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

Abstract

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 φ⁴ 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 T², when the frequency is not zero and Γ(ω) is larger than Γ(0). Its magnitude is hundred times as large as that of the φ⁴ kink.