Question: EXERCISE 10.4. The dynamic density correlation function for a fluid in a box of volume V may be written where N is the total number

EXERCISE 10.4. The dynamic density correlation function for a fluid in a box of volume V may be written

Cmn (p, 7) = dr = dr(n(r+p, r)n(r, 0), N

where N is the total number of particles. The dynamic structure factor is given by

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Compute both C (p, 7) and Snn (k,) for a fluid of point particles in equilibrium. For such a fluid, the average, (), is taken over the equilibrium distribution of fluctuations. Assume that fluctuations in the average velocity are independent of temperature and density fluctuations.

Cmn (p, 7) = dr = dr(n(r+p, r)n(r, 0), N

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