High-frequency conductivity of charge-density-wave condensates at low temperatures

Making use of Zamolodchikov's $S$ matrix for the sine-Gordon system in (1 + 1) dimensions, we calculate the frequency-dependent electric conductivity of the charge-density-wave (CDW) condensate at $T=0\mathrm{}$ K. It is assumed that the phase of the CDW wave function obeys a sine-Gordon equation. The conductivity has a square-root threshold structure at $\omega =2m$ associated with soliton-antisoliton pair production, where $m$ is the soliton energy. Furthermore below $\left|\omega \right|=2m$, the conductivity has a series of resonance peaks due to the creation of the soliton-antisoliton bound states at ${\omega }_n=2msin\left[\frac{\pi \mathrm{}(2n+1)\mathrm{}}{2\lambda }\right]$, with $n$ the integer and $\lambda$ the dimensionless coupling constant ($\lambda \gg 1$) of the system.