About the sign ambiguity in the evaluation of Grand Canonical traces for quasi-particle statistical density operators

G. Puddu

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arXiv · 0909.0333

About the sign ambiguity in the evaluation of Grand Canonical traces for quasi-particle statistical density operators

G. Puddu

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Abstract

A simple and general prescription for evaluating unambiguously the sign of the grand-canonical trace of quasi-particle statistical density operators (the so-called sign ambiguity in taking the square root of determinants) is given. Sign ambiguities of this kind appear in the evaluation of the grand-canonical partition function projected to good quantum numbers (angular momentum, parity and particle number) in the Hartree-Fock-Bogoliubov approximation at finite temperature, since traces are usually expressed as the square root of determinants. A comparison is made with the numerical continuity method.

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G. Puddu. 2009-09-02. About the sign ambiguity in the evaluation of Grand Canonical traces for quasi-particle statistical density operators. https://arxiv.org/abs/0909.0333

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