EXERCISE 12.4. The Fourier amplitude, uk (t) =k er u(r,t), of a fluctuating mode, u(r,t), in a
Question:
EXERCISE 12.4. The Fourier amplitude, uk (t) =k er u(r,t), of a fluctuating mode, u(r,t), in a nonequilibrium system (V is the volume) is assumed to satisfy a time-dependent Ginzburg-Landau equation
where k is a wavevector, F is a free energy functional, and m (t) is a random noise. In the Gaussian approximation, the free energy functional can be written F(t) = dk kuk(t)u-k(t), where A is a function of k and other relevant parameters of the system. The random noise satisfies the conditions
The variational derivative is (Suk, (t)/uk (t))=6(kk2). Assume that the medium is isotropic and that the correlation functions are time translation invariant but not time reversal invariant (since we are far from equilibrium). What is the strength, Ik, of the random noise [27]?
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