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SOLVED: 32 Brownian particle is placed in a very long narrow channel. The particle is trapped in a harmonic potential V(z) = kz^2 (where k is a constant and z is the distance from the origin) and is subject to random thermal noise. In other words, we have a one-dimensional harmonic oscillator coupled to a thermal bath. At time t = 0, the particle is at the position x(0) = c0. Assuming the inertia can be neglected (the so-called overdamped limit), the equation of motion of the particle is dx(t) =

SOLVED: 32 Brownian particle is placed in a very long narrow channel. The particle is trapped in a harmonic potential V(z) = kz^2 (where k is a constant and z is the

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