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 noninteracting $n$ -particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for noncorrelated 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.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 noninteracting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for noncorrelated 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.

arXiv:1102.4814Physical Review BMar 26, 201232 citations

Generalized Wick's theorem for multiquasiparticle overlaps as a limit of Gaudin's theorem

S. Pérez-Martín, Luis Miguel Robledo

By using the extension of the statistical Wick's theorem (Gaudin's theorem) to deal with generalized statistical density operators (those which can be expressed as the product of and operator carrying out a canonical transformations times a density operator) and using the appropriate limits we are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean-field wave functions. Due to the simplicity of the derivation it is now straightforward to consider more involved cases and some of them are discussed. The present derivation also allows us to obtain general and compact formulas for other particular cases of the generalized Wick theorem involving overlaps of multiquasiparticle excitations of product wave functions. The new expressions allow us to reduce the combinatorial complexity of the standard calculation of the above overlaps.By using the extension of the statistical Wick's theorem (Gaudin's theorem) to deal with generalized statistical density operators (those which can be expressed as the product of and operator carrying out a canonical transformations times a density operator) and using the appropriate limits we are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean-field wave functions. Due to the simplicity of the derivation it is now straightforward to consider more involved cases and some of them are discussed. The present derivation also allows us to obtain general and compact formulas for other particular cases of the generalized Wick theorem involving overlaps of multiquasiparticle excitations of product wave functions. The new expressions allow us to reduce the combinatorial complexity of the standard calculation of the above overlaps.

arXiv:0707.3365Physical Review CDec 17, 200728 citations

The structure of the kinetic equation for time correlation functions

R. M. Yulmetyev

Physics Letters AFeb 1, 19734 citations

n

-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for noncorrelated 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.