# Functions of time 0?

1. Aug 23, 2013

### 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

2. Aug 23, 2013

### 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 $t_0$.

3. Aug 23, 2013

### Steve Drake

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