Wick Theorem for General Initial States

Details Wick Theorem for General Initial States Wick Theorem for General Initial States

2011-02-23

arxiv.org/abs/1102.4814v2

Phys. Rev. B 85, 115119 (2012)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 5 figure; extended version published in Phys. Rev. B

Scientific paper

We present a compact and simplified proof of a generalized Wick theorem to calculate the Green's function of bosonic and fermionic systems in an arbitrary initial state. It is shown that the decomposition of the non-interacting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for non-correlated initial states a one-line proof of the standard Wick theorem is given. Our result leads to new self-energy diagrams and an elegant relation with those of the imaginary-time formalism is derived. The theorem is easy to use and can be combined with any ground-state numerical technique to calculate time-dependent properties.

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