Brownian Motion of a Soliton in trans-Polyacetylene. I. Random Walk Mechanism

Diffusive motion of a soliton in trans-polyacetylene is studied theoretically within the adiabatic approximation of the Takayama Lin-Liu and Maki model. The collective coordinate method is applied to obtain an equation of motion of the soliton. It bears a remarkable similarity to that in the φ 4 model. Shift of the soliton location is induced by collision with classical phonon, which is excited thermally. It leads to a random walk of the soliton. The dynamical diffusion constant D (ω) and the friction Γ(ω) are calculated in the low temperature expansion. It is shown that the real part of D (ω) is proportional to T 2 , when the frequency is not zero and Γ(0) is larger than Γ(ω). Its magnitude is hundred times as large as that of the φ 4 kink.