LINKED-DIAGRAM EXPANSIONS FOR QUANTUM STATISTICAL MECHANICS

Journal Article · Tue Sep 15 04:00:00 EDT 1959 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.115.1374· OSTI ID:4220707

Glassgold, A E; Heckrotte, W; Watson, K M

A general method of calculation is described for quantum statistical mechanics, It is based on a simplification of the Laplace transform of the density matrix which follows from a theorem due to Hugenholtz, The basic result is that an element of the density matrix can be written as a sum over graphs, with the contribution of each graph factored into contributions from connected or linked graphs. Applied to the grand partition function, the exponential formula of Bloch and DeDominicis is obtained in a simple way, A similar formula is then derived for the canonical ensemble for the case of a nondegenerate gas. In this way the familiar result of Uhlenbeck and Beth is obtained for the second virial coefficient, Techniques are also introduced for evaluating ensemble averages of operators. in thus connection, some care must be exercised in the case of diagonal operators, These methods are used to calculate the pair-correlation function for a system of fermions interacting through short-range forces. (auth)

• Research Organization: Univ. of California, Berkeley
• NSA Number: NSA-14-003937
• OSTI ID: 4220707
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 115; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

FERMIONS
GASES
INTERACTIONS
MATRICES
PHYSICS
QUANTUM MECHANICS
STATISTICS