Question

Use the solution (2) of Problem 15.4 to find the velocity correlation function $(v(0) v(t))$. Express the result in terme of $T, m, \gamma$, and $\boldsymbol{l}$.

   Use the solution (2) of Problem 15.4 to find the velocity correlation function $(v(0) v(t))$. Express the result in terme of $T, m, \gamma$, and $\boldsymbol{l}$.

Fundamentals of Statistical and Thermal Physics

Fundamentals of Statistical and Thermal Physics

Rief F. 1st Edition

Chapter 15, Problem 12

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4 refers to. This appears to be the solution to the Langevin equation for a Brownian particle. The solution gives the velocity v(t) of a particle at time t as: v(t) = v(0)e^(-γt) + (1/m)∫₀ᵗ e^(-γ(t-t'))f(t')dt' where v(0) is the initial velocity, γ is the Show more…

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Use the solution (2) of Problem 15.4 to find the velocity correlation function $(v(0) v(t))$. Express the result in terme of $T, m, \gamma$, and $\boldsymbol{l}$.

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