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- Definitions
- Correlation Function
- Relaxation in Fourier Space
- Example: Velocity Autocorrelation Function
- Example: Diffusion

We applied Fourier transform for space-dependent problems--and we were successful. Let us do the same for time-dependent problems:

(1) |

The product of *x*'s is

If *t*=0, we obtain

We obtained for correlation function

Take Fourier transform:(3) |

Relaxation with one characteristic time is Lorentzian.

Many characteristic times--more complex formulae.

Consider a large particle surrounded by small particles (a colloidal particle among molecules). Equation for average velocity:

with(4) |

In particular, if

Consider particles with concentration *c*. Diffusion equation with
diffusion coefficient *D*:

with .

We immediately obtain:

Or, in Fourier space This is© 1997

Tue Oct 28 22:16:24 EST 1997