Finite Temperature Correction to the Mobility of the Strongly Damped Sine-Gordon Soliton–Effect of the Frequency Cut-Off–

Abstract

The mobility of the damped sine-Gordon soliton with the damping constant Γ is calculated up to the first order in temperature in the presence of the frequency cut-off ω c in the spectrum of the heat bath. The first order finite temperature correction turns out to be different in the two limiting cases: (I) ω c →∞, Γ→∞ with ω c /Γ→0 and (II) ω c →∞, Γ→∞ with ω c /Γ→∞. It is also found that the first limit corresponds to the mobility of the overdamped sine-Gordon model without inertia calculated by Kaup and the second to that of the heavily damped limit of the damped sine Gordon model with inertia calculated by Kaup and Osman both assuming the white noise spectrum. Our result gives the physical interpretation of the discrepancy between these two calculations.