Problem 5.7. Consider a random walk on the lattice shown in Fig. 5.5. The transition rates are

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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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A Modern Course In Statistical Physics

ISBN: 9780471595205

2nd Edition

Authors: Linda E. Reichl

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Question Posted: Sep 18, 2024 08:00 AM

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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...
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Problem 5.7. Consider a random walk on the lattice shown in Fig. 5.5. The transition rates are

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A Modern Course In Statistical Physics

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