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 Abstract: We re-examine a long-standing problem of a finite-frequency conductivity of a weakly pinned two-dimensional classical Wigner crystal. In this system an inhomogeneously broadened absorption line (pinning mode) centered at disorder and magnetic field dependent frequency $\omega_p$ is known to appear. We show that the relative linewidth $\Delta \omega_p / \omega_p$ of the pinning mode is of the order of one in weak magnetic fields, exhibits a power-law decrease in intermediate fields, and eventually saturates at a small value in strong magnetic fields. The linewidth narrowing is due to a peculiar mechanism of mixing between the stiffer longitudinal and the softer transverse components of the collective excitations. The width of the high-field resonance proves to be related to the density of states in the low-frequency tail of the zero-field phonon spectrum. We find a qualitative agreement with recent experiments and point out differences from the previous theoretical work on the subject. Citation: Fogler, Michael M, Huse, David A. (Dynamical response of a pinned two-dimensional Wigner crystal. Phys. Rev. B, 62 (7553 - ?. doi:10.1103/PhysRevB.62.7553 DOI: doi:10.1103/PhysRevB.62.7553 Pages: 7553 - ? Type of Material: Journal Article Journal/Proceeding Title: Phys. Rev. B Version: Author's manuscript