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We describe the low-temperature optical conductivity as a function offrequency for a quantum-mechanical system of electrons that hop along a polymerchain. To this end, we invoke the Su-Schrieffer-Heeger \emph{tight-binding}Hamiltonian for non-interacting spinless electrons on a one-dimensional (1D)lattice. Our goal is to show via asymptotics how the interband conductivity ofthis system behaves as the smallest energy bandgap tends to close. Ouranalytical approach includes: (i) the Kubo-type formulation for the opticalconductivity with a nonzero damping due to microscopic collisions; (ii)reduction of this formulation to a 1D momentum integral over the Brillouinzone; and (iii) evaluation of this integral in terms of elementary functionsvia the three-dimensional Mellin transform with respect to key physicalparameters and subsequent inversion in a region of the respective complexspace. Our approach reveals an intimate connection of the behavior of theconductivity to particular singularities of its Mellin transform. Theanalytical results are found in good agreement with direct numericalcomputations.

On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform