Wick Theorem for General Initial States

Abstract

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.

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

References in corpus (6)

• The Luttinger model following a sudden interaction switch-on
• Quantum quench dynamics of the Luttinger model
• Time-dependent second Born calculations for model atoms and molecules in strong laser fields
• Crossover from adiabatic to sudden interaction quench in a Luttinger liquid
• On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches
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