What Does Bilinear Response Mean in Mathematical Terms?

[hokhani]

I don't know what is "bilinear responce". I would be grateful for any help.

 

[DrDu]

Context?

 

[hokhani]

Context?

Yes, I saw the term "bilinear response" in a paper and I don't understand it.

 

[DrDu]

"In a paper". Do you think this is helpful? Maybe you could give a citation and quote the relevant part?

 

[hokhani]

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.58.R10135

You can see the term "bilinear response" in the first paragraph of page 3 in the above article.

 

[DrDu]

It means that it is linear in both $\delta X_1$ and $\delta X_2$. This is generally used for expressions of the form xy. Also the scalar product $\langle \phi|\psi \rangle$ is bilinear in $\psi$ and $\phi^*$.