- #1

Xenosum

- 20

- 2

*Equilibrium Statistical Physics*, they make the following approximation

[tex]

\sum_{k,k^{'}}V_{k,k^{'}}b^{\dagger}_{k}b_{k^{'}} \approx \sum_{k,k^{'}}V_{k,k^{'}}\left( b^{\dagger}_k <b_{k^{'}}> + <b^{\dagger}_k > b_{k^{'}} - <b^{\dagger}_k > <b_{k^{'}}>\right)

[/tex]

where [itex] b_k [/itex] is a bosonic annihilation operator.

Can someone explain this? This is pretty much an invokation of mean field theory, but I'd like to generalize the approximation to other operators, e.g. [itex] J\sum_{i} a^{\dagger}_i a_i \vec{S}_i \vec{S}_{i+1} a^{\dagger}_{i+1} a_{i+1} [/itex]. My guess is it has something to do with Wick's theorem, but I've only ever seen this in the context of QFT.

Thanks.