Understand Physical Significance of Functions at Time 0

[Steve Drake]

Hi Guys,

In a lot of books dealing with spectroscopy, correlation functions or any kind of functions involving time sometimes take the form like this:

\left\langle A[q,u(t)]A^{*}[q,u(o)] \right\rangle

Where A is some function that depends on say q and u, and u is another function that depends on time t.

What is the physical significance of the multiplication by its conjugate at time t = 0?

Thanks

 

[Khashishi]

It would probably have been clearer if it was written
\left\langle A[q,u(t_0+t)]A^{*}[q,u(t_0)] \right\rangle

The average is over $t_0$.

 

[Steve Drake]

It would probably have been clearer if it was written
\left\langle A[q,u(t_0+t)]A^{*}[q,u(t_0)] \right\rangle

The average is over $t_0$.

Hmm does that mean if i was trying to work out one of these equations for say a series of 5 $t_0$ values eg $[1, 2, 3, 4, 5]$, does that mean for $t_3$ I would do
\left\langle A[q,u(3)]A^{*}[q,u(1)] \right\rangle, or
\left\langle A[q,u(3)]A^{*}[q,u(0)] \right\rangle or
\left\langle A[q,u(3)]A^{*}[q,u(2)] \right\rangle

and similarly for the next time $t_4$ eg...

\left\langle A[q,u(4)]A^{*}[q,u(1)] \right\rangle, or
\left\langle A[q,u(4)]A^{*}[q,u(0)] \right\rangle or
\left\langle A[q,u(4)]A^{*}[q,u(3)] \right\rangle

Thanks for your time.