Consider two Brownian particles connected by a harmonic
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Consider two Brownian particles connected by a harmonic spring (see Fig. 6.12(a)). The Langevin equations for their posi
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Consider two Brownian particles connected by a harmonic spring (see Fig. 6.12(a)). The Langevin equations for their positions x1 and x2 are written as ? dx1 dt = ?k(x1 ? x2) + Fr1(t) (6.95) ? dx2 dt = ?k(x2 ? x1) + Fr2(t) (6.96) Answer the following questions. (a) Suppose that a constant force F1(e) is applied to the particle 1 for t > 0. Calculate the average displacements of the particles x1(t)?x1(0) F (e) 1 and x2(t) ? x2(0) F (e) 1 in this situation. (b) Calculate the time correlation function (x1(t) ? x1(0))2 and (x1(t) ? x1(0))(x2(t) ? x2(0)) using the fluctuation
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