Contractions of product density operators of systems of identical fermions and bosons

Details Contractions of product density operators of systems of identical fermions and bosons Contractions of product density operators of systems of identical fermions and bosons

2008-09-02

arxiv.org/abs/0809.0474v2

International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 890523, 26 pages, 2010

Physics

Quantum Physics

20 pages. The manuscript has been shortened. A few typos corrected

Scientific paper

10.1155/2010/890523

Recurrence and explicit formulae for contractions (partial traces) of antisymmetric and symmetric products of identical trace class operators are derived. Contractions of product density operators of systems of identical fermions and bosons are proved to be asymptotically equivalent to, respectively, antisymmetric and symmetric products of density operators of a single particle, multiplied by a normalization integer. The asymptotic equivalence relation is defined in terms of the thermodynamic limit of expectation values of observables in the states represented by given density operators. For some weaker relation of asymptotic equivalence, concerning the thermodynamic limit of expectation values of product observables, normalized antisymmetric and symmetric products of density operators of a single particle are shown to be equivalent to tensor products of density operators of a single particle. This paper presents the results of a part of the author's thesis [W. Radzki, "Kummer contractions of product density matrices of systems of $n$ fermions and $n$ bosons" (Polish), MS thesis, Institute of Physics, Nicolaus Copernicus University, Toru\'{n}, 1999].

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