physics, vol. 11, no. 3, pp. 1029-1036.
Kunkin, William ; Percus, Jerome. / Space-temperature correlations in quantum-statistical mechanics. In: Journal of Mathematical Physics. 1970 ; Vol. 11, No. 3. pp. 1029-1036.
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