Question: Problem 5.7. Consider a random walk on the lattice shown in Fig. 5.5. The transition rates are w,2 =W1,3 = W2,1 = w2,3 = w2,4

Problem 5.7. Consider a random walk on the lattice shown in Fig. 5.5. The transition rates are w,2 =W1,3 = W2,1 = w2,3 = w2,4 = W3,1 = W3,2 = W3,4 = 3, W4,2= W4,3 and w,4w4,1 = 0.

(a) Write the transition matrix, W, and show that this system obeys detailed balance.

(b) Compute the symmetric matrix, V, and find its eigenvalues and eigenvectors.

(c) Write P(n,t) for the case P(n, 0) = 8,1. What is P(4,1)?

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