- #1

Tim667

- 12

- 0

- TL;DR Summary
- How does one calculate the correlation function?

So the Langevin equation of Brownian motion is a stochastic differential equation defined as

$$m {d \textbf{v} \over{dt} } = - \lambda \textbf{v} + \eta(t)$$

where the noise function eta has correlation function $$\langle \eta_i(t) \eta_j(t') \rangle=2 \lambda k_B T \delta_{ij} \delta(t - t')$$.

I have two questions. How does one actually calculate a correlation function and where exactly do the constants (with temperature, the Boltzmann constants etc) proceeding the delta functions originate here? I understand that the delta functions ensure that there is no correlation at different times etc, but I don't get where the rest comes from.

Thanks

$$m {d \textbf{v} \over{dt} } = - \lambda \textbf{v} + \eta(t)$$

where the noise function eta has correlation function $$\langle \eta_i(t) \eta_j(t') \rangle=2 \lambda k_B T \delta_{ij} \delta(t - t')$$.

I have two questions. How does one actually calculate a correlation function and where exactly do the constants (with temperature, the Boltzmann constants etc) proceeding the delta functions originate here? I understand that the delta functions ensure that there is no correlation at different times etc, but I don't get where the rest comes from.

Thanks